Publications

Order by: publication date number of citations

• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains

  Ke Wang, T. A. Sedrakyan

  SciPost Phys. 12, 134 (2022) · published 20 April 2022 | Toggle abstract · pdf

  We consider Lifshitz criticalities with dynamical exponent $z=2$ that emerge in a class of topological chains. There, such a criticality plays a fundamental role in describing transitions between symmetry-enriched conformal field theories (CFTs). We report that, at such critical points in one spatial dimension, the finite-size correction to the energy scales with system size, $L$, as $\sim L^{-2}$, with universal and anomalously large coefficient. The behavior originates from the specific dispersion around the Fermi surface, $\epsilon \propto \pm k^2$. We also show that the entanglement entropy exhibits at the criticality a non-logarithmic dependence on $l/L$, where $l$ is the length of the sub-system. In the limit of $l\ll L$, the maximally-entangled ground state has the entropy, $S(l/L)=S_0+(l/L)\log(l/L)$. Here $S_0$ is some non-universal entropy originating from short-range correlations. We show that the novel entanglement originates from the long-range correlation mediated by a zero mode in the low energy sector. The work paves the way to study finite-size effects and entanglement entropy around Lifshitz criticalities and offers an insight into transitions between symmetry-enriched criticalities.

  4 citations

• Boundary criticality of the O(N) model in d = 3 critically revisited

  Max A. Metlitski

  SciPost Phys. 12, 131 (2022) · published 19 April 2022 | Toggle abstract · pdf

  It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. For the ordinary transition the bulk and the boundary order simultaneously; the extra-ordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra- ordinary and special fixed points when d = 3 and N ≥ 2. Here we show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For 2 ≤ N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. We discuss several scenarios for the evolution of the phase diagram past N = Nc. Our findings appear to be consistent with recent Monte Carlo studies of classical models with N = 2 and N = 3. We also compare our results to numerical studies of boundary criticality in 2+1D quantum spin models.

  34 citations

• Quantum bounds and fluctuation-dissipation relations

  Silvia Pappalardi, Laura Foini, Jorge Kurchan

  SciPost Phys. 12, 130 (2022) · published 14 April 2022 | Toggle abstract · pdf

  In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and derivation of quantum bounds on the transport coefficients or on the chaos rate. However, the physical meaning and the mechanism enforcing such bounds is still an open question. Here, we discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, we show that the quantum bound to chaos is a direct consequence of the KMS condition, as applied to a particular pair of two-time correlation and response functions. Encouraged by this, we describe how quantum fluctuation-dissipation relations act in general as a blurring of the time-dependence of correlations, which can imply bounds on their decay rates. Thinking in terms of fluctuation-dissipation opens a direct connection between bounds and other thermodynamic properties.

  14 citations

• Asymmetric transport in long-range interacting chiral spin chains

  Javad Vahedi

  SciPost Phys. Core 5, 021 (2022) · published 13 April 2022 | Toggle abstract · pdf

  Harnessing power-law interactions ($1/r^\alpha$) in a large variety of physical systems are increasing. We study the dynamics of chiral spin chains as a possible multi-directional quantum channel. This arises from the nonlinear character of the dispersion with complex quantum interference effects. Using complementary numerical and analytical techniques, we propose a model to guide quantum states to a desired direction. We illustrate our approach using the long-range XXZ model modulated by Dzyaloshinskii-Moriya (DM) interaction. By exploring non-equilibrium dynamics after a local quantum quench, we identify the interplay of interaction range $\alpha$ and Dzyaloshinskii-Moriya coupling giving rise to an appreciable asymmetric spin excitations transport. This could be interesting for quantum information protocols to transfer quantum states, and it may be testable with current trapped-ion experiments. We further explore the growth of block entanglement entropy in these systems, and an order of magnitude reduction is distinguished.

  2 citations

• Proposal for realizing anomalous Floquet insulators via Chern band annihilation

  Carolyn Zhang, Tobias Holder, Netanel H. Lindner, Mark Rudner, Erez Berg

  SciPost Phys. 12, 124 (2022) · published 11 April 2022 | Toggle abstract · pdf

  Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI). The AFAI features a quasi-energy spectrum with chiral edge modes and a fully localized bulk, leading to non-adiabatic but quantized charge pumping. Here, we show how such a Floquet phase can be realized in a driven, disordered Quantum Anomalous Hall insulator, which is assumed to have two critical energies where the localization length diverges, carrying states with opposite Chern numbers. Driving the system at a frequency close to resonance between these two energies localizes the critical states and annihilates the Chern bands, giving rise to an AFAI phase. We exemplify this principle by studying a model for a driven, magnetically doped topological insulator film, where the annihilation of the Chern bands and the formation of the AFAI phase is demonstrated using the rotating wave approximation. This is complemented by a scaling analysis of the localization length for two copies of a quantum Hall network model with a tunable coupling between them. We find that by tuning the frequency of the driving close to resonance, the driving strength required to stabilize the AFAI phase can be made arbitrarily small.

• Quantum oscillations in interaction-driven insulators

  Andrew A. Allocca, Nigel R. Cooper

  SciPost Phys. 12, 123 (2022) · published 8 April 2022 | Toggle abstract · pdf

  In recent years it has become understood that quantum oscillations of the magnetization as a function of magnetic field, long recognized as phenomena intrinsic to metals, can also manifest in insulating systems. Theory has shown that in certain simple band insulators, quantum oscillations can appear with a frequency set by the area traced by the minimum gap in momentum space, and are suppressed for weak fields by an intrinsic "Dingle damping" factor reflecting the size of the bandgap. Here we examine quantum oscillations of the magnetization in excitonic and Kondo insulators, for which interactions play a crucial role. In models of these systems, self-consistent parameters themselves oscillate with changing magnetic field, generating additional contributions to quantum oscillations. In the low-temperature, weak-field regime, we find that the lowest harmonic of quantum oscillations of the magnetization are unaffected, so that the zero-field bandgap can still be extracted by measuring the Dingle damping factor of this harmonic. However, these contributions dominate quantum oscillations at all higher harmonics, thereby providing a route to measure this interaction effect.

  13 citations

• Low-energy effective theory and anomalous Hall effect in monolayer $\mathrm{WTe}_2$

  S. Nandy, D. A. Pesin

  SciPost Phys. 12, 120 (2022) · published 7 April 2022 | Toggle abstract · pdf

  We develop a symmetry-based low-energy theory for monolayer $\mathrm{WTe}_2$ in its 1T$^{\prime}$ phase, which includes eight bands (four orbitals, two spins). This model reduces to the conventional four-band spin-degenerate Dirac model near the Dirac points of the material. We show that measurements of the spin susceptibility, and of the magnitude and time dependence of the anomalous Hall conductivity induced by injected or equilibrium spin polarization can be used to determine the magnitude and form of the spin-orbit coupling Hamiltonian, as well as the dimensionless tilt of the Dirac bands.

  6 citations

• Thermalization and hydrodynamics of two-dimensional quantum field theories

  Luca V. Delacretaz, A. Liam Fitzpatrick, Emanuel Katz, Matthew T. Walters

  SciPost Phys. 12, 119 (2022) · published 7 April 2022 | Toggle abstract · pdf

  We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically in terms of the temperature and the scale associated with the relevant deformation. This bound is typically much stronger than $\frac{1}{T}$, the expected quantum equilibration time. Subluminality of sound further allows us to define a thermodynamic $C$-function, and constrain the sign of the $\mathcal T\bar{\mathcal T}$ term in EFTs.

  15 citations

• Topological lattice models with constant Berry curvature

  Daniel Varjas, Ahmed Abouelkomsan, Kang Yang, Emil J. Bergholtz

  SciPost Phys. 12, 118 (2022) · published 6 April 2022 | Toggle abstract · pdf

  Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with Landau levels, constant Berry curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while the Berry curvature cannot be made constant in a topological two-band model, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. However, contrary to the intuitive expectation, we find that making the Berry curvature constant does not always improve the properties of fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.

  18 citations

• Information Scrambling with Conservation Laws

  Jonah Kudler-Flam, Ramanjit Sohal, Laimei Nie

  SciPost Phys. 12, 117 (2022) · published 4 April 2022 | Toggle abstract · pdf

  The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as stochastic systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an information-theoretic perspective. For general non-integrable models, we use the equilibrium approximation to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the time-evolution operator) at late times even when a system conserves energy. In contrast, we explicate how when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of holographic conformal field theories (CFTs) and the Sachdev-Ye-Kitaev (SYK) model. Due to the large Virasoro symmetry in 1+1D CFTs, we argue that, in a sense, these holographic theories are not maximally chaotic, which is explicitly seen by the non-saturation of the second R\'enyi tripartite mutual information. The roles of particle-hole and U(1) symmetries in the SYK model are milder due to the degeneracies being only two-fold, which we confirm explicitly at both large- and small-$N$. We reinterpret the operator entanglement in terms the growth of local operators, connecting our results with the information scrambling described by out-of-time-ordered correlators, identifying the mechanism for suppressed scrambling from the Heisenberg perspective.

  11 citations