Topological Multipartite Entanglement in a Fermi Liquid

• URL: http://arxiv.org/abs/2204.06559v2
• Date: Thu, 4 Aug 2022 03:43:19 GMT
• Title: Topological Multipartite Entanglement in a Fermi Liquid
• Authors: Pok Man Tam, Martin Claassen, Charles L. Kane
• Abstract summary: We show that the topology of the Fermi sea of a $D$-dimensional Fermi gas is reflected in the multipartite entanglement characterizing $D+1$ regions that meet at a point. For odd $D$ we introduce the multipartite mutual information, and show that it exhibits a $logD L$ divergence as a function of system size $L$ with a universal coefficient that is proportional to the Euler characteristic $chi_F$ of the Fermi sea.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the topology of the Fermi sea of a $D$-dimensional Fermi gas is reflected in the multipartite entanglement characterizing $D+1$ regions that meet at a point. For odd $D$ we introduce the multipartite mutual information, and show that it exhibits a $\log^D L$ divergence as a function of system size $L$ with a universal coefficient that is proportional to the Euler characteristic $\chi_F$ of the Fermi sea. This provides a generalization, for a Fermi gas, of the well-known result for $D=1$ that expresses the $\log L$ divergence of the bipartite entanglement entropy in terms of the central charge $c$ characterizing a conformal field theory. For even $D$ we introduce a charge-weighted entanglement entropy that is manifestly odd under a particle-hole transformation. We show that the corresponding charge-weighted mutual information exhibits a similar $\log^D L$ divergence proportional to $\chi_F$. Our analysis relates the universal behavior of the multipartite mutual information in the absence of interactions to the $D+1$'th order equal-time density correlation function, which we show exhibits a universal behavior in the long wavelength limit proportional to $\chi_F$. Our analytic results are based on the replica method. In addition we perform a numerical study of the charge-weighted mutual information for $D=2$ that confirms several aspects of the analytic theory. Finally, we consider the effect of interactions perturbatively within the replica theory. We show that for $D=3$ the $\log^3 L$ divergence of the topological mutual information is not perturbed by weak short-ranged interactions, though for $D=2$ the charge-weighted mutual information is perturbed. Thus, for $D=3$ the multipartite mutual information provides a robust classification that distinguishes distinct topological Fermi liquid phases.

Related papers

• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model [44.84660857803376]
  We study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The robustness of $pi$ pairings against longitudinal disorder may be useful for quantum information processing.
  arXiv  Detail & Related papers  (2024-01-09T20:37:48Z)
• Correlated volumes for extended wavefunctions on a random-regular graph [0.0]
  We analyze the ergodic properties of a metallic wavefunction for the Anderson model in a disordered random-regular graph with branching number $k=2. We extract their corresponding fractal dimensions $D_q$ in the thermodynamic limit together with correlated volumes $N_q$ that control finite-size effects.
  arXiv  Detail & Related papers  (2023-11-13T19:15:18Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Fast Rates for Maximum Entropy Exploration [52.946307632704645]
  We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. We study the maximum entropy exploration problem two different types. For visitation entropy, we propose a game-theoretic algorithm that has $widetildemathcalO(H3S2A/varepsilon2)$ sample complexity. For the trajectory entropy, we propose a simple algorithm that has a sample of complexity of order $widetildemathcalO(mathrmpoly(S,
  arXiv  Detail & Related papers  (2023-03-14T16:51:14Z)
• Full counting statistics of interacting lattice gases after an expansion: The role of the condensate depletion in the many-body coherence [55.41644538483948]
  We study the full counting statistics (FCS) of quantum gases in samples of thousands of interacting bosons. FCS reveals the many-body coherence from which we characterize iconic states of interacting lattice bosons.
  arXiv  Detail & Related papers  (2022-07-28T13:21:57Z)
• Beyond-mean-field effects in Rabi-coupled two-component Bose-Einstein condensate [0.0]
  We calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently-coupled two-component Bose-Einstein condensate (BEC) We show that with increasing the Rabi-coupling frequency $Omega$, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang scaling $propto n5/2$ to an expansion in integer powers of density. We experimentally evidence this two contributions, thanks to their different scaling with $Omega$, in the expansion of a Rabi-coupled two-component $39$K condensate in
  arXiv  Detail & Related papers  (2021-05-25T07:46:47Z)
• Shannon entropy in confined He-like ions within a density functional formalism [0.0]
  Shannon entropy in position ($S_rvec$) and momentum ($S_pvec$) spaces, along with their sum ($S_t$) are presented. The radial Kohn-Sham equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method.
  arXiv  Detail & Related papers  (2021-02-26T16:29:07Z)
• Diffusion and operator entanglement spreading [0.0]
  We argue that for integrable models the dynamics of the $OSEE$ is related to the diffusion of the underlying quasiparticles. We numerically check that the bound is saturated in the rule $54$ chain, which is representative of interacting integrable systems. We show that strong finite-time effects are present, which prevent from probing the behavior of the $OSEE$.
  arXiv  Detail & Related papers  (2020-06-04T11:28:39Z)
• Homogeneous electron gas in arbitrary dimensions [0.0]
  We compute the exchange and correlation energy, as a function of the Wigner-Seitz radius $r_s, for arbitrary dimension $D$. In the large-$D$ limit, the value of $c_D$ is found to depend linearly with the dimension. In this limit, the concepts of exchange and correlation merge, sharing a common $1/r_s$ dependence.
  arXiv  Detail & Related papers  (2020-05-11T09:01:57Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.