Phase transition in von Neumann entanglement entropy from replica symmetry breaking

• URL: http://arxiv.org/abs/2108.11973v2
• Date: Tue, 14 Sep 2021 19:45:15 GMT
• Title: Phase transition in von Neumann entanglement entropy from replica symmetry breaking
• Authors: Shao-Kai Jian, Brian Swingle
• Abstract summary: We study the entanglement transition in monitored Brownian SYK chains in the large-$N$ limit. As the monitoring rate increases, a continuous von Neumann entanglement entropy transition from volume-law to area-law occurs at the point of replica symmetry unbreaking.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the entanglement transition in monitored Brownian SYK chains in the large-$N$ limit. Without measurement the steady state $n$-th R\'enyi entropy is obtained by summing over a class of solutions, and is found to saturate to the Page value in the $n\rightarrow 1$ limit. In the presence of measurements, the analytical continuation $n\rightarrow 1$ is performed using the cyclic symmetric solution. The result shows that as the monitoring rate increases, a continuous von Neumann entanglement entropy transition from volume-law to area-law occurs at the point of replica symmetry unbreaking.

Related papers

• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• 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 phase transition due to reciprocity breaking without measurement or post-selection [59.63862802533879]
  EPT occurs for a system undergoing purely unitary evolution. We analytically derive the entanglement entropy out of and at the critical point for the $l=1$ and $l/N ll 1$ case.
  arXiv  Detail & Related papers  (2023-08-28T14:28:59Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain [0.0]
  We compute the entanglement entropy's dynamics in the thermodynamic limit and demonstrate an entanglement transition between volume-law and area-law scaling. Interestingly we show that the entanglement transition and the $mathcalPT$-symmetry breaking do not coincide, the former occurring when the entire decay spectrum of the quasiparticle becomes gapped.
  arXiv  Detail & Related papers  (2022-10-21T13:13:16Z)
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code [0.0]
  We study the dynamics of a $(1+1)$-dimensional measurement-only circuit defined by the stabilizers of the quantum error correcting code. The code corrects arbitrary single-qubit errors and it stabilizes an area law entangled with a $D = mathbbZ times mathbbZ$ symmetry protected topological (SPT) order. The Pauli measurements break the topological order and induce a phase transition into a trivial area law phase.
  arXiv  Detail & Related papers  (2022-04-18T18:00:04Z)
• Symmetry-resolved entanglement in a long-range free-fermion chain [0.0]
  We study the symmetry-resolved entanglement entropy in the ground state of a fermionic chain. We find entanglement, but comparing with the short-range counterpart its breaking occurs at a different order and it does depend on the hopping amplitudes.
  arXiv  Detail & Related papers  (2022-02-11T19:38:38Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Measurement-induced criticality in $\mathbb{Z}_2$-symmetric quantum automaton circuits [6.723539428281127]
  We study entanglement dynamics in hybrid $mathbbZ$-symmetric quantum automaton circuits. We show that there exists an entanglement phase transition from a volume law phase to a critical phase by varying the measurement rate $p$.
  arXiv  Detail & Related papers  (2021-10-20T18:52:14Z)
• SYK meets non-Hermiticity II: measurement-induced phase transition [16.533265279392772]
  We analytically derive the effective action in the large-$N$ limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. We also verify the large-$N$ critical exponents by numerically solving the Schwinger-Dyson equation.
  arXiv  Detail & Related papers  (2021-04-16T17:55:08Z)

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.