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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:
 [1];  [2];  [3]
  1. Boston College
  2. Harvard University
  3. University of Colorado Boulder
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1712538
Grant/Contract Number:  
SC0019030
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

Citation Formats

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

Journal Article:
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https://doi.org/10.21468/SciPostPhys.9.5.071

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Works referenced in this record:

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


Anomalous subdiffusion from subsystem symmetries
journal, December 2019


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

  • Gu, Yingfei; Kitaev, Alexei; Sachdev, Subir
  • Journal of High Energy Physics, Vol. 2020, Issue 2
  • DOI: 10.1007/JHEP02(2020)157

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

  • Piroli, Lorenzo; Sünderhauf, Christoph; Qi, Xiao-Liang
  • Journal of High Energy Physics, Vol. 2020, Issue 4
  • DOI: 10.1007/JHEP04(2020)063

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


Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography
journal, April 2017


Black holes and the butterfly effect
journal, March 2014

  • Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)067

Fast scrambling on sparse graphs
journal, March 2019

  • Bentsen, Gregory; Gu, Yingfei; Lucas, Andrew
  • Proceedings of the National Academy of Sciences, Vol. 116, Issue 14
  • DOI: 10.1073/pnas.1811033116

Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
journal, May 2017

  • Gu, Yingfei; Qi, Xiao-Liang; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)125

Locality of Temperature
journal, July 2014


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

  • Lucas, Andrew
  • Journal of Mathematical Physics, Vol. 61, Issue 8
  • DOI: 10.1063/1.5133964

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

  • Lieb, Elliott H.; Robinson, Derek W.
  • Communications in Mathematical Physics, Vol. 28, Issue 3
  • DOI: 10.1007/BF01645779

Locality from the Spectrum
journal, February 2019

  • Cotler, Jordan S.; Penington, Geoffrey R.; Ranard, Daniel H.
  • Communications in Mathematical Physics, Vol. 368, Issue 3
  • DOI: 10.1007/s00220-019-03376-w

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

  • Qi, Xiao-Liang; Streicher, Alexandre
  • Journal of High Energy Physics, Vol. 2019, Issue 8
  • DOI: 10.1007/JHEP08(2019)012

Operator growth in the SYK model
journal, June 2018

  • Roberts, Daniel A.; Stanford, Douglas; Streicher, Alexandre
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/JHEP06(2018)122

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


A bound on chaos
journal, August 2016

  • Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)106

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

  • Sünderhauf, Christoph; Piroli, Lorenzo; Qi, Xiao-Liang
  • Journal of High Energy Physics, Vol. 2019, Issue 11
  • DOI: 10.1007/JHEP11(2019)038

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

  • Ageev, Dmitry S.; Aref’eva, Irina Ya.
  • Journal of High Energy Physics, Vol. 2019, Issue 1
  • DOI: 10.1007/JHEP01(2019)100

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


Observation of Quantum-Limited Spin Transport in Strongly Interacting Two-Dimensional Fermi Gases
journal, March 2017


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


Similarity of Scattering Rates in Metals Showing T-Linear Resistivity
journal, February 2013


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

  • Rakovszky, Tibor; Pollmann, Frank; von Keyserlingk, C. W.
  • Physical Review X, Vol. 8, Issue 3
  • DOI: 10.1103/PhysRevX.8.031058

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


On the chaos bound in rotating black holes
journal, May 2019

  • Jahnke, Viktor; Kim, Keun-Young; Yoon, Junggi
  • Journal of High Energy Physics, Vol. 2019, Issue 5
  • DOI: 10.1007/JHEP05(2019)037

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


Many-body chaos at weak coupling
journal, October 2016


Toy model for decoherence in the black hole information problem
journal, October 2020


Finite Speed of Quantum Scrambling with Long Range Interactions
journal, December 2019


Bekenstein-Hawking Entropy and Strange Metals
journal, November 2015


Facilitated quantum cellular automata as simple models with non-thermal eigenstates and dynamics
journal, August 2018