Symmetry restoration and quantum Mpemba effect in symmetric random circuits

• URL: http://arxiv.org/abs/2403.08459v4
• Date: Fri, 08 Nov 2024 08:08:51 GMT
• Title: Symmetry restoration and quantum Mpemba effect in symmetric random circuits
• Authors: Shuo Liu, Hao-Kai Zhang, Shuai Yin, Shi-Xin Zhang,
• Abstract summary: Entanglement asymmetry serves as a diagnostic tool for symmetry breaking and a proxy for thermalization. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits.
• Score: 3.326868738829707
• License:
• Abstract: Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to non-symmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and $Z_{2}$ symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges.

Related papers

• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model [32.553027955412986]
  We investigate the anisotropic coupled-top model, which describes the interactions between two large spins along both $x-$ and $y-$directions. We can manipulate the system's symmetry, inducing either discrete $Z$ or continuous U(1) symmetry. The framework provides an ideal platform for experimentally controlling symmetries and investigating associated physical phenomena.
  arXiv  Detail & Related papers  (2025-02-13T15:14:29Z)
• Symmetry Breaking Dynamics in Quantum Many-Body Systems [5.39331199837589]
  Entanglement asymmetry has emerged as a powerful tool for characterizing symmetry breaking in quantum many-body systems. In this Letter, we explore how symmetry is dynamically broken through the lens of entanglement asymmetry in two distinct scenarios.
  arXiv  Detail & Related papers  (2025-01-23T08:17:07Z)
• Eigenmodes of latent-symmetric quantum photonic networks [37.69303106863453]
  We study the eigenmodes of a 9-site latent-symmetric photonic network. Latent symmetries introduce a powerful new set of tools to the design of systems with desired functionality on any nanophotonic platform.
  arXiv  Detail & Related papers  (2025-01-22T17:21:21Z)
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases [20.518529676631122]
  We develop a method to detect quantum anomalies in systems with subsystem symmetry. Using numerical simulations, we demonstrate the power of this method by identifying strong and weak $Ztautimes Zsigma$ SSPT phases. We extend the anomaly indicator to mixed-state density matrices and show that quantum anomalies of subsystem symmetry can persist under both uniform and alternating disorders.
  arXiv  Detail & Related papers  (2024-12-10T14:53:54Z)
• Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators [20.572965801171225]
  Recent developments have extended the discussion of symmetry and its breaking to mixed states. We propose the Wightman correlator as an alternative diagnostic tool.
  arXiv  Detail & Related papers  (2024-10-12T02:04:40Z)
• Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect [0.0]
  We show how, by tuning the initial state, the symmetry dynamics in free fermionic systems can display much richer behaviour than seen previously. In particular, for certain classes of initial states, including ground states of free fermionic models with long-range couplings, the entanglement asymmetry can exhibit multiple crossings.
  arXiv  Detail & Related papers  (2024-05-07T15:57:45Z)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• Efficient quantum algorithms for testing symmetries of open quantum systems [17.55887357254701]
  In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
  arXiv  Detail & Related papers  (2023-09-05T18:05:26Z)
• Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective [0.0]
  We discuss some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are reviewed.
  arXiv  Detail & Related papers  (2022-08-24T14:19:13Z)
• Entanglement asymmetry as a probe of symmetry breaking [0.0]
  In extended quantum systems, quantifying how much a symmetry is broken is intrinsically bound to the subsystem of interest. We introduce a subsystem measure of symmetry breaking that we dub entanglement asymmetry. We find, expectedly, that larger is the subsystem, slower is the restoration, but also the counterintuitive result that more the symmetry is initially broken, faster it is restored.
  arXiv  Detail & Related papers  (2022-07-29T14:03:30Z)
• Quantum Error Mitigation using Symmetry Expansion [0.0]
  Noise remains the biggest challenge for the practical applications of any near-term quantum devices. We develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification.
  arXiv  Detail & Related papers  (2021-01-08T18:30:48Z)

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.