SciPost Physics

SciPost Phys. 12, 117 (2022) · published 4 April 2022

• doi: 10.21468/SciPostPhys.12.4.117
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as stochastic systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an information-theoretic perspective. For general non-integrable models, we use the equilibrium approximation to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the time-evolution operator) at late times even when a system conserves energy. In contrast, we explicate how when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of holographic conformal field theories (CFTs) and the Sachdev-Ye-Kitaev (SYK) model. Due to the large Virasoro symmetry in 1+1D CFTs, we argue that, in a sense, these holographic theories are not maximally chaotic, which is explicitly seen by the non-saturation of the second R\'enyi tripartite mutual information. The roles of particle-hole and U(1) symmetries in the SYK model are milder due to the degeneracies being only two-fold, which we confirm explicitly at both large- and small-$N$. We reinterpret the operator entanglement in terms the growth of local operators, connecting our results with the information scrambling described by out-of-time-ordered correlators, identifying the mechanism for suppressed scrambling from the Heisenberg perspective.

• Zhang, Quantum entanglement in the Sachdev—Ye—Kitaev model and its generalizations
  Front. Phys. 17, 43201 (2022) [Crossref]
• Carollo et al., Entangled multiplets and spreading of quantum correlations in a continuously monitored tight-binding chain
  Phys. Rev. B 106, L220304 (2022) [Crossref]
• Goto et al., Information scrambling versus quantum revival through the lens of operator entanglement
  J. High Energ. Phys. 2022, 100 (2022) [Crossref]
• Kudler-Flam, Rényi Mutual Information in Quantum Field Theory
  Phys. Rev. Lett. 130, 021603 (2023) [Crossref]
• Liu et al., Approximate symmetries and quantum error correction
  npj Quantum Inf 9, 119 (2023) [Crossref]
• Varikuti et al., Out-of-time ordered correlators in kicked coupled tops: Information scrambling in mixed phase space and the role of conserved quantities
  34, 063124 (2024) [Crossref]
• Zhou et al., Full counting statistics across the entanglement phase transition of non-Hermitian Hamiltonians with charge conservation
  Phys. Rev. B 108, 094308 (2023) [Crossref]
• Xu et al., Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems
  PRX Quantum 5, 010201 (2024) [Crossref]
• Varikuti et al., Unraveling the emergence of quantum state designs in systems with symmetry
  Quantum 8, 1456 1456 (2024) [Crossref]
• van Enk, Quantum partial information decomposition
  Phys. Rev. A 108, 062415 (2023) [Crossref]
• Goto et al., Scrambling and recovery of quantum information in inhomogeneous quenches in two-dimensional conformal field theories
  Phys. Rev. Research 6, 023001 (2024) [Crossref]