Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond

• URL: http://arxiv.org/abs/2012.05248v2
• Date: Wed, 10 Mar 2021 09:32:23 GMT
• Title: Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond
• Authors: Mahdieh Pourjafarabadi, Hanieh Najafzadeh, Mohammad-Sadegh Vaezi, and Abolhassan Vaezi
• Abstract summary: We investigate the second quantization form of the entanglement Hamiltonian of various subregions for the ground-state of lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground-state of generic local Hamiltonians.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground-state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground-state of generic local Hamiltonians. In this letter, we demonstrate that the EH is practically local and its dominant components are related to the terms present in the model Hamiltonian up to a smooth spatially varying temperature even for (a) discrete lattice systems, (b) systems with no emergent conformal or Lorentz symmetry, and (c) for subsystems with non-flat boundaries, up to relatively strong interactions. We show that the mentioned local temperature at a given point decays inversely proportional to its distance from the boundary between the subsystem and the environment. We find the subdominant terms in the EH as well and show that they are severely suppressed away from the boundaries of subsystem and are relatively small near them.

Related papers

• Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
  We show topologically ordered states in the complex-valued spectra of non-Hermitian systems. These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated. We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
  arXiv  Detail & Related papers  (2024-10-24T10:16:47Z)
• Edge state behavior of interacting Bosons in a Su-Schrieffer-Heeger lattice [0.9553307596675152]
  We develop an effective Hamiltonian to model ultra cold interacting Bosons on an SSH like lattice. To pinpoint the boundary states, we have developed an algorithm by generalizing the imaginary time propagator. We draw a parallel to an experimentally physical setup involving a gas of ultra cold Bosons confined to an array of potential wells with alternating depths.
  arXiv  Detail & Related papers  (2024-10-24T04:55:05Z)
• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
  We study the Hamiltonian for a Bose gas in three dimensions of $N geq 3$ spinless particles interacting via zero-range or contact interactions.
  arXiv  Detail & Related papers  (2024-03-19T10:00:12Z)
• The frustration-free fully packed loop model [4.965221313169878]
  We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace. We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
  arXiv  Detail & Related papers  (2022-06-03T18:00:04Z)
• Boundary-induced singularity in strongly-correlated quantum systems at finite temperature [2.2451981098432516]
  We study the bulk-boundary competition in a simulative Hamiltonian, with which the thermodynamic properties of the infinite-size translationally-invariant system can be optimally mimicked. Our results show that such a singularity differs from those in the conventional thermodynamic phase transition points that normally fall into the Landau-Ginzburg paradigm.
  arXiv  Detail & Related papers  (2022-04-14T08:30:30Z)
• Preferred basis derived from eigenstate thermalization hypothesis [1.7606558873844536]
  We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system. We consider a class of interaction Hamiltonian, whose environmental part satisfies the so-called eigenstate thermalization hypothesis (ETH) ansatz with a constant diagonal part in the energy region concerned.
  arXiv  Detail & Related papers  (2022-01-17T09:41:39Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Entanglement dualities in supersymmetry [0.0]
  We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. We find a peculiar phenomenon, namely, an amplified scaling of the entanglement entropy ("super area law") in bosonic subsystems when the dual fermionic subsystems develop almost maximally entangled modes.
  arXiv  Detail & Related papers  (2021-03-17T13:55:44Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.