Publications

Order by: publication date number of citations

• Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators

  Frederik Nathan, Dmitry A. Abanin, Netanel H. Lindner, Erez Berg, Mark S. Rudner

  SciPost Phys. 10, 128 (2021) · published 3 June 2021 | Toggle abstract · pdf

  We uncover a new family of few-body topological phases in periodically driven fermionic systems in two dimensions. These phases, which we term correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by quantized contributions to the bulk magnetization from multi-particle correlations, and are classified by a family of integer-valued topological invariants. The CIAFI phases do not require many-body localization, but arise in the generic situation of $k$-particle localization, where the system is localized (due to disorder) for any finite number of particles up to a maximum number, $k$. We moreover show that, when fully many-body localized, periodically driven systems of interacting fermions in two dimensions are characterized by a quantized magnetization in the bulk, thus confirming the quantization of magnetization of the anomalous Floquet insulator. We demonstrate our results with numerical simulations.

  9 citations

• Finite-temperature photoemission in the extended Falicov-Kimball model: a case study for Ta$_2$NiSe$_5$

  Satoshi Ejima, Florian Lange, Holger Fehske

  SciPost Phys. 10, 077 (2021) · published 26 March 2021 | Toggle abstract · pdf

  Utilizing the unbiased time-dependent density-matrix renormalization group technique, we examine the photoemission spectra in the extended Falicov-Kimball model at zero and finite temperatures, particularly with regard to the excitonic insulator state most likely observed in the quasi-one-dimensional material Ta$_2$NiSe$_5$. Working with infinite boundary conditions, we are able to simulate all dynamical correlation functions directly in the thermodynamic limit. For model parameters best suited for Ta$_2$NiSe$_5$ the photoemission spectra show a weak but clearly visible two-peak structure, around the Fermi momenta $k\simeq\pm k_{\rm F}$, which suggests that Ta$_2$NiSe$_5$ develops an excitonic insulator of BCS-like type. At higher temperatures, the leakage of the conduction-electron band beyond the Fermi energy becomes distinct, which provides a possible explanation for the bare non-interacting band structure seen in time- and angle-resolved photoemission spectroscopy experiments.

  9 citations

• Assessing the role of interatomic position matrix elements in tight-binding calculations of optical properties

  Julen Ibañez-Azpiroz, Fernando de Juan, Ivo Souza

  SciPost Phys. 12, 070 (2022) · published 22 February 2022 | Toggle abstract · pdf

  We study the role of hopping matrix elements of the position operator $\mathbf{\hat{r}}$ in tight-binding calculations of linear and nonlinear optical properties of solids. Our analysis relies on a Wannier-interpolation scheme based on ab initio calculations, which automatically includes matrix elements of $\mathbf{\hat{r}}$ between different Wannier orbitals. A common approximation, both in empirical tight-binding and in Wannier-interpolation calculations, is to discard those matrix elements, in which case the optical response only depends on the on-site energies, Hamiltonian hoppings, and orbital centers. We find that interatomic $\mathbf{\hat{r}}$-hopping terms make a sizeable contribution to the shift photocurrent in monolayer BC$_2$N, a covalent acentric crystal. If a minimal basis of $p_z$ orbitals on the carbon atoms is used to model the band-edge response, even the dielectric function becomes strongly dependent on those terms.

  9 citations

• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope

  Botao Wang, Xiao-Yu Dong, André Eckardt

  SciPost Phys. 12, 095 (2022) · published 17 March 2022 | Toggle abstract · pdf

  The recent progress in engineering topological band structures in optical-lattice systems makes it promising to study fractional Chern insulator states in these systems. Here we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantum-gas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlin-like state at filling $\nu=1/2$ can be stabilized and its fractional excitations probed. Using numerical simulations, we find an incompressible bulk density at the expected filling for systems, whose linear extent is as small as 6-8 sites. This is a promising result, since such small systems are favorable with respect to the required adiabatic state preparation. Moreover, we also see very clear signatures of excitations with fractional charge in response both to static pinning potentials and dynamical flux insertion. Since the compressible edges, which are found to feature chiral currents, can serve as a reservoir, these observations are robust against changes in the total particle number. Our results suggest that signatures of both a fractional Chern insulator state and its fractional excitations can be found under realistic experimental conditions.

  9 citations

• A beginner's guide to non-abelian iPEPS for correlated fermions

  Benedikt Bruognolo, Jheng-Wei Li, Jan von Delft, Andreas Weichselbaum

  SciPost Phys. Lect. Notes 25 (2021) · published 25 February 2021 | Toggle abstract · pdf

  Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension $D=24$ on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with $2$ bands of spinful fermions of $\mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}$ symmetry, the other with $3$ flavors of spinless fermions of $\mathrm{SU}(3)_\mathrm{flavor}$ symmetry.

  9 citations

• Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy

  Satoshi Ejima, Tomoki Yamaguchi, Fabian H. L. Essler, Florian Lange, Yukinori Ohta, Holger Fehske

  SciPost Phys. 5, 059 (2018) · published 7 December 2018 | Toggle abstract · pdf

  We consider the dimerized spin-1 $XXZ$ chain with single-ion anisotropy $D$. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.

  9 citations

• A degeneracy bound for homogeneous topological order

  Jeongwan Haah

  SciPost Phys. 10, 011 (2021) · published 20 January 2021 | Toggle abstract · pdf

  We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace, rather than on the Hamiltonian, and demands that given a collection of ball-like regions, any linear transformation on the ground space be realized by an operator that avoids the ball-like regions. We derive a bound on the ground state degeneracy $\mathcal D$ for systems with homogeneous topological order on an arbitrary closed Riemannian manifold of dimension $d$, which reads \[ \log \mathcal D \le c \mu (L/a)^{d-2}.\] Here, $L$ is the diameter of the system, $a$ is the lattice spacing, and $c$ is a constant that only depends on the isometry class of the manifold, and $\mu$ is a constant that only depends on the density of degrees of freedom. If $d=2$, the constant $c$ is the (demi)genus of the space manifold. This bound is saturated up to constants by known examples.

  9 citations

• Hall anomaly and moving vortex charge in layered superconductors

  Assa Auerbach, Daniel P. Arovas

  SciPost Phys. 8, 061 (2020) · published 17 April 2020 | Toggle abstract · pdf

  Magnetotransport theory of layered superconductors in the flux flow steady state is revisited. Longstanding controversies concerning observed Hall sign reversals are resolved. The conductivity separates into a Bardeen-Stephen vortex core contribution, and a Hall conductivity due to moving vortex charge. This charge, which is responsible for Hall anomaly, diverges logarithmically at weak magnetic field. Its values can be extracted from magetoresistivity data by extrapolation of vortex core Hall angle from the normal phase. Hall anomalies in YBCO, BSCCO, and NCCO data are consistent with theoretical estimates based on doping dependence of London penetration depths. In the appendices, we derive the Streda formula for the hydrodynamical Hall conductivity, and refute previously assumed relevance of Galilean symmetry to Hall anomalies.

  9 citations

• One step replica symmetry breaking and extreme order statistics of logarithmic REMs

  Xiangyu Cao, Yan V. Fyodorov, Pierre Le Doussal

  SciPost Phys. 1, 011 (2016) · published 19 December 2016 | Toggle abstract · pdf

  Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance ("ultraviolet", UV) limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for log-REMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$-noise.

  9 citations

• Critical energy landscape of linear soft spheres

  Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani

  SciPost Phys. 9, 012 (2020) · published 23 July 2020 | Toggle abstract · pdf

  We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.

  9 citations