Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2110.10529 · Physical review. B./Physical review. B

Scrambling and many-body localization in the XXZ chain

Niklas Bölter, Stefan K. Kehrein

Published Mar 8, 2022• 19 citations
arXivHTMLPDF

Abstract

The tripartite information is an observable-independent measure for scrambling and delocalization of information. Therefore, one can expect that the tripartite information is a good observable-independent indicator for distinguishing between many-body localized and delocalized regimes, which we confirm for the XXZ chain in a random field. Specifically, we find that the tripartite information signal spreads inside a light cone that grows only logarithmically in time in the many-body localized regime, similar to entanglement entropy. We also find that the tripartite information eventually reaches a plateau with an asymptotic value that is suppressed by strong disorder.

DOI
10.1103/physrevb.105.104202

Related papers

Tripartite Information and Scrambling in Quantum Many-Body Systems

Niklas Bölter

This thesis contributes to the study of quantum chaos and thermalization of closed quantum systems by applying tools from quantum information theory. We study scrambling – the delocalization of quantum information – in one-dimensional quantum many-body systems using the observable-independent tripartite information 𝐼3. We consider closed quantum systems that undergo unitary time evolution governed by a Hamiltonian, and compare them to the strong scrambling caused by random unitary operators (Haar scrambling). The tripartite information is a tool from quantum information theory that allows us to quantify correlations in space and time by considering the unitary operator evolving the system as a state |𝑈 (𝑡)⟩ in a doubled Hilbert space H ⊗ H. We found a ballistic spreading of information in translation invariant systems of spinless fermions that causes Haar scrambling in interacting models. For strongly disordered versions of the XXZ chain and the transverse-field Ising chain we found a complete breakdown of in- formation transport in non-interacting Anderson localized systems, as well as a logarithmically slow spreading of the information signal in systems that are said to be many-body localized (MBL).

•Jan 1, 2023•0 citations

Operator and entanglement growth in nonthermalizing systems: Many-body localization and the random singlet phase

Ian MacCormack, Mao Tian Tan, Jonah Kudler-Flam +1 more

We characterize the growth and spreading of operators and entanglement in two paradigmatic nonthermalizing phases---the many-body localized (MBL) phase and the random singlet phase (RSP)---using the entanglement contour and multipartite operator entanglement measures. The entanglement contour characterizes the spacetime spreading of entanglement and reveals logarithmically growing entanglement light cones in the MBL and RSP phases, sharply contrasting the linear light cones of clean, thermalizing systems. The operator entanglement characterizes scrambling, i.e., the delocalization of information. We find slow scrambling behavior in the MBL phase; the late-time value of the tripartite mutual information scales linearly with system size, but is submaximal. The tripartite logarithmic negativity is also negative and nonzero, but smaller in magnitude, revealing an intriguing distinction between classical and quantum information scrambling in the MBL phase. This is in contrast with the RSP, which, as a noninteracting model, is nonscrambling.

arXiv:2001.08222•Physical review. B./Physical review. B•Dec 2, 2021•50 citations

Many-body localization for the random XXZ spin chain in fixed energy intervals

Alexander Elgart, Abel Klein

It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits slow propagation of information (logarithmic light cone), a key signature of many-body localization (MBL), in any fixed energy interval at the bottom of the spectrum. The relevant parameter regime, which covers both weak interaction and strong disorder, is determined solely by the energy interval.

arXiv:2602.01441•Feb 1, 2026•0 citations

Information Scrambling in Quantum Many-Body Systems

Yongliang Zhang

A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.

•Feb 28, 2020•5 citations

Slowest and fastest information scrambling in the strongly disordered XXZ model

Myeonghyeon Kim, DH Kim

We present a perturbation method to compute the out-of-time-ordered correlator in the strongly disordered Heisenberg XXZ model in the deep many-body localized regime. We characterize the discrete structure of the information propagation across the eigenstates, revealing a highly structured light cone confined by the strictly logarithmic upper and lower bounds representing the slowest and fastest scrambling available in this system. We explain these bounds by deriving the closed-form expression of the effective interaction for the slowest scrambling and by constructing the effective model of a half length for the fastest scrambling. We extend our lowest-order perturbation formulations to the higher dimensions, proposing that the logarithmic upper and lower light cones may persist in a finite two-dimensional system in the limit of strong disorder and weak hopping.

arXiv:2303.08801•Physical review. B./Physical review. B•Jun 22, 2023•3 citations

Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models

Oskar H Schnaack, Niklas Bölter, Sebastian Paeckel +3 more

For the characterization of the dynamics in quantum many-body systems the question of how information spreads and becomes distributed over the constituent degrees of freedom is of fundamental interest. The delocalization of information under many-body dynamics has been dubbed scrambling, and out-of-time-order correlators were proposed to probe this behavior. In this work we investigate the time evolution of tripartite information as a natural operator-independent measure of scrambling, which quantifies to what extent the initially localized information can be recovered only by global measurements. Studying the dynamics of quantum lattice models with tunable integrability breaking, we demonstrate that in contrast to quadratic models generic interacting systems scramble information irrespective of the chosen partitioning of the Hilbert space, which justifies the characterization as a scrambler. Without interactions the dynamics of tripartite information in momentum space reveals unambiguously the absence of scrambling.

arXiv:1808.05646•Physical review. B./Physical review. B•Dec 11, 2019•41 citations
The tripartite information is an observable-independent measure for scrambling and delocalization of information. Therefore, one can expect that the tripartite information is a good observable-independent indicator for distinguishing between many-body localized and delocalized regimes, which we confirm for the XXZ chain in a random field. Specifically, we find that the tripartite information signal spreads inside a light cone that grows only logarithmically in time in the many-body localized regime, similar to entanglement entropy. We also find that the tripartite information eventually reaches a plateau with an asymptotic value that is suppressed by strong disorder.
This thesis contributes to the study of quantum chaos and thermalization of closed quantum systems by applying tools from quantum information theory. We study scrambling – the delocalization of quantum information – in one-dimensional quantum many-body systems using the observable-independent tripartite information 𝐼3. We consider closed quantum systems that undergo unitary time evolution governed by a Hamiltonian, and compare them to the strong scrambling caused by random unitary operators (Haar scrambling). The tripartite information is a tool from quantum information theory that allows us to quantify correlations in space and time by considering the unitary operator evolving the system as a state |𝑈 (𝑡)⟩ in a doubled Hilbert space H ⊗ H. We found a ballistic spreading of information in translation invariant systems of spinless fermions that causes Haar scrambling in interacting models. For strongly disordered versions of the XXZ chain and the transverse-field Ising chain we found a complete breakdown of in- formation transport in non-interacting Anderson localized systems, as well as a logarithmically slow spreading of the information signal in systems that are said to be many-body localized (MBL).
We characterize the growth and spreading of operators and entanglement in two paradigmatic nonthermalizing phases---the many-body localized (MBL) phase and the random singlet phase (RSP)---using the entanglement contour and multipartite operator entanglement measures. The entanglement contour characterizes the spacetime spreading of entanglement and reveals logarithmically growing entanglement light cones in the MBL and RSP phases, sharply contrasting the linear light cones of clean, thermalizing systems. The operator entanglement characterizes scrambling, i.e., the delocalization of information. We find slow scrambling behavior in the MBL phase; the late-time value of the tripartite mutual information scales linearly with system size, but is submaximal. The tripartite logarithmic negativity is also negative and nonzero, but smaller in magnitude, revealing an intriguing distinction between classical and quantum information scrambling in the MBL phase. This is in contrast with the RSP, which, as a noninteracting model, is nonscrambling.
It is shown that the infinite random Heisenberg XXZ spin-12\frac1221​ chain exhibits slow propagation of information (logarithmic light cone), a key signature of many-body localization (MBL), in any fixed energy interval at the bottom of the spectrum. The relevant parameter regime, which covers both weak interaction and strong disorder, is determined solely by the energy interval.
A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
We present a perturbation method to compute the out-of-time-ordered correlator in the strongly disordered Heisenberg XXZ model in the deep many-body localized regime. We characterize the discrete structure of the information propagation across the eigenstates, revealing a highly structured light cone confined by the strictly logarithmic upper and lower bounds representing the slowest and fastest scrambling available in this system. We explain these bounds by deriving the closed-form expression of the effective interaction for the slowest scrambling and by constructing the effective model of a half length for the fastest scrambling. We extend our lowest-order perturbation formulations to the higher dimensions, proposing that the logarithmic upper and lower light cones may persist in a finite two-dimensional system in the limit of strong disorder and weak hopping.
For the characterization of the dynamics in quantum many-body systems the question of how information spreads and becomes distributed over the constituent degrees of freedom is of fundamental interest. The delocalization of information under many-body dynamics has been dubbed scrambling, and out-of-time-order correlators were proposed to probe this behavior. In this work we investigate the time evolution of tripartite information as a natural operator-independent measure of scrambling, which quantifies to what extent the initially localized information can be recovered only by global measurements. Studying the dynamics of quantum lattice models with tunable integrability breaking, we demonstrate that in contrast to quadratic models generic interacting systems scramble information irrespective of the chosen partitioning of the Hilbert space, which justifies the characterization as a scrambler. Without interactions the dynamics of tripartite information in momentum space reveals unambiguously the absence of scrambling.