skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Anomalous relaxation and the high-temperature structure factor of XXZ spin chains

Abstract

We compute the spin-structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics, including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to s-spin magnon bound states (“strings”) of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the spin-structure factor, with continuously varying exponents, at any fixed separation in the late-time limit. We elucidate the cross-over to diffusion (in the gapped phase) and to superdiffusion (at the isotropic point) in the half-filling limit. We verify our results via extensive matrix product operator calculations.

Authors:
ORCiD logo; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1557027
Grant/Contract Number:  
SC0019168
Resource Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 116 Journal Issue: 33; Journal ID: ISSN 0027-8424
Publisher:
Proceedings of the National Academy of Sciences
Country of Publication:
United States
Language:
English

Citation Formats

Gopalakrishnan, Sarang, Vasseur, Romain, and Ware, Brayden. Anomalous relaxation and the high-temperature structure factor of XXZ spin chains. United States: N. p., 2019. Web. doi:10.1073/pnas.1906914116.
Gopalakrishnan, Sarang, Vasseur, Romain, & Ware, Brayden. Anomalous relaxation and the high-temperature structure factor of XXZ spin chains. United States. doi:10.1073/pnas.1906914116.
Gopalakrishnan, Sarang, Vasseur, Romain, and Ware, Brayden. Tue . "Anomalous relaxation and the high-temperature structure factor of XXZ spin chains". United States. doi:10.1073/pnas.1906914116.
@article{osti_1557027,
title = {Anomalous relaxation and the high-temperature structure factor of XXZ spin chains},
author = {Gopalakrishnan, Sarang and Vasseur, Romain and Ware, Brayden},
abstractNote = {We compute the spin-structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics, including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to s-spin magnon bound states (“strings”) of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the spin-structure factor, with continuously varying exponents, at any fixed separation in the late-time limit. We elucidate the cross-over to diffusion (in the gapped phase) and to superdiffusion (at the isotropic point) in the half-filling limit. We verify our results via extensive matrix product operator calculations.},
doi = {10.1073/pnas.1906914116},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 33,
volume = 116,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1073/pnas.1906914116

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

  • Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
  • Nature, Vol. 452, Issue 7189
  • DOI: 10.1038/nature06838

Relaxation and Prethermalization in an Isolated Quantum System
journal, September 2012


Hydrodynamic Diffusion in Integrable Systems
journal, October 2018


Superdiffusion in One-Dimensional Quantum Lattice Models
journal, December 2018


Transport in Out-of-Equilibrium X X Z Chains: Exact Profiles of Charges and Currents
journal, November 2016


Microscopic Origin of Ideal Conductivity in Integrable Quantum Models
journal, July 2017


Correlations after Quantum Quenches in the X X Z Spin Chain: Failure of the Generalized Gibbs Ensemble
journal, September 2014


Anomalous Spin Diffusion in One-Dimensional Antiferromagnets
journal, October 2019


Spin Transport in a One-Dimensional Anisotropic Heisenberg Model
journal, May 2011


Computation of Dynamical Correlation Functions of Heisenberg Chains in a Magnetic Field
journal, August 2005


Reducing the numerical effort of finite-temperature density matrix renormalization group calculations
journal, August 2013


Spin diffusion from an inhomogeneous quench in an integrable system
journal, July 2017

  • Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms16117

Dynamical structure factor at small q for the XXZ spin-1/2 chain
journal, August 2007


Dynamical Spin Structure Factor for the Anisotropic Spin- 1 / 2 Heisenberg Chain
journal, June 2006


Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain
journal, January 2018


Generalized Hydrodynamics on an Atom Chip
journal, March 2019


Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
journal, March 2017


Analytic solution of the domain-wall nonequilibrium stationary state
journal, February 2018


Quasi-soliton scattering in quantum spin chains
journal, December 2015


Real-Time Evolution Using the Density Matrix Renormalization Group
journal, August 2004


On classical integrability of the hydrodynamics of quantum integrable systems
journal, October 2017

  • Bulchandani, Vir B.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 43
  • DOI: 10.1088/1751-8121/aa8c62

Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics
journal, November 2017


Anomalous and regular transport in spin- 1 2 chains: ac conductivity
journal, August 2018


Lower Bounding Diffusion Constant by the Curvature of Drude Weight
journal, August 2017


Finite-Temperature Dynamical Density Matrix Renormalization Group and the Drude Weight of Spin- 1 / 2 Chains
journal, May 2012


“Light-Cone” Dynamics After Quantum Quenches in Spin Chains
journal, October 2014


Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
journal, April 1998


Entanglement and thermodynamics after a quantum quench in integrable systems
journal, July 2017

  • Alba, Vincenzo; Calabrese, Pasquale
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 30
  • DOI: 10.1073/pnas.1703516114

Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
journal, May 2019


Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods
journal, April 2018


The density-matrix renormalization group in the age of matrix product states
journal, January 2011


Low Temperature Spin Diffusion in the One-Dimensional Quantum O ( 3 ) Nonlinear σ Model
journal, February 1997


Finite Temperature Drude Weight of the One-Dimensional Spin- 1 / 2 Heisenberg Model
journal, February 1999


Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
journal, December 2018


Soliton Gases and Generalized Hydrodynamics
journal, January 2018


Real-time and real-space spin and energy dynamics in one-dimensional spin- 1 2 systems induced by local quantum quenches at finite temperatures
journal, February 2014


Conservation laws, integrability, and transport in one-dimensional quantum systems
journal, January 2011


Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
journal, December 2013


Quantum dynamics of a mobile spin impurity
journal, February 2013

  • Fukuhara, Takeshi; Kantian, Adrian; Endres, Manuel
  • Nature Physics, Vol. 9, Issue 4
  • DOI: 10.1038/nphys2561

Nonequilibrium spin transport in integrable spin chains: Persistent currents and emergence of magnetic domains
journal, July 2017


Solvable Hydrodynamics of Quantum Integrable Systems
journal, November 2017


Kinetic Theory of Spin Diffusion and Superdiffusion in X X Z Spin Chains
journal, March 2019


Integrable spin chains with random interactions
journal, July 2018

  • Essler, Fabian H. L.; van den Berg, Rianne; Gritsev, Vladimir
  • Physical Review B, Vol. 98, Issue 2
  • DOI: 10.1103/PhysRevB.98.024203

Extending the range of real time density matrix renormalization group simulations
journal, March 2016


Boson decay and the dynamical structure factor for the XXZ chain at finite magnetic field
journal, April 2008


Time Evolution of Local Observables After Quenching to an Integrable Model
journal, June 2013


A note on generalized hydrodynamics: inhomogeneous fields and other concepts
journal, January 2017


Expansion Potentials for Exact Far-from-Equilibrium Spreading of Particles and Energy
journal, December 2015


Kardar-Parisi-Zhang Physics in the Quantum Heisenberg Magnet
journal, May 2019


Complete Generalized Gibbs Ensembles in an Interacting Theory
journal, October 2015


Drude Weight for the Lieb-Liniger Bose Gas
journal, January 2017


Prethermalization and universal dynamics in near-integrable quantum systems
journal, June 2016

  • Langen, Tim; Gasenzer, Thomas; Schmiedmayer, Jörg
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
  • DOI: 10.1088/1742-5468/2016/06/064009

Quasilocal charges in integrable lattice systems
journal, June 2016

  • Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
  • DOI: 10.1088/1742-5468/2016/06/064008

Universal Relaxational Dynamics of Gapped One-Dimensional Models in the Quantum Sine-Gordon Universality Class
journal, October 2005


Spin-Exchange Dynamical Structure Factor of the S = 1 / 2 Heisenberg Chain
journal, April 2011


Dynamic Scaling of Growing Interfaces
journal, March 1986


Diffusion in generalized hydrodynamics and quasiparticle scattering
journal, January 2019


Ballistic transport in the one-dimensional Hubbard model: The hydrodynamic approach
journal, August 2017


The One-Dimensional KPZ Equation and Its Universality Class
journal, April 2015


Efficient Classical Simulation of Slightly Entangled Quantum Computations
journal, October 2003


Low-temperature transport in out-of-equilibrium XXZ chains
journal, March 2018

  • Bertini, Bruno; Piroli, Lorenzo
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, Issue 3
  • DOI: 10.1088/1742-5468/aab04b

Exact large-scale correlations in integrable systems out of equilibrium
journal, January 2018


Entanglement evolution and generalised hydrodynamics: interacting integrable systems
journal, January 2019


A quantum Newton's cradle
journal, April 2006

  • Kinoshita, Toshiya; Wenger, Trevor; Weiss, David S.
  • Nature, Vol. 440, Issue 7086
  • DOI: 10.1038/nature04693

Diffusion and Ballistic Transport in One-Dimensional Quantum Systems
journal, November 2009


Far-from-Equilibrium Spin Transport in Heisenberg Quantum Magnets
journal, October 2014


Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions
journal, September 2017