[Show abstract][Hide abstract]ABSTRACT: We report on a detailed investigation of the spin-1 $J_1-J_2-J_3$ Heisenberg model, a frustrated model with nearest-neighbor coupling $J_1$, next-nearest neighbor coupling $J_2$, and a three site interaction $J_3\left[({\bf S}_{i-1}\cdot {\bf S}_i)({\bf S}_i\cdot {\bf S}_{i+1})+{\mathrm H.c.}\right]$ previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using DMRG and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the $SU(2)_2$ Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the $SU(2)_2$ transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while those between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.
[Show abstract][Hide abstract]ABSTRACT: We show that, when $N$ is a multiple of 6 ($N=6m$, $m$ integer), the \SU{N} Heisenberg model on the honeycomb lattice with $m$ particles per site has a clear tendency toward chiral order as soon as $m\geq 2$. This conclusion has been reached by a systematic variational Monte Carlo investigation of Gutzwiller projected wave-functions as a function of $m$ between the case of one particle per site ($m=1$), for which the ground state has recently been shown to be in a plaquette singlet state, and the $m\rightarrow \infty$ limit, where a mean-field approach has established that the ground state has chiral order. This demonstrates that the chiral phase can indeed be stabilized for not too large values of $m$, opening the way to its experimental realisations in other lattices.
[Show abstract][Hide abstract]ABSTRACT: The phase diagram of the spin-1 chain with bilinear-biquadratic and next-nearest neighbor inter- actions, recently investigated by Pixley, Shashi and Nevidomskyy [Phys. Rev. B 90, 214426 (2014)], has been revisited in the light of results we have recently obtained on a similar model. Combining extensive Density Matrix Renormalization Group (DMRG) simulations with conformal-field theory arguments, we confirm the presence of the three phases identified by Pixley et al, a Haldane phase, a next-nearest neighbor (NNN) Haldane phase, and a dimerized phase, but we come to significantly different conclusions regarding the nature of the phase transitions to the dimerized phase: i) We provide numerical evidence of a continuous Ising transition between the NNN-Haldane phase and the dimerized phase; ii) We show that the tri-critical end point, where the continuous transition between the Haldane phase and the dimerized phase turns into a first order transition, is distinct from the triple point where the three phases meet; iii) Finally, we demonstrate that the tri-critical end point is in the same Wess-Zumino-Witten (WZW) SU(2) level 2 universality class as the continuous transition line that ends at this point
[Show abstract][Hide abstract]ABSTRACT: Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu$_2$(BO$_3$)$_2$ show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist to all the way to infinite temperature. Our results offer new insight into the physics of finite-temperature spectral functions in SrCu$_2$(BO$_3$)$_2$ and many other highly frustrated spin systems.
[Show abstract][Hide abstract]ABSTRACT: We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011)]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.
[Show abstract][Hide abstract]ABSTRACT: Motivated by the numerous examples of 1/3 magnetization plateaux in the triangular lattice Heisenberg an- tiferromagnet with spins ranging from 1/2 to 5/2, we revisit the semiclassical calculation of the magnetization curve of that model, with the aim of coming up with a simple method that allows one to calculate the full mag- netization curve, and not just the critical fields of the 1/3 plateau. We show that it is actually possible to calculate the magnetization curve including the first quantum corrections and the appearance of the 1/3 plateau entirely within linear spin-wave theory, with predictions for the critical fields that agree to order 1/S with those derived a long-time ago on the basis of arguments that required to go beyond linear spin-wave theory. This calculation relies on the central observation that there is a kink in the semiclassical energy at the field where the classical ground state is the collinear up-up-down structure, and that this kink gives rise to a locally linear behavior of the energy with the field when all semiclassical ground states are compared to each other for all fields. The magnetization curves calculated in this way for spin 1/2, 1 and 5/2 are shown to be in good agreement with available experimental data.
[Show abstract][Hide abstract]ABSTRACT: We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest neighbor (NNN) and 3-site interactions using extensive numerical simulations and a conformal field theory analysis. We show that the transition can be second order in the WZW SU(2)$_2$ or Ising universality class, or first-order. We argue that these features are generic because of a marginal operator in the WZW SU(2)$_2$ model, and because of two topologically distinct non-dimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.
[Show abstract][Hide abstract]ABSTRACT: Quantum antiferromagnets have proven to be some of the cleanest realizations
available for theoretical, numerical, and experimental studies of quantum
fluctuation effects. At finite temperatures, however, the additional effects of
thermal fluctuations in the restricted phase space of a low-dimensional system
have received much less attention, particularly the situation in frustrated
quantum magnets, where the excitations may be complex collective (bound or even
fractionalized) modes. We investigate this problem by studying the
thermodynamic properties of the frustrated two-leg S=1/2 spin ladder, with
particular emphasis on the fully frustrated case. We present numerical results
for the magnetic specific heat and susceptibility, obtained from exact
diagonalization and quantum Monte Carlo studies, which we show can be rendered
free of the sign problem even in a strongly frustrated system and which allow
us to reach unprecedented sizes of L=200 ladder rungs. We find that frustration
effects cause an unconventional evolution of the thermodynamic response across
the full parameter regime of the model. However, close to the first-order
transition they cause a highly anomalous reduction in temperature scales with
no concomitant changes in the gap; the specific heat shows a very narrow peak
at very low energies and the susceptibility rises abruptly at extremely low
temperatures. Unusually, the two quantities have different gaps over an
extended region of the parameter space. We demonstrate that these results
reflect the presence of large numbers of multi-particle bound-state
excitations, whose energies fall below the one-triplon gap in the transition
region.
[Show abstract][Hide abstract]ABSTRACT: Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond nearest neighbour. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kasteleyn transition between them. Experimental implications are briefly discussed.
[Show abstract][Hide abstract]ABSTRACT: We show that the critical fields of the magnetization plateaus of the
Shastry-Sutherland model decrease significantly upon increasing the ratio of
inter- to intra-dimer coupling, and accordingly that the magnetization plateaus
of SrCu_2(BO_3)_2 shift to lower field under pressure, making the first two
plateaus at 1/8 and 2/15 potentially accessible to neutron scattering
experiments. These conclusions are based on the derivation of an effective
classical model of interacting pinwheel-shaped spin-2 bound states using a
combination of perturbative and graph-based continuous unitary transformations,
showing that pinwheel crystals are indeed the lowest-energy plateau structures
at low magnetization, and that a simple model of intermediate-range two-body
repulsion between pinwheels is able to account quantitatively for the plateau
sequence.
[Show abstract][Hide abstract]ABSTRACT: We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has
been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et
al., Phys. Rev. A 84, 011611 (2011)]. Using exact diagonalizations of finite
clusters, infinite projected entangled pair states simulations, and variational
Monte Carlo simulations based on Gutzwiller projected wave functions, we
provide strong evidence in favour of the competing plaquette state, which was
reported to be higher but close by in energy according to mean-field theory.
This is further confirmed by the investigation of the model with a ring
exchange term, which shows that there is a transition between the plaquette
state and the chiral state at a finite value of the ring exchange term.
[Show abstract][Hide abstract]ABSTRACT: We show that, in the presence of a $\pi/2$ artificial gauge field per
plaquette, Mott insulating phases of ultra-cold fermions with $SU(N)$ symmetry
and one particle per site generically possess an extended chiral phase with
intrinsic topological order characterized by a multiplet of $N$ low-lying
singlet excitations for periodic boundary conditions, and by chiral edge states
described by the $SU(N)_1$ Wess-Zumino-Novikov-Witten conformal field theory
for open boundary conditions. This has been achieved by extensive exact
diagonalizations for $N$ between $3$ and $9$, and by a parton construction
based on a set of $N$ Gutzwiller projected fermionic wave-functions with flux
$\pi/N$ per triangular plaquette. Experimental implications are briefly
discussed.
[Show abstract][Hide abstract]ABSTRACT: Motivated by recent experimental progress in the context of ultra-cold
multi-color fermionic atoms in optical lattices, we have developed a method to
exactly diagonalize the Heisenberg $SU(N)$ Hamiltonian with several particles
per site living in a fully symmetric or antisymmetric representation of
$SU(N)$. The method, based on the use of standard Young tableaux, takes
advantage of the full $SU(N)$ symmetry, allowing one to work directly in each
irreducible representations of the global $SU(N)$ group. Since the $SU(N)$
singlet sector is often much smaller than the full Hilbert space, this enables
one to reach much larger system sizes than with conventional exact
diagonalizations. The method is applied to the study of Heisenberg chains in
the symmetric representation with two and three particles per site up to $N=10$
and up to 20 sites. For the length scales accessible to this approach, all
systems except the Haldane chain ($SU(2)$ with two particles per site) appear
to be gapless, and the central charge and scaling dimensions extracted from the
results are consistent with a critical behaviour in the $SU(N)$ level $k$
Wess-Zumino-Witten universality class, where $k$ is the number of particles per
site. These results point to the existence of a cross-over between this
universality class and the asymptotic low-energy behavior with a gapped
spectrum or a critical behavior in the $SU(N)$ level $1$ WZW universality
class.
[Show abstract][Hide abstract]ABSTRACT: Recent experiments on the Ba3XSb2O9 family have revealed materials that potentially realize spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X2+-Sb5+ dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, Tfrz, at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba3CuSb2O9. At T=Tfrz we find a complicated "branching" structure of superexchange-linked X2+ clusters, which form a fractal pattern with fractal dimension df=1.90. We show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalized orphan spins.
[Show abstract][Hide abstract]ABSTRACT: Using quantum Monte Carlo simulations along with higher-order spin-wave
theory, bond-operator and strong-coupling expansions, we analyse the dynamical
spin structure factor of the spin-half Heisenberg model on the square-lattice
bilayer. We identify distinct contributions from the low-energy Goldstone modes
in the magnetically ordered phase and the gapped triplon modes in the quantum
disordered phase. In the antisymmetric (with respect to layer inversion)
channel, the dynamical spin structure factor exhibits a continuous evolution of
spectral features across the quantum phase transition, connecting the two types
of modes. Instead, in the symmetric channel we find a depletion of the spectral
weight when moving from the ordered to the disordered phase. While the
dynamical spin structure factor does not exhibit a well-defined distinct
contribution from the amplitude (or Higgs) mode in the ordered phase, we
identify an only marginally-damped amplitude mode in the dynamical singlet
structure factor, obtained from interlayer bond correlations, in the vicinity
of the quantum critical point. These findings provide quantitative information
in direct relation to possible neutron or light scattering experiments in a
fundamental two-dimensional quantum-critical spin system.
[Show abstract][Hide abstract]ABSTRACT: The magnetic excitation spectrum in the bilayer iridate Sr$_3$Ir$_2$O$_7$ has
been investigated using high-resolution resonant inelastic x-ray scattering
(RIXS) performed at the iridium L$_3$ edge and theoretical techniques. A study
of the systematic dependence of the RIXS spectrum on the orientation of the
wavevector transfer, $\mathbf{Q}$, with respect to the iridium-oxide bilayer
has revealed that the magnon dispersion is comprised of two branches well
separated in energy and gapped across the entire Brillouin zone. Our results
contrast with those of an earlier study which reported the existence of a
single dominant branch. While these earlier results were interpreted as two
overlapping modes within a spin-wave model of weakly coupled iridium-oxide
planes, our results are more reminiscent of those expected for a system of
weakly coupled dimers. In this latter approach the lower and higher energy
modes find a natural explanation as those corresponding to transverse and
longitudinal fluctuations, respectively. We have therefore developed a
bond-operator theory which describes the magnetic dispersion in
Sr$_3$Ir$_2$O$_7$ in terms of quantum dimer excitations. In our model
dimerisation is produced by the leading Heisenberg exchange, $J_c$, which
couples iridium ions in adjacent planes of the bilayer. The Hamiltonian also
includes in plane exchange, $J$, as well as further neighbour couplings and
relevant anisotropies. The bond-operator theory provides an excellent account
of the dispersion of both modes, while the measured $\mathbf{Q}$ dependence of
the RIXS intensities is in reasonable qualitative accord with the spin-spin
correlation function calculated from the theory. We discuss our results in the
context of the quantum criticality of bilayer dimer systems in the presence of
anisotropic interactions derived from strong spin-orbit coupling.
[Show abstract][Hide abstract]ABSTRACT: The magnetic excitation spectrum in the bilayer iridate Sr3Ir2O7 has been investigated using high-resolution resonant inelastic x-ray scattering (RIXS) performed at the iridium L3 edge and theoretical techniques. A study of the systematic dependence of the RIXS spectrum on the orientation of the wave-vector transfer Q, with respect to the iridium-oxide bilayer, has revealed that the magnon dispersion is comprised of two branches well separated in energy and gapped across the entire Brillouin zone. Our results contrast with those of an earlier study which reported the existence of a single dominant branch. While these earlier results were interpreted as two overlapping modes within a spin-wave model of weakly coupled iridium-oxide planes, our results are more reminiscent of those expected for a system of weakly coupled dimers. In this latter approach, the lower- and higher-energy modes find a natural explanation as those corresponding to transverse and longitudinal fluctuations, respectively. We have therefore developed a bond-operator theory which describes the magnetic dispersion in Sr3Ir2O7 in terms of quantum dimer excitations. In our model, dimerization is produced by the leading Heisenberg exchange Jc, which couples iridium ions in adjacent planes of the bilayer. The Hamiltonian also includes in-plane exchange J, as well as further neighbor couplings and relevant anisotropies. The bond-operator theory provides an excellent account of the dispersion of both modes, while the measured Q dependence of the RIXS intensities is in reasonable qualitative accord with the spin-spin correlation function calculated from the theory. We discuss our results in the context of the quantum criticality of bilayer dimer systems in the presence of anisotropic interactions derived from strong spin-orbit coupling.
[Show abstract][Hide abstract]ABSTRACT: Recent experiments on the Ba$_3$XSb$_2$O$_9$ family have revealed materials
that potentially realise spin- and spin-orbital liquid physics. However, the
lattice structure of these materials is complicated due to the presence of
charged X$^{2+}$-Sb$^{5+}$ dumbbells, with two possible orientations. To model
the lattice structure, we consider a frustrated model of charged dumbbells on
the triangular lattice, with long-range Coulomb interactions. We study this
model using Monte Carlo simulation, and find a freezing temperature, $T_{\sf
frz}$, at which the simulated structure factor matches well to low-temperature
x-ray diffraction data for Ba$_3$CuSb$_2$O$_9$. At $T=T_{\sf frz}$ we find a
complicated "branching" structure of superexchange-linked X$^{2+}$ clusters,
and show that this gives a natural explanation for the presence of orphan
spins. Finally we provide a plausible mechanism by which such dumbbell disorder
can promote a spin-orbital resonant state with delocalised orphan spins.