# William Witczak-Krempa's research while affiliated with Université de Montréal and other places

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## Publications (89)

We investigate separability and entanglement of Rokhsar-Kivelson (RK) states and resonating valence-bond (RVB) states. These states play a prominent role in condensed matter physics, as they can describe quantum spin liquids and quantum critical states of matter, depending on their underlying lattices. For dimer RK states on arbitrary tileable grap...

Multiorbital quantum materials with strong interactions can host a variety of novel phases. In this work we study the possibility of interaction-driven superconductivity in the iridate compound Sr2IrO4 under strain and doping. We find numerous regimes of strain-induced superconductivity in which the pairing structure depends on model parameters. Sp...

We give evidence for the web of 3d bosonization dualities in conformal field theories (CFTs) by computing monopole operator scaling dimensions in (2+1)-dimensional quantum electrodynamics (QED3) with Chern-Simons level k and N complex bosons in a large-N, k expansion. We first consider the k=0 case, where we show that scaling dimensions previously...

We grow the web of dualities for conformal field theories (CFTs) in 2+1 spacetime dimensions to include quantum critical transitions of Dirac fermions. Our construction uses the seed duality, equating a free Dirac fermion with a complex boson coupled to a Chern-Simons gauge field, to express various Gross-Neveu-Yukawa (GNY) critical points of N fer...

We investigate separability and entanglement of Rokhsar-Kivelson (RK) states and resonating valence-bond (RVB) states. These states play a prominent role in condensed matter physics, as they can describe quantum critical states of matter and quantum spin liquids, depending on their underlying lattices. For dimer RK states on arbitrary tileable grap...

Multi-orbital quantum materials with strong interactions can host a variety of novel phases. In this work we study the possibility of interaction-driven superconductivity in the iridate compound Sr$_2$IrO$_4$ under strain and doping. We find numerous regimes of strain-induced superconductivity in which the pairing structure depends on model paramet...

We study the cumulants of the charge distribution of a subregion for two-dimensional quantum Hall states of bosons and fermions at both integer and fractional fillings, focusing on subregions with corners. Even cumulants, which include the variance, satisfy an area law with subleading corrections sensitive to finer geometric details of the subregio...

We give evidence for 3d bosonization in Conformal Field Theories (CFTs) by computing monopole operator scaling dimensions in 2+1 dimensional quantum electrodynamics (QED3) with Chern-Simons level $k$ and $N$ complex bosons in a large $N,k$ expansion. We first consider the $k=0$ case, where we show that scaling dimensions previously computed to subl...

We study a vast family of continuum Rokhsar-Kivelson (RK) states, which have their ground state encoded by a local quantum field theory. These describe certain quantum magnets, and are also important in quantum information. We prove the separability of the reduced density matrix of two disconnected subsystems, implying the absence of entanglement b...

We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice subjected to constrained spin interactions, such that some or even all multipole moments of the effective spin...

We study two entanglement measures in a large family of systems including incompressible quantum Hall states: the logarithmic negativity (LN), and mutual information (MI). For pure states, obtained for example from a bipartition at zero temperature, these provide distinct characterizations of the entanglement present between two spatial subregions,...

Monopole operators are studied in a large family of quantum critical points between Dirac spin liquids and topological quantum spin liquids (QSLs): chiral and Z2 QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions a...

We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising coupli...

The entanglement entropy (EE) encodes key properties of quantum many-body systems. It is usually calculated for subregions of finite volume (or area in 2D). Here, we study the EE of skeletal regions that have no volume, such as a line in 2D. We show that skeletal entanglement displays new behavior compared with its bulk counterpart, and leads to di...

We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice subjected to constrained spin interactions, such that some or even all multipole moments of the effective spin...

Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations in a subregion of the full system, focusing on geometries with sharp corners. We report that the angle dependence is super-universal: up to a numerical prefactor, this function...

EuB6 has for a long time captured the attention of the physics community, as it shows a ferromagnetic phase transition leading to a insulator the metal transition together with colossal magnetoresistance (CMR). EuB6 has a very low carrier density, which is known to drastically change the interaction between the localised Eu moments and the conducti...

The entanglement entropy (EE) encodes key properties of quantum many-body systems. It is usually calculated for a subregion of finite volume (or area in 2d). In this work, we study the EE of skeletal regions that have \textit{no} volume, such as a line in 2d/3d. We show that skeletal entanglement displays new behavior compared to its bulk counterpa...

Starting from the $(d+1)$-dimensional Lifshitz critical boson with dynamical exponent $z=2$, we propose two nontrivial deformations that preserve the Rokhsar-Kivelson structure where the groundstate is encoded in an underlying, local $d$-dimensional QFT. Specializing to $d=1$ spatial dimension, the first deformation maps the groundstate to the quan...

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether s...

Monopole operators are studied at certain quantum critical points between a Dirac spin liquid and topological quantum spin liquids (QSLs): chiral and Z$_{2}$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a...

We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising coupli...

Quantum spin liquids host novel emergent excitations, such as monopoles of an emergent gauge field. Here, we study the hierarchy of monopole operators that emerges at quantum critical points (QCPs) between a two-dimensional Dirac spin liquid and various ordered phases. This is described by a confinement transition of quantum electrodynamics in two...

We present a comprehensive study of a three-orbital lattice model suitable for the layered iridate Sr2IrO4. Our analysis includes various on-site interactions (including Hubbard and Hund's) as well as compressive strain, and a Zeeman magnetic field. We use a self-consistent mean-field approach with multiple order parameters to characterize the resu...

We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum, and entanglement entropy (EE) of the density matrix for various ground and excited states, with or without mass anisotropy. We focus on an important class of regions th...

Understanding the fluctuations of observables is one of the main goals in physics, be it quantum or classical, theoretical or experimental. We investigate such fluctuations when only a subregion of the full system can be observed, focusing on geometries with sharp corners. We report that the dependence on the opening angle is super-universal: up to...

Quantum spin liquids host novel emergent excitations, such as monopoles of an emergent gauge field. Here, we study the hierarchy of monopole operators that emerges at quantum critical points (QCPs) between a two-dimensional Dirac spin liquid and various ordered phases. This is described by a confinement transition of quantum electrodynamics in two...

This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montréal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of...

Monopole operators are topological disorder operators in 2 + 1 dimensional compact gauge field theories appearing notably in quantum magnets with fractionalized excitations. For example, their proliferation in a spin-1/2 kagome Heisenberg antiferromagnet triggers a quantum phase transition from a Dirac spin liquid phase to an antiferromagnet. The q...

We present a comprehensive study of a three-orbital lattice model suitable for the layered iridate Sr2IrO4. Our analysis includes various on-site interactions (including Hubbard and Hund's) as well as compressive strain, and a Zeeman magnetic field. We use a self-consistent mean field approach with multiple order parameters to characterize the resu...

We investigate the response of three-dimensional Luttinger semimetals to localized charge and spin impurities as a function of doping. The strong spin-orbit coupling of these materials strongly influences the Friedel oscillations and RKKY interactions. This can be seen at short distances with an 1/r4 divergence of the responses and anisotropic beha...

Boundaries constitute a rich playground for quantum many-body systems because they can lead to novel degrees of freedom such as protected boundary states in topological phases. Here, we study the ground state of integer quantum Hall systems in the presence of boundaries through the reduced density matrix of a spatial region. We work in the lowest L...

We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for various ground and excited states, with or without mass anisotropy. We focus on an important class of regions tha...

Quantum nematic phases are analogous to classical liquid crystals. Like liquid crystals, which break the rotational symmetries of space, their quantum analogues break the point-group symmetry of the crystal due to strong electron-electron interactions, as in quantum Hall states, Sr3Ru2O7, and high temperature superconductors. Here, we present angle...

We investigate the response of 3D Luttinger semimetals to localized charge and spin impurities as a function of doping. The strong spin-orbit coupling of these materials strongly influences the Friedel oscillations and RKKY interactions. This can be seen at short distances with an $1/r^4$ divergence of the responses, and anisotropic behavior. Certa...

The experimental discovery of the fractionalized Hall conductivity revealed new types of quantum particles beyond bosons and fermions. These anyons are usually studied deep inside a topological phase. But can such fractionalization be detected at the phase transition point to a conventional phase? To answer this question, we study a quantum phase t...

We study superconductivity driven by screened Coulomb repulsion in three-dimensional Luttinger semimetals with a quadratic band touching and strong spin-orbit coupling. In these semimetals, the Cooper pairs are formed by spin-32 fermions with nontrivial wave functions. We numerically solve the linear Eliashberg equation to obtain the critical tempe...

Quantum many-body systems have a rich structure in the presence of boundaries. We study the ground states of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a family of theories in general dimensions, we relate the universal terms in the entanglement entropy...

Boundaries constitute a rich playground for quantum many-body systems because they can lead to novel degrees of freedom such as protected boundary states in topological phases. Here, we study the groundstate of integer quantum Hall systems in the presence of boundaries through the reduced density matrix of a spatial region. We work in the lowest La...

Monopole operators are topological disorder operators in 2+1 dimensional compact gauge field theories appearing notably in quantum magnets with fractionalized excitations. For example, their proliferation in a spin-1/2 kagome Heisenberg antiferromagnet triggers a quantum phase transition from a Dirac spin liquid phase to an antiferromagnet. The qua...

We investigate the superconductivity of 3D Luttinger semimetals, such as YPtBi, where Cooper pairs are constituted of spin-3/2 quasiparticles. Various pairing mechanisms have already been considered for these semimetals, such as from polar phonons modes, and in this work we explore pairing from the screened electron-electron Coulomb repulsion. In t...

We study superconductivity driven by screened Coulomb repulsion in three-dimensional Luttinger semimetals with a quadratic band touching and strong spin-orbit coupling. In these semimetals, the Cooper pairs are formed by spin-3/2 fermions with non-trivial wavefunctions. We numerically solve the linear Eliashberg equation to obtain the critical temp...

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We co...

Due to strong spin-orbit coupling, charge carriers in three-dimensionsal quadratic-band-touching Luttinger semimetals have nontrivial wave functions characterized by a pseudospin of 3/2. We compute the dielectric permittivity of such semimetals at finite doping, within the random phase approximation. Because of interband coupling, the dielectric sc...

A bstract
We study the structure of divergences and universal terms of the entanglement and Rényi entropies for singular regions. First, we show that for (3 + 1)-dimensional free conformal field theories (CFTs), entangling regions emanating from vertices give rise to a universal contribution $$ {S}_n^{\mathrm{univ}}=-\frac{1}{8\pi }{f}_b(n){\int}_{...

Quantum field theories have a rich structure in the presence of boundaries. We study the groundstates of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a family of theories in general dimensions, we relate the universal terms in the entanglement entropy of...

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We co...

We study the structure of divergences and universal terms of the entanglement and R\'enyi entropies for singular regions. First, we show that for $(3+1)$-dimensional free conformal field theories (CFTs), entangling regions emanating from vertices give rise to a universal contribution $S_n^{\rm univ}= -\frac{1}{8\pi}f_b(n) \int_{\gamma} k^2 \log^2(R...

Due to strong spin-orbit coupling, charge carriers in 3D quadratic band touching Luttinger semimetals have non-trivial wavefunctions characterized by a pseudospin of 3/2. We compute the dielectric permittivity for such semimetals at finite doping, within the random phase approximation. Because of interband coupling, the dielectric screening shows a...

The entanglement entropy (EE) can measure the entanglement between a spatial subregion and its complement, which provides key information about quantum states. Here, rather than focusing on specific regions, we study how the entanglement entropy changes with small deformations of the entangling surface. This leads to the notion of entanglement susc...

The entanglement entropy (EE) can measure the entanglement between a spatial subregion and its complement, which provides key information about quantum states. Here, rather than focusing on specific regions, we study how the entanglement entropy changes with small deformations of the entangling surface. This leads to the notion of entanglement susc...

Quantum spin liquids (QSL) are exotic phases of matter that host fractionalized excitations. Since the underlying physics is root in long-ranged quantum entanglement, local probes are hardly capable of characterizing them whereas quantum entanglement can serve as a diagnostic tool due to its non-locality. The kagome antiferromagnetic Heisenberg mod...

We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the groundstates in the continuum which allows for the calculation of spin and entanglement properties in a unified fashion. Doing so, we uncover an emergent conf...

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultra-cold atoms. Here, we investigate such non-trivial quantum dynamics in a spin-1 bilinear-biquadratic chain. It has a solvable entangled groundstate, but a gapless excitation spectrum that is di...

We discuss dynamical response functions near quantum critical points, allowing for both a finite temperature and detuning by a relevant operator. When the quantum critical point is described by a conformal field theory (CFT), conformal perturbation theory and the operator product expansion can be used to fix the first few leading terms at high freq...

We study the universal contributions to the entanglement entropy (EE) of 2+1-dimensional and 3+1-dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti–de Sitter-soliton geometries. We characterize the properties of these regulator-independent EE term...

We study the universal contributions to the entanglement entropy (EE) of 2+1d and 3+1d holographic conformal field theories (CFTs) on topologically non-trivial manifolds, focusing on tori. The holographic bulk corresponds to AdS-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size...

We study the von Neumann and R\'enyi entanglement entropy (EE) of scale-invariant theories defined on tori in 2+1 and 3+1 spacetime dimensions. We focus on spatial bi-partitions of the torus into two cylinders, and allow for twisted boundary conditions along the non-contractible cycles. Various analytical and numerical results are obtained for the...

We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry....

DOI:http://dx.doi.org/10.1103/PhysRevLett.117.149903

In this addendum we modify the acknowledgements to include the support provided by MURI grant W911NF-14-1-0003 from ARO.

We study high frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz...

A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions when the partition involves a corner of angle $\theta$, the subleading term is logarithmic with coefficient $a_\alpha(\theta)$ for the $\alpha$-R\'enyi entropy. In the smooth limit $\theta\!\to\!\pi$, $a_1(\theta)...

Topological states of electrons present new avenues to explore the rich phenomenology of correlated quantum matter. Topological insulators (TIs) in particular offer an experimental setting to study novel quantum critical points (QCPs) of massless Dirac fermions, which exist on the sample’s surface. Here, we obtain exact results for the zero- and fi...

The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless theories on tori in 2d/3d, denoted by $\chi$. Focusing on scale invariant systems, we derive general non-perturbative properties regarding the shape dependence of $\chi$, and re...

We analyze the dynamical response functions of strongly interacting quantum critical states described by conformal field theories (CFTs). We construct a self-consistent holographic model that incorporates the relevant scalar operator driving the quantum critical phase transition. Focusing on the finite temperature dynamical conductivity $\sigma(\om...

In general three-dimensional conformal field theories (CFTs), the entanglement entropy receives a logarithmic contribution whenever the entangling surface contains a sharp corner of opening angle θ. Such contribution is controlled by a regulator-independent function a(θ) which vanishes as a(θ)=σ(θ-π)2 in the smooth-surface limit (θ→π). We review ou...

The entanglement entropy in many gapless quantum systems receives a
contribution from corners in the entangling surface in 2+1d. It is
characterized by a universal function $a(\theta)$ depending on the opening
angle $\theta$, and contains pertinent low energy information. For conformal
field theories (CFTs), the leading expansion coefficient in the...

We obtain exact, nonperturbative results for the zero- and finite-temperature
dynamical responses at the semimetal-superconductor quantum critical point
(QCP) of two-dimensional Dirac fermions, which can occur on the surface of a
topological insulator. This strongly interacting QCP is described by a
conformal field theory with emergent $\mathcal{N}...

The entanglement entropy in three-dimensional conformal field theories (CFTs)
receives a logarithmic contribution characterized by a regulator-independent
function $a(\theta)$ when the entangling surface contains a sharp corner with
opening angle $\theta$. In the limit of a smooth surface
($\theta\rightarrow\pi$), this corner contribution vanishes...

We study the contribution to the entanglement entropy of (2+1)-dimensional
conformal field theories coming from a sharp corner in the entangling surface.
This contribution is encoded in a function $a(\theta)$ of the corner opening
angle, and was recently proposed as a measure of the degrees of freedom in the
underlying CFT. We show that the ratio $...

Quantum critical (QC) phase transitions generally lead to the absence of
quasiparticles. The resulting correlated quantum fluid, when thermally excited,
displays rich universal dynamics. We establish non-perturbative constraints on
the linear-response dynamics of conformal QC systems, in spatial dimensions
above one. Specifically, we analyze the la...

We compute the non-zero temperature conductivity of conserved flavor currents
in conformal field theories (CFTs) in 2+1 spacetime dimensions. At frequencies
much greater than the temperature, $\hbar\omega>> k_B T$, the $\omega$
dependence can be computed from the operator product expansion (OPE) between
the currents and operators which acquire a no...

Understanding the real time dynamics of systems near quantum critical points
at non-zero temperatures constitutes an important yet challenging problem,
especially in two spatial dimensions where interactions are strong. We present
detailed quantum Monte Carlo results for two separate realizations of the
superfluid-insulator transition of bosons on...

Weyl semimetals (WSMs) constitute a 3D phase with linearly-dispersing
Weyl-like excitations at low energy. Unusual properties arise from the latter,
such as anomalous electrodynamic responses and open Fermi arcs on boundaries.
We derive a simple criterion to identify and characterize WSMs in an
interacting setting using the exact electronic Green's...

We present new possibilities for the charge response in the quantum critical
regime in 2+1D using holography, and compare them with field theory and recent
quantum Monte Carlo results. We show that a family of (infinitely many) higher
derivative terms in the gravitational bulk leads to behavior far richer than
what was previously obtained. For exam...

We discuss phenomena arising from the combined influence of electron
correlation and spin-orbit coupling, with an emphasis on emergent quantum
phases and transitions in heavy transition metal compounds with 4d and 5d
elements. A common theme is the influence of spin-orbital entanglement produced
by spin-orbit coupling, which influences the electron...

We study the charge response of conformal field theories (CFTs) at non-zero
temperature in 2+1 dimensions using the AdS/CFT correspondence. A central role
is played by the quasinormal modes (QNMs), specifically, the poles and zeros of
the current correlators. We generalize our recent study of the QNMs of the a.c.
charge conductivity to include mome...

We study charge transport of quantum critical points described by conformal
field theories in 2+1 spacetime dimensions. The transport is described by an
effective field theory on an asymptotically anti-de Sitter spacetime, expanded
to fourth order in spatial and temporal gradients. The presence of a horizon at
non-zero temperatures implies that thi...

We study the finite temperature and magnetic field phase diagram of electrons
on the pyrochlore lattice subject to a local repulsion as a model for the
pyrochlore iridates. We provide the most general symmetry-allowed Hamiltonian,
including next-nearest neighbour hopping, and relate it to a Slater-Koster
based Hamiltonian for the iridates. It captu...

We discuss the universal transport signatures near a zero-temperature
continuous Mott transition between a Fermi liquid (FL) and a quantum spin
liquid in two spatial dimensions. The correlation-driven transition occurs at
fixed filling and involves fractionalization of the electron: upon entering the
spin liquid, a Fermi surface of neutral spinons...

Topological phases of quantum matter defy characterization by conventional
order parameters but can exhibit quantized electro-magnetic response and/or
protected surface states. We examine such phenomena in a model for
three-dimensional correlated complex oxides, the pyrochlore iridates. The model
realizes interacting topological insulators with and...

We discuss the universal transport signatures near a zero-temperature
continuous Mott transition between a Fermi liquid and a spin liquid in 2
spatial dimensions. This transition can be described using a slave-rotor
field theory, where the electron is decomposed into a fermionic spinon
and charge-carrying rotor, both interacting with an emergent U(...

We construct a model for interacting electrons with strong spin orbit
coupling in the pyrochlore iridates. We establish the importance of the direct
hopping process between the Ir atoms and use the relative strength of the
direct and indirect hopping as a generic tuning parameter to study the
correlation effects across the iridates family. We predi...

We study the low-energy properties of three-dimensional (3D) topological Mott insulators which can be viewed as strong topological insulators of spinons interacting with a three-dimensional gauge field. The low-energy behavior of such systems is dominated by the two-dimensional (2D) gapless surface spinons coupled to the bulk gauge field. We find t...

We present a theory of nonequilibrium quantum criticality in a coupled bilayer system of itinerant electron magnets. The model studied consists of the first layer subjected to an inplane current and open to an external substrate. The second layer is closed and subject to no direct external drive, but couples to the first layer via short-ranged spin...

## Citations

... In higher dimensions, the study of skeletal regions [112], i.e. regions A, B that have no volume, could lead to new analytical results for reflected entropies and CCNR negativities. Finally, it is worth investigating reflected entropies and CCNR negativities for other mixed quantum states, such as Rokhsar-Kivelson states [113,114] whose Hilbert space is spanned by the configurations of an underlying statistical model (see Refs. [115,116] for recent developments on their entanglement structure). ...

... The rotations increase under compression and as a result the hopping between orbitals at neighboring sites is modified to reflect the new geometry [4,[21][22][23][24]. Moreover, the orbitals are modified by different amounts such that the bands belonging to the j = 3/2 subspace move closer to the Fermi surface [25]. Naturally, the number of Fermi pockets and their orbital composition are important factors for superconductivity. ...

Reference: Strain-induced superconductivity in Sr2IrO4

... In the normalization (2), the charge q is restricted by Dirac quantization to take the values q ∈ Z=2. As in [21,22,25,[31][32][33][34][35][36][37][38][39], we will compute the scaling dimension of the lowest dimension monopole operators using the state-operator correspondence, which identifies the scaling dimensions of monopole operators of charge q with the energies of states in the Hilbert space on S 2 × R with 4πq magnetic flux through the sphere [21]. The ground state energy on S 2 × R can then be computed in the large-N and large-k limit using a saddle point expansion. ...

... In higher dimensions, the study of skeletal regions [112], i.e. regions A, B that have no volume, could lead to new analytical results for reflected entropies and CCNR negativities. Finally, it is worth investigating reflected entropies and CCNR negativities for other mixed quantum states, such as Rokhsar-Kivelson states [113,114] whose Hilbert space is spanned by the configurations of an underlying statistical model (see Refs. [115,116] for recent developments on their entanglement structure). ...

... The additional U(1) symmetry is expected to influence Hilbert space fragmentation beyond the picture presented in previously studied models [8,14,31]. Second, the presence of a conserved charge allows the study of transport [7,12,13]. While transport without restriction to a particular sector of fragmented Hilbert space results in slow subdiffusive dynamics [7, 12], a recent work [36] demonstrated that a restriction to a particular sector of fragmented Hilbert space can give rise to superdiffusion. ...

... via the tJ z -model at finite J z or via adding diagonal interactions to the folded XXZ model. For example, a stochastic spin chain closely related to the folded XXZ model is the so-called Ising-Kawasaki model [86,87], taken in a particular limit: the Hamiltonian H fXXZ is supplemented by nearest-neighbor (NN) and nextnearest-neighbor (NNN) Ising terms. The name derives from the fact that the quantum Hamiltonian is obtained from the Markov operator of a classical Ising chain undergoing Kawasaki magnetization-conserving dynamics. ...

... It would be interesting to derive new exact lattice results for the reflected entropies and CCNR negativities, both in and out of equilibrium. In higher dimensions, the study of skeletal regions [112], i.e. regions A, B that have no volume, could lead to new analytical results for reflected entropies and CCNR negativities. Finally, it is worth investigating reflected entropies and CCNR negativities for other mixed quantum states, such as Rokhsar-Kivelson states [113,114] whose Hilbert space is spanned by the configurations of an underlying statistical model (see Refs. [115,116] for recent developments on their entanglement structure). ...

... and as shown previously, it should obey a perimeter law, with a universal logarithmic contribution from the sharp corners of the loop C [57,58,65]. The coefficient of the universal logarithmic contribution arising from the corner is proportional to the universal conductivity of the scalar boson current at the (2 + 1)d CFT in the ac limit ω/T → ∞. ...

... Electronic inhomogeneity in EuB 6 was also observed in an angle resolved magnetoresistance experiment [23]. This concurrence of magnetic polarons and electronic inhomogeneity, as seen here in EuB 6 also manifests itself in the high-T c 's. ...

... According to Eq. (5), the slope of the curves give rise to the log-coefficient s(θ) and the obtained results are shown in Fig. 3 (a). As was pointed out in previous works [55,81,82,95], for small θ, the log-coefficient s(θ) arising from the corner of the subsystem is proportional to the charge conductivity σ [96]. More precisely, s(θ) ∼ α s θ 2 for small θ, and the coefficient α s is proportional to σ. ...