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

Title: Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics

Abstract

The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying “nonlinear sound waves” emanating from initial density accumulations in the Lieb-Liniger model. Here, we show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- ormore » strong-repulsion regimes.« less

Authors:
 [1];  [2]; ORCiD logo [3];  [1]
  1. King’s College London, Strand, London (United Kingdom)
  2. Univ. de Lorraine, Vandoeuvre-lès-Nancy (France)
  3. Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Division
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1462405
Alternate Identifier(s):
OSTI ID: 1408183
Report Number(s):
BNL-207874-2018-JAAM
Journal ID: ISSN 0031-9007; PRLTAO; TRN: US1902165
Grant/Contract Number:  
SC0012704; AC02-98CH10886
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 119; Journal Issue: 19; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Doyon, Benjamin, Dubail, Jerome, Konik, Robert, and Yoshimura, Takato. Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.119.195301.
Doyon, Benjamin, Dubail, Jerome, Konik, Robert, & Yoshimura, Takato. Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics. United States. doi:10.1103/PhysRevLett.119.195301.
Doyon, Benjamin, Dubail, Jerome, Konik, Robert, and Yoshimura, Takato. Wed . "Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics". United States. doi:10.1103/PhysRevLett.119.195301. https://www.osti.gov/servlets/purl/1462405.
@article{osti_1462405,
title = {Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics},
author = {Doyon, Benjamin and Dubail, Jerome and Konik, Robert and Yoshimura, Takato},
abstractNote = {The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying “nonlinear sound waves” emanating from initial density accumulations in the Lieb-Liniger model. Here, we show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.},
doi = {10.1103/PhysRevLett.119.195301},
journal = {Physical Review Letters},
number = 19,
volume = 119,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 27 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Quantum shock waves and population inversion in collisions of ultracold atomic clouds
journal, January 2014


One-dimensional hard rod caricature of hydrodynamics
journal, June 1983

  • Boldrighini, C.; Dobrushin, R. L.; Sukhov, Yu. M.
  • Journal of Statistical Physics, Vol. 31, Issue 3
  • DOI: 10.1007/BF01019499

Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction
journal, July 1969

  • Yang, C. N.; Yang, C. P.
  • Journal of Mathematical Physics, Vol. 10, Issue 7
  • DOI: 10.1063/1.1664947

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

Observations of Density Fluctuations in an Elongated Bose Gas: Ideal Gas and Quasicondensate Regimes
journal, April 2006


On the renormalisation group for the boundary truncated conformal space approach
journal, June 2012


Generalized Gibbs ensemble in integrable lattice models
journal, June 2016


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


Quench dynamics and relaxation in isolated integrable quantum spin chains
journal, June 2016


Colloquium : Nonequilibrium dynamics of closed interacting quantum systems
journal, August 2011

  • Polkovnikov, Anatoli; Sengupta, Krishnendu; Silva, Alessandro
  • Reviews of Modern Physics, Vol. 83, Issue 3
  • DOI: 10.1103/RevModPhys.83.863

The renormalization group: Critical phenomena and the Kondo problem
journal, October 1975


Yang-Yang Thermodynamics on an Atom Chip
journal, March 2008


Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas
journal, September 2008

  • Bettelheim, Eldad; Abanov, Alexander G.; Wiegmann, Paul B.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 39
  • DOI: 10.1088/1751-8113/41/39/392003

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
journal, April 2016


Constructing the Generalized Gibbs Ensemble after a Quantum Quench
journal, October 2012


Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator
journal, March 2004


Thermodynamics of strongly correlated one-dimensional Bose gases
journal, September 2013


Quench-Induced Breathing Mode of One-Dimensional Bose Gases
journal, July 2014


Integrable hydrodynamics of Calogero–Sutherland model: bidirectional Benjamin–Ono equation
journal, March 2009

  • Abanov, Alexander G.; Bettelheim, Eldad; Wiegmann, Paul
  • Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 13
  • DOI: 10.1088/1751-8113/42/13/135201

Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps
journal, March 2015


On the Quantum Correction For Thermodynamic Equilibrium
journal, June 1932


Violation of self-similarity in the expansion of a one-dimensional Bose gas
journal, October 2003


Quantum Hydrodynamics, the Quantum Benjamin-Ono Equation, and the Calogero Model
journal, August 2005


Finite-temperature hydrodynamics for one-dimensional Bose gases: Breathing-mode oscillations as a case study
journal, November 2016


Dynamical Transition from a Quasi-One-Dimensional Bose-Einstein Condensate to a Tonks-Girardeau Gas
journal, November 2002


Shock waves in a one-dimensional Bose gas: From a Bose-Einstein condensate to a Tonks gas
journal, April 2006


Dynamics of waves in one-dimensional electron systems: Density oscillations driven by population inversion
journal, January 2013


Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
journal, August 1998


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


Truncated-Fermionic-Space Approach to the Critical 2d Ising Model with Magnetic Field
journal, October 1991

  • Yurov, V. P.; Zamolodchikov, Al. B.
  • International Journal of Modern Physics A, Vol. 06, Issue 25
  • DOI: 10.1142/S0217751X91002161

Nonlinear Quantum Shock Waves in Fractional Quantum Hall Edge States
journal, December 2006


Observation of a One-Dimensional Tonks-Girardeau Gas
journal, August 2004


Pulse propagation in the interacting one-dimensional Bose liquid
journal, July 2016


Orthogonality Catastrophe and Shock Waves in a Nonequilibrium Fermi Gas
journal, December 2006


Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
journal, December 2015


Nonequal-time current correlation function in a one-dimensional Bose gas
journal, March 1990

  • Slavnov, N. A.
  • Theoretical and Mathematical Physics, Vol. 82, Issue 3
  • DOI: 10.1007/BF01029221

A renormalization group for the truncated conformal space approach
journal, March 2008


Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium
journal, December 2016

  • Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Yoshimura, Takato
  • Physical Review X, Vol. 6, Issue 4
  • DOI: 10.1103/PhysRevX.6.041065

Collective oscillations of a one-dimensional trapped Bose-Einstein gas
journal, October 2002


Generalized TBA and generalized Gibbs
journal, May 2012


Dynamical density-density correlations in the one-dimensional Bose gas
journal, September 2006


One-particle dynamical correlations in the one-dimensional Bose gas
journal, January 2007

  • Caux, Jean-Sébastien; Calabrese, Pasquale; Slavnov, Nikita A.
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 01
  • DOI: 10.1088/1742-5468/2007/01/P01008

Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
journal, August 2015


Dissipationless kinetics of one-dimensional interacting fermions
journal, April 2014


Universal Fermi distribution of semiclassical nonequilibrium Fermi states
journal, August 2011


Thermodynamic Bethe ansatz in relativistic models: Scaling 3-state potts and Lee-Yang models
journal, October 1990


Experimental observation of a generalized Gibbs ensemble
journal, April 2015


Momentum-Space Correlations of a One-Dimensional Bose Gas
journal, February 2016


Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
journal, May 1963


Quantum many-body systems out of equilibrium
journal, February 2015

  • Eisert, J.; Friesdorf, M.; Gogolin, C.
  • Nature Physics, Vol. 11, Issue 2
  • DOI: 10.1038/nphys3215

Correlation functions of integrable models: A description of the ABACUS algorithm
journal, September 2009

  • Caux, Jean-Sébastien
  • Journal of Mathematical Physics, Vol. 50, Issue 9
  • DOI: 10.1063/1.3216474

Exciting Collective Oscillations in a Trapped 1D Gas
journal, December 2003


Quantum Ripples Over a Semiclassical Shock
journal, December 2012


Exciton Hierarchies in Gapped Carbon Nanotubes
journal, March 2011


One dimensional bosons: From condensed matter systems to ultracold gases
journal, December 2011


Truncated Comformal Space Approach to Scaling Lee-Yang Model
journal, August 1990

  • Yurov, V. P.; Zamolodchikov, Al. B.
  • International Journal of Modern Physics A, Vol. 05, Issue 16
  • DOI: 10.1142/S0217751X9000218X

Numerical Renormalization Group for Continuum One-Dimensional Systems
journal, April 2007


Calculation of scalar products of wave functions and form factors in the framework of the alcebraic Bethe ansatz
journal, May 1989

  • Slavnov, N. A.
  • Theoretical and Mathematical Physics, Vol. 79, Issue 2
  • DOI: 10.1007/BF01016531

Dynamics of hard rods with initial domain wall state
journal, July 2017

  • Doyon, Benjamin; Spohn, Herbert
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 7
  • DOI: 10.1088/1742-5468/aa7abf

A quantum Newton's cradle
journal, April 2006

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

Dynamics of Bose-Einstein condensed gases in highly deformed traps
journal, September 1998


    Works referencing / citing this record:

    Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains
    journal, June 2019