Publications

Order by: publication date number of citations

• Density matrices in integrable face models

  Holger Frahm, Daniel Westerfeld

  SciPost Phys. 11, 057 (2021) · published 14 September 2021 | Toggle abstract · pdf

  Using the properties of the local Boltzmann weights of integrable interaction-round-a-face (IRF or face) models we express local operators in terms of generalized transfer matrices. This allows for the derivation of discrete functional equations for the reduced density matrices in inhomogeneous generalizations of these models. We apply these equations to study the density matrices for IRF models of various solid-on-solid type and quantum chains of non-Abelian ${SU(2)_3}$ or Fibonacci anyons. Similar as in the six vertex model we find that reduced density matrices for a sequence of consecutive sites can be 'factorized', i.e.\ expressed in terms of nearest-neighbour correlators with coefficients which are independent of the model parameters. Explicit expressions are provided for correlation functions on up to three neighbouring sites.

  4 citations

• Axion Mie theory of electron energy loss spectroscopy in topological insulators

  Johannes Schultz, Flavio S. Nogueira, Bernd Büchner, Jeroen van den Brink, Axel Lubk

  SciPost Phys. Core 4, 023 (2021) · published 14 September 2021 | Toggle abstract · pdf

  Electronic topological states of matter exhibit novel types of responses to electromagnetic fields. The response of strong topological insulators, for instance, is characterized by a so-called axion term in the electromagnetic Lagrangian which is ultimately due to the presence of topological surface states. Here we develop the axion Mie theory for the electromagnetic response of spherical particles including arbitrary sources of fields, i.e., charge and current distributions. We derive an axion induced mixing of transverse magnetic and transverse electric modes which are experimentally detectable through small induced rotations of the field vectors. Our results extend upon previous analyses of the problem. Our main focus is on the experimentally relevant problem of electron energy loss spectroscopy in topological insulators, a technique that has so far not yet been used to detect the axion electromagnetic response in these materials.

  5 citations

• Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach

  Paola Ruggiero, Pasquale Calabrese, Laura Foini, Thierry Giamarchi

  SciPost Phys. 11, 055 (2021) · published 13 September 2021 | Toggle abstract · pdf

  We study the quantum quench in two coupled Tomonaga-Luttinger Liquids (TLLs), from the off-critical to the critical regime, relying on the conformal field theory approach and the known solutions for single TLLs. We consider a squeezed form of the initial state, whose low energy limit is fixed in a way to describe a massive and a massless mode, and we encode the non-equilibrium dynamics in a proper rescaling of the time. In this way, we compute several correlation functions, which at leading order factorize into multipoint functions evaluated at different times for the two modes. Depending on the observable, the contribution from the massive or from the massless mode can be the dominant one, giving rise to exponential or power-law decay in time, respectively. Our results find a direct application in all the quench problems where, in the scaling limit, there are two independent massless fields: these include the Hubbard model, the Gaudin-Yang gas, and tunnel-coupled tubes in cold atoms experiments.

  14 citations

• Fermionic duality: General symmetry of open systems with strong dissipation and memory

  Valentin Bruch, Konstantin Nestmann, Jens Schulenborg, Maarten R. Wegewijs

  SciPost Phys. 11, 053 (2021) · published 10 September 2021 | Toggle abstract · pdf

  We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schr\"odinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamio{\l}kowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.

  9 citations

• Entanglement in the quantum Hall fluid of dipoles

  Jackson R. Fliss

  SciPost Phys. 11, 052 (2021) · published 9 September 2021 | Toggle abstract · pdf

  We revisit a model for gapped fractonic order in (2+1) dimensions (a symmetric-traceless tensor gauge theory with conservation of dipole and trace-quadrupole moments described in \cite{Prem:2017kxc}) and compute its ground-state entanglement entropy on $\mathbb R^2$. Along the way, we quantize the theory on open subsets of $\mathbb R^2$ which gives rise to gapless edge excitations that are Lifshitz-type scalar theories. We additionally explore varieties of gauge-invariant extended operators and rephrase the fractonic physics in terms of the local deformability of these operators. We explore similarities of this model to the effective field theories describing quantum Hall fluids: in particular, quantization of dipole moments through a novel compact symmetry leads us to interpret the vacuum of this theory as a dipole condensate atop of which dipoles with fractionalized moments appear as quasi-particle excitations with Abelian anyonic statistics. This interpretation is reflected in the subleading ``topological entanglement" correction to the entanglement entropy. We extend this result to a series of models with conserved multipole moments.

  4 citations

• Importance sampling scheme for the stochastic simulation of quantum spin dynamics

  Stefano De Nicola

  SciPost Phys. 11, 048 (2021) · published 2 September 2021 | Toggle abstract · pdf

  The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or the presence of the so-called sign problem. In this work, we develop an importance sampling scheme for the simulation of quantum spin dynamics, building on a recent approach mapping quantum spin systems to classical stochastic processes. The importance sampling scheme is based on identifying the classical trajectory that yields the largest contribution to a given quantum observable. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the stochastic quantities, thus extending the range of accessible times and system sizes compared to direct sampling. We discuss advantages and limitations of the proposed approach, outlining directions for further developments.

  2 citations

• Chiral anomaly trapped in Weyl metals: Nonequilibrium valley polarization at zero magnetic field

  Pablo M. Perez-Piskunow, Nicandro Bovenzi, Anton R. Akhmerov, Maxim Breitkreiz

  SciPost Phys. 11, 046 (2021) · published 31 August 2021 | Toggle abstract · pdf

  In Weyl semimetals the application of parallel electric and magnetic fields leads to valley polarization -- an occupation disbalance of valleys of opposite chirality -- a direct consequence of the chiral anomaly. In this work, we present numerical tools to explore such nonequilibrium effects in spatially confined three-dimensional systems with a variable disorder potential, giving exact solutions to leading order in the disorder potential and the applied electric field. Application to a Weyl-metal slab shows that valley polarization also occurs without an external magnetic field as an effect of chiral anomaly "trapping": Spatial confinement produces chiral bulk states, which enable the valley polarization in a similar way as the chiral states induced by a magnetic field. Despite its finite-size origin, the valley polarization can persist up to macroscopic length scales if the disorder potential is sufficiently long ranged, so that direct inter-valley scattering is suppressed and the relaxation then goes via the Fermi-arc surface states.

  4 citations

• Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

  Ivan M. Khaymovich, Vladimir E. Kravtsov

  SciPost Phys. 11, 045 (2021) · published 31 August 2021 | Toggle abstract · pdf

  We consider the static and the dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the {\it averaged} survival probability may decay with time as a simple exponent, as a stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. As an example, we consider the mapping of the Anderson localization model on Random Regular Graph onto the RP model and find exact values of the stretch-exponent $\kappa$ in the thermodynamic limit. As another example we consider the logarithmically-normal RP random matrix ensemble and find analytically its phase diagram and the exponent $\kappa$. Our theory allows to describe analytically the finite-size multifractality and to compute the critical length with the exponent $\nu_{MF}=1$ associated with it.

  48 citations

• Statistical Floquet prethermalization of the Bose-Hubbard model

  Emanuele G. Dalla Torre, David Dentelski

  SciPost Phys. 11, 040 (2021) · published 24 August 2021 | Toggle abstract · pdf

  The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

  10 citations

• Displaced Drude peak and bad metal from the interaction with slow fluctuations.

  Simone Fratini, Sergio Ciuchi

  SciPost Phys. 11, 039 (2021) · published 24 August 2021 | Toggle abstract · pdf

  Scattering by slowly fluctuating degrees of freedom can cause a transient localization of the current-carrying electrons in metals, driving the system away from normal metallic behavior. We illustrate and characterize this general phenomenon by studying how signatures of localization emerge in the optical conductivity of electrons interacting with slow bosonic fluctuations. The buildup of quantum localization corrections manifests itself in the emergence of a displaced Drude peak (DDP), whose existence strongly alters the low frequency optical response and suppresses the d.c. conductivity. We find that for sufficiently strong interactions, many-body renormalization of the fluctuating field induced at metallic densities enhances electron localization and the ensuing DDP phenomenon in comparison with the well-studied low concentration limit. Our results are compatible with the frequent observation of DDPs in electronic systems where slowly fluctuating degrees of freedom couple significantly to the charge carriers.

  22 citations