A tractable model of monitored fermions with conserved $\mathrm{U}(1)$ charge

• URL: http://arxiv.org/abs/2407.08045v2
• Date: Thu, 1 Aug 2024 09:45:29 GMT
• Title: A tractable model of monitored fermions with conserved $\mathrm{U}(1)$ charge
• Authors: Michele Fava, Lorenzo Piroli, Denis Bernard, Adam Nahum,
• Abstract summary: We study measurement-induced phases of free fermion systems with U(1) symmetry. We derive a field theory description for the purity and bipartite entanglement at large space and time scales.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and time scales. We focus on a multi-flavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) non-linear sigma model (NL$\sigma$M) coupled to fluctuating hydrodynamics. Contrary to the case of non-interacting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates, but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NL$\sigma$M and also discuss higher dimensional generalizations.

Related papers

• 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)
• Generalized Zeno effect and entanglement dynamics induced by fermion counting [0.0]
  We study a one-dimensional lattice system of free fermions subjected to a generalized measurement process. We find that instantaneous correlations and entanglement properties of free fermions subjected to fermion counting and local occupation measurements are strikingly similar.
  arXiv  Detail & Related papers  (2024-06-11T19:46:26Z)
• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Diffusive entanglement growth in a monitored harmonic chain [0.0]
  We find that entanglement grows diffusively ($S sim t1/2$) for a large class of initial Gaussian states. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results.
  arXiv  Detail & Related papers  (2024-03-06T20:07:25Z)
• Theory of free fermions dynamics under partial post-selected monitoring [49.1574468325115]
  We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement. We show that the passage to the monitored universality occurs abruptly at finite partial post-selection. Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
  arXiv  Detail & Related papers  (2023-12-21T16:53:42Z)
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions [0.0]
  We investigate the entanglement structure and wave function characteristics of continuously monitored free fermions with U$(1)$-symmetry in two spatial dimensions (2D) By deriving the exact fermion replica-quantum master equation, we line out two approaches: (i) a nonlinear sigma model analogous to disordered free fermions, resulting in an SU$(R)$-symmetric field theory of symmetry class AIII in (2+1) space-time dimensions, or (ii) for bipartite lattices, third quantization leading to a non-Hermitian SU$ (2R)$-symmetric Hubbard model.
  arXiv  Detail & Related papers  (2023-09-21T18:00:01Z)
• 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)
• Nonlinear sigma models for monitored dynamics of free fermions [0.0]
  We derive descriptions for measurement-induced phase transitions in free fermion systems. We use the replica trick to map the dynamics to the imaginary time evolution of an effective spin chain. This is a nonlinear sigma model for an $Ntimes N$ matrix, in the replica limit $Nto 1$.
  arXiv  Detail & Related papers  (2023-02-24T18:56:37Z)
• Universal features of entanglement entropy in the honeycomb Hubbard model [44.99833362998488]
  This paper introduces a new method to compute the R'enyi entanglement entropy in auxiliary-field quantum Monte Carlo simulations. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two dimensional model of interacting fermions.
  arXiv  Detail & Related papers  (2022-11-08T15:52:16Z)
• Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
  We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
  arXiv  Detail & Related papers  (2021-05-20T14:46:09Z)

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.