Publications

Order by: publication date number of citations

• A supervised learning algorithm for interacting topological insulators based on local curvature

  Paolo Molignini, Antonio Zegarra, Evert van Nieuwenburg, R. Chitra, Wei Chen

  SciPost Phys. 11, 073 (2021) · published 28 September 2021 | Toggle abstract · pdf

  Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the curvature function diverges and changes sign at certain high symmetry points in the Brillouin zone. These generic properties suggest the introduction of a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We apply this scheme to a variety of interacting topological insulators in different dimensions and symmetry classes. We demonstrate that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases with very little numerical effort. Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality in the examples studied.

  14 citations

• On the Q operator and the spectrum of the XXZ model at root of unity

  Yuan Miao, Jules Lamers, Vincent Pasquier

  SciPost Phys. 11, 067 (2021) · published 22 September 2021 | Toggle abstract · pdf

  The spin-1/2 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We construct Baxter's Q operator at arbitrary anisotropy from a two-parameter transfer matrix associated to a complex-spin auxiliary space. A decomposition of this transfer matrix provides a simple proof of the transfer matrix fusion and Wronskian relations. At root of unity a truncation allows us to construct the Q operator explicitly in terms of finite-dimensional matrices. From its decomposition we derive truncated fusion and Wronskian relations as well as an interpolation-type formula that has been conjectured previously. We elucidate the Fabricius-McCoy (FM) strings and exponential degeneracies in the spectrum of the six-vertex transfer matrix at root of unity. Using a semicyclic auxiliary representation we give a conjecture for creation and annihilation operators of FM strings for all roots of unity. We connect our findings with the 'string-charge duality' in the thermodynamic limit, leading to a conjecture for the imaginary part of the FM string centres with potential applications to out-of-equilibrium physics.

  14 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

• Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases

  Shenghan Jiang, Meng Cheng, Yang Qi, Yuan-Ming Lu

  SciPost Phys. 11, 024 (2021) · published 6 August 2021 | Toggle abstract · pdf

  We propose and prove a family of generalized Lieb-Schultz-Mattis (LSM) theorems for symmetry protected topological (SPT) phases on boson/spin models in any dimensions. The "conventional" LSM theorem, applicable to e.g. any translation invariant system with an odd number of spin-1/2 particles per unit cell, forbids a symmetric short-range-entangled ground state in such a system. Here we focus on systems with no LSM anomaly, where global/crystalline symmetries and fractional spins within the unit cell ensure that any symmetric SRE ground state must be a nontrivial SPT phase with anomalous boundary excitations. Depending on models, they can be either strong or "higher-order" crystalline SPT phases, characterized by nontrivial surface/hinge/corner states. Furthermore, given the symmetry group and the spatial assignment of fractional spins, we are able to determine all possible SPT phases for a symmetric ground state, using the real space construction for SPT phases based on the spectral sequence of cohomology theory. We provide examples in one, two and three spatial dimensions, and discuss possible physical realization of these SPT phases based on condensation of topological excitations in fractionalized phases.

  14 citations

• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

  Sibaram Ruidas, Sumilan Banerjee

  SciPost Phys. 11, 087 (2021) · published 3 November 2021 | Toggle abstract · pdf

  Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ model. We show that spatio-temporal chaotic properties have crossovers across the transitions and distinct temperature dependence in the high and low-temperature phases which show normal and anomalous diffusions, respectively. Our results also provide new insights into the dynamics of interacting quantum systems in the semiclassical limit.

  14 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.

  14 citations

• Semiconductor electron-phonon equations: A rung above Boltzmann in the many-body ladder

  Gianluca Stefanucci, Enrico Perfetto

  SciPost Phys. 16, 073 (2024) · published 13 March 2024 | Toggle abstract · pdf

  Starting from the ab initio many-body theory of electrons and phonons, we go through a series of well defined simplifications to derive a set of coupled equations of motion for the electronic occupations and polarizations, nuclear displacements as well as phononic occupations and coherences. These are the semiconductor electron-phonon equations (SEPE), sharing the same scaling with system size and propagation time as the Boltzmann equations. At the core of the SEPE is the mirrored Generalized Kadanoff-Baym Ansatz (GKBA) for the Green's functions, an alternative to the standard GKBA which we show to lead to unstable equilibrium states. The SEPE treat coherent and incoherent degrees of freedom on equal footing, widen the scope of the semiconductor Bloch equations and Boltzmann equations, and reduce to them under additional simplifications. The new features of the SEPE pave the way for first-principles studies of phonon squeezed states and coherence effects in time-resolved absorption and diffraction experiments.

  14 citations

• Curvature induced magnonic crystal in nanowires

  Anastasiia Korniienko, Volodymyr P. Kravchuk, Oleksandr V. Pylypovskyi, Denis D. Sheka, Jeroen van den Brink, Yuri Gaididei

  SciPost Phys. 7, 035 (2019) · published 20 September 2019 | Toggle abstract · pdf

  A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well confirmed by simulations. An application to nanoscale spintronic devices with the geometrically tunable parameters is proposed, namely, to filter elements.

  14 citations

• Electric manipulation of domain walls in magnetic Weyl semimetals via the axial anomaly

  Julia D. Hannukainen, Alberto Cortijo, Jens H. Bardarson, Yago Ferreiros

  SciPost Phys. 10, 102 (2021) · published 11 May 2021 | Toggle abstract · pdf

  We show how the axial (chiral) anomaly induces a spin torque on the magnetization in magnetic Weyl semimetals. The anomaly produces an imbalance in left- and right-handed chirality carriers when non-orthogonal electric and magnetic fields are applied. Such imbalance generates a spin density which exerts a torque on the magnetization, the strength of which can be controlled by the intensity of the applied electric field. We show how this results in an electric control of the chirality of domain walls, as well as in an improvement of the domain wall dynamics, by delaying the onset of the Walker breakdown. The measurement of the electric field mediated changes in the domain wall chirality would constitute a direct proof of the axial anomaly. Additionally, we show how quantum fluctuations of electronic Fermi arc states bound to the domain wall naturally induce an effective magnetic anisotropy, allowing for high domain wall velocities even if the intrinsic anisotropy of the magnetic Weyl semimetal is small.

  14 citations

• Non-perturbative intertwining between spin and charge correlations: A ``smoking gun'' single-boson-exchange result

  Severino Adler, Friedrich Krien, Patrick Chalupa-Gantner, Giorgio Sangiovanni, Alessandro Toschi

  SciPost Phys. 16, 054 (2024) · published 23 February 2024 | Toggle abstract · pdf

  We study the microscopic mechanism controlling the interplay between local charge and local spin fluctuations in correlated electron systems via a thorough investigation of the generalized on-site charge susceptibility of several fundamental many-electron models, such as the Hubbard atom, the Anderson impurity model, and the Hubbard model. By decomposing the numerically determined generalized susceptibility in terms of physically transparent single-boson exchange processes, we unveil the microscopic mechanisms responsible for the breakdown of the self-consistent many-electron perturbation expansion. In particular, we unambiguously identify the origin of the significant suppression of its diagonal entries in (Matsubara) frequency space and the slight increase of the off-diagonal ones which cause the breakdown. The suppression effect on the diagonal elements originates directly from the electronic scattering on local magnetic moments, reflecting their increasingly longer lifetime as well as their enhanced effective coupling with the electrons. Instead, the slight and diffuse enhancement of the off-diagonal terms can be mostly ascribed to multiboson scattering processes. The strong intertwining between spin and charge sectors is partly weakened at the Kondo temperature due to a progressive reduction of the effective spin-fermion coupling of local magnetic fluctuations in the low frequency regime. Our analysis, thus, clarifies the precise mechanism through which the physical information is transferred between different scattering channels of interacting electron problems and highlights the pivotal role played by such an intertwining in the physics of correlated electrons beyond the perturbative regime.

  14 citations