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

We study the properties of 2+1d conformal field theories (CFTs) in a background magnetic field. Using generalized particle-vortex duality, we argue that in many cases of interest the theory becomes gapped, which allows us to make a number of predictions for the magnetic response, background monopole operators, and more. Explicit calculations at large N for Wilson-Fisher and Gross-Neveu CFTs support our claim, and yield the spectrum of background (defect) monopole operators. Finally, we point out that other possibilities exist: certain CFTs can become metallic in a magnetic field. Such a scenario occurs, for example, with a Dirac fermion coupled to a Chern-Simons gauge field, where a non-Fermi liquid is argued to emerge. Published by the American Physical Society 2024

We show that, in finite dimensions, around any m-partite product state $\rho_{\rm prod}=\rho_1\otimes...\otimes\rho_m$, there exists an ellipsoid of separable states centered around $\rho_{\rm prod}$. The volume of this separable ellipsoid is typically exponentially larger than that of the separable ball proposed in previous works, due to the large hierarchy of eigenvalues occurring in typical states. We further refine this ellipsoidal criterion to a trace formula, generalize it to characterize the separable region around all separable states, and further study biseparability. Our criterion will help numerical procedures to rigorously detect separability. We apply the procedure for separability detection on three-qubit X state in a dephasing environment, and the 1d transverse field Ising model at finite temperature to illustrate the power of our procedure for understanding entanglement in physical systems.

Fluctuations of observables provide unique insights into the nature of physical systems, and their study stands as a cornerstone of both theoretical and experimental science. Generalized fluctuations, or cumulants, provide information beyond the mean and variance of an observable. In this letter, we develop a systematic method to determine the asymptotic behavior of cumulants of local observables as the region becomes large. Our analysis reveals that the expansion is closely tied to the geometric characteristics of the region and its boundary, with coefficients given by convex moments of the connected correlation function: the latter is integrated against intrinsic volumes of convex polytopes built from the coordinates, which can be interpreted as averaged shadows. A particular application of our method shows that, in two dimensions, the leading behavior of odd cumulants of conserved quantities is topological, specifically depending on the Euler characteristic of the region. We illustrate these results with the paradigmatic strongly-interacting system of two-dimensional quantum Hall state at filling fraction 1/2, by performing Monte-Carlo calculations of the skewness (third cumulant) of particle number in the Laughlin state.

We study the entanglement between disjoint subregions in quantum critical systems through the lens of the logarithmic negativity. We work with systems in arbitrary dimensions, including conformal field theories and their corresponding lattice Hamiltonians, as well as resonating valence-bond states. At small separations, the logarithmic negativity is big and displays universal behavior, but we show nonperturbatively that it decays faster than any power at large separations. This can already be seen in the minimal setting of single-spin subregions. The corresponding absence of distillable entanglement at large separations generalizes the one-dimensional result, and indicates that quantum critical ground states do not possess long-range bipartite entanglement, at least for bosons. For systems with fermions, a more suitable definition of the logarithmic negativity exists that takes into account fermion parity, and we show that it decays algebraically. Along the way we obtain general results for the moments of the partially transposed density matrix. Published by the American Physical Society 2024

The thermal Hall effect, which arises when heat flows transversely to an applied thermal gradient, has become an important observable in the study of quantum materials. Recent experiments found a large thermal Hall conductivity κxy in many high-temperature cuprate superconductors, including deep inside the Mott insulator, but the underlying mechanism remains unknown. Here, we uncover a surprising linear temperature dependence for the inverse thermal Hall resistivity, 1/ϱH=−κxx2/κxy, in the Mott insulating cuprates La2CuO4 and Sr2CuO2Cl2. We also find this linear scaling in the pseudogap state of La1.6−xNd0.4SrxCuO4 (Nd-LSCO) in the out-of-plane direction, highlighting the importance of phonons. On the electron-doped side, the linear inverse thermal Hall signal emerges in Nd2−xCexCuO4 (NCCO) and Pr2−xCexCuO4 (PCCO) at various dopings, including in the strange metal. Although such dependence arises in the simple Drude model for itinerant electrons, its origin is unclear in strongly correlated Mott insulating or pseudogap states. We perform a Boltzmann analysis for phonons that incorporates skew scattering, and we are able to identify regimes where a linear T inverse Hall resistivity appears. Finally, we suggest future experiments that would further our fundamental understanding of heat transport in the cuprates and other quantum materials.

The outcomes of measurements are characterized by an infinite family of generalized uncertainties, or cumulants, which provide information beyond the mean and variance of the observable. Here, we investigate the cumulants of a conserved charge in a subregion with corners. We derive nonperturbative relations for the area law, and more interestingly, the angle dependence, showing how it is determined by geometric moments of the correlation function. These hold for translation invariant systems under great generality, including strongly interacting ones. We test our findings by using two-dimensional topological quantum Hall states of bosons and fermions at both integer and fractional fillings. We find that the odd cumulants' shape dependence differs from the even ones. For instance, the third cumulant shows nearly universal behavior for integer and fractional Laughlin Hall states in the lowest Landau level. Furthermore, we examine the relation between even cumulants and the Rényi entanglement entropy, where we use our results for the fractional state at filling 1/3 to compare these quantities in the strongly interacting regime. We discuss the implications of these findings for other systems, including gapless Dirac fermions, and more general conformal field theories.

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 graphs, we prove the exact separability of the reduced density matrix of k k disconnected subsystems, implying the absence of bipartite and multipartite entanglement between the subsystems. For more general RK states with local constraints, we argue separability in the thermodynamic limit, and show that any local RK state has zero logarithmic negativity, even if the density matrix is not exactly separable. In the case of adjacent subsystems, we find an exact expression for the logarithmic negativity in terms of partition functions of the underlying statistical model. For RVB states, we show separability for disconnected subsystems up to exponentially small terms in the distance d d between the subsystems, and that the logarithmic negativity is exponentially suppressed with d d . We argue that separability does hold in the scaling limit, even for arbitrarily small ratio d/L d / L , where L L is the characteristic size of the subsystems. Our results hold for arbitrary lattices, and encompass a large class of RK and RVB states, which include certain gapped quantum spin liquids and gapless quantum critical systems.

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. Spin-fluctuation mediated superconductivity is modeled by a Hubbard-Kanamori model with an effective particle-particle interaction, calculated via the random phase approximation. Magnetic orders are found using the Stoner criterion. The most likely superconducting order we find has d-wave pairing, predominantly in the total angular momentum J=12 states. Moreover, an s± order which mixes different bands is found at high Hund's coupling, and at high strain anisotropic s- and d-wave orders emerge. Finally, we show that in a fine-tuned region of parameters a spin-triplet p-wave order exists. The combination of strong spin-orbit coupling, interactions, and a sensitivity of the band structure to strain proves a fruitful avenue for engineering new quantum phases.

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 computed to subleading order in 1/N can be extrapolated to N=1 and matched to O(2) Wilson-Fisher CFT scaling dimensions with around 5% error, which is evidence for particle-vortex duality. We then generalize the subleading calculation to large N, k and fixed k/N, extrapolate to N=k=1, and consider monopole operators that are conjectured to be dual to nondegenerate scalar operators in a theory of a single Dirac fermion. We find matches typically with 1% error or less, which is strong evidence of this so-called “seed” duality that implies a web of 3d bosonization dualities among CFTs.

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 fermions in terms of the same number of complex bosons and partner gauge fields. In some instances, monopole operators appear explicitly in the dual action, such as for the superconducting transition of a single Dirac fermion, which is a CFT with emergent supersymmetry. We match phase diagrams, symmetries and their anomalies. By further gauging certain symmetries, we derive offspring dualities. For example, starting with the duality for the regular GNY transition of 2 Dirac fermions, we arrive at the duality between a Neel-to-VBS deconfined quantum critical point and a gauged-Gross-Neveu transition. Finally, we use a large-N expansion for monopole operators, and compare with known scaling dimensions in the simplest single-flavour GNY transition.