Many-body quantum dynamics slows down at low density

Chen, Xiao; Gu, Yingfei; Lucas, Andrew

doi:10.21468/SciPostPhys.9.5.071

Title: Many-body quantum dynamics slows down at low density

Abstract

We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of N interacting fermions with charge conservation, or N interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature.

Authors:

Chen, Xiao ^[1]; Gu, Yingfei ^[2]; Lucas, Andrew ^[3]

Boston College
Harvard University
University of Colorado Boulder

Publication Date:: 2020-11-12

Research Org.:: Harvard Univ., Cambridge, MA (United States); Boston College, Chestnut Hill, MA (United States)

Sponsoring Org.:: USDOE; Alfred P. Sloan Foundation; Gordon and Betty Moore Foundation

OSTI Identifier:: 1712538

Alternate Identifier(s):: OSTI ID: 1852768

Grant/Contract Number:: SC0019030; GBMF-4306

Resource Type:: Published Article

Journal Name:: SciPost Physics Proceedings

Additional Journal Information:: Journal Name: SciPost Physics Proceedings Journal Volume: 9 Journal Issue: 5; Journal ID: ISSN 2542-4653

Publisher:: Stichting SciPost

Country of Publication:: Netherlands

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Chen, Xiao, Gu, Yingfei, and Lucas, Andrew. Many-body quantum dynamics slows down at low density.  Netherlands: N. p., 2020. 
Web.  doi:10.21468/SciPostPhys.9.5.071.

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                    Chen, Xiao, Gu, Yingfei, & Lucas, Andrew. Many-body quantum dynamics slows down at low density.  Netherlands.  https://doi.org/10.21468/SciPostPhys.9.5.071

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                    Chen, Xiao, Gu, Yingfei, and Lucas, Andrew. Thu .  
"Many-body quantum dynamics slows down at low density".  Netherlands.  https://doi.org/10.21468/SciPostPhys.9.5.071.

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@article{osti_1712538,

  title        = {Many-body quantum dynamics slows down at low density},

  author       = {Chen, Xiao and Gu, Yingfei and Lucas, Andrew},

  abstractNote = {We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of N interacting fermions with charge conservation, or N interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature.},

  doi          = {10.21468/SciPostPhys.9.5.071},

  journal      = {SciPost Physics Proceedings},

  number       = 5,

  volume       = 9,

  place        = {Netherlands},

  year         = {2020},

  month        = {11}

}

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Title: Many-body quantum dynamics slows down at low density

Abstract

Citation Formats

Why does the quark–gluon plasma at RHIC behave as a nearly ideal fluid? journal, July 2004

Notes on the complex Sachdev-Ye-Kitaev model journal, February 2020

Decoherence in the quantum walk on the line journal, March 2005

Chaos in the butterfly cone journal, January 2020

A random unitary circuit model for black hole evaporation journal, April 2020

Quantum scrambling and state dependence of the butterfly velocity journal, January 2019

Fast scrambling on sparse graphs journal, March 2019

Locality of Temperature journal, July 2014

Non-perturbative dynamics of the operator size distribution in the Sachdev–Ye–Kitaev model journal, August 2020

Universal bound on dynamical relaxation times and black-hole quasinormal ringing journal, March 2007

The finite group velocity of quantum spin systems journal, September 1972

Locality from the Spectrum journal, February 2019

Quantum epidemiology: operator growth, thermal effects, and SYK journal, August 2019

Operator growth in the SYK model journal, June 2018

Operator Size at Finite Temperature and Planckian Bounds on Quantum Dynamics journal, May 2019

Operator Entanglement in Interacting Integrable Quantum Systems: The Case of the Rule 54 Chain journal, June 2019

Universal Charge Diffusion and the Butterfly Effect in Holographic Theories journal, August 2016

Universal T-linear resistivity and Planckian dissipation in overdoped cuprates journal, November 2018

Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories journal, August 2016

Locality, Quantum Fluctuations, and Scrambling journal, September 2019

Operator growth and eigenstate entanglement in an interacting integrable Floquet system journal, August 2018

Universal relaxational dynamics near two-dimensional quantum critical points journal, June 1999

Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions journal, July 2020

Why the temperature is high journal, July 2004

Quantum butterfly effect in polarized Floquet systems journal, February 2020

Quantum chaos dynamics in long-range power law interaction systems journal, August 2019

Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information journal, November 2019

When things stop falling, chaos is suppressed journal, January 2019

Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws journal, September 2018

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Bound on quantum scrambling with all-to-all interactions journal, August 2020

Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems journal, May 2020

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Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation journal, September 2018

Hierarchy of Linear Light Cones with Long-Range Interactions journal, July 2020

On the relation between the magnitude and exponent of OTOCs journal, February 2019

Theory of universal incoherent metallic transport journal, December 2014

Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves journal, December 2016

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Why does the quark–gluon plasma at RHIC behave as a nearly ideal fluid?
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Notes on the complex Sachdev-Ye-Kitaev model
journal, February 2020

Decoherence in the quantum walk on the line
journal, March 2005

Chaos in the butterfly cone
journal, January 2020

A random unitary circuit model for black hole evaporation
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Quantum scrambling and state dependence of the butterfly velocity
journal, January 2019

Fast scrambling on sparse graphs
journal, March 2019

Locality of Temperature
journal, July 2014

Non-perturbative dynamics of the operator size distribution in the Sachdev–Ye–Kitaev model
journal, August 2020

Universal bound on dynamical relaxation times and black-hole quasinormal ringing
journal, March 2007

The finite group velocity of quantum spin systems
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journal, February 2019

Quantum epidemiology: operator growth, thermal effects, and SYK
journal, August 2019

Operator growth in the SYK model
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Operator Size at Finite Temperature and Planckian Bounds on Quantum Dynamics
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Operator Entanglement in Interacting Integrable Quantum Systems: The Case of the Rule 54 Chain
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Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
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Operator growth and eigenstate entanglement in an interacting integrable Floquet system
journal, August 2018

Universal relaxational dynamics near two-dimensional quantum critical points
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Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions
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journal, July 2004

Quantum butterfly effect in polarized Floquet systems
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When things stop falling, chaos is suppressed
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Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws
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Observation of Quantum-Limited Spin Transport in Strongly Interacting Two-Dimensional Fermi Gases
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Bound on quantum scrambling with all-to-all interactions
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Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems
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Similarity of Scattering Rates in Metals Showing T-Linear Resistivity
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Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation
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