DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Excitations in the Yang–Gaudin Bose gas

Abstract

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known as $$\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\Lambda$$-string dressed energies $$\epsilon_n(\lambda)$$ and the dressed energy $$\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.

Authors:
 [1];  [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1433966
Report Number(s):
BNL-203499-2018-JAAM
Journal ID: ISSN 1742-5468
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Statistical Mechanics
Additional Journal Information:
Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 1742-5468
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; integrable quantum field theory; quantum integrability (bethe Ansatz); quantum gases

Citation Formats

Robinson, Neil J., and Konik, Robert M. Excitations in the Yang–Gaudin Bose gas. United States: N. p., 2017. Web. doi:10.1088/1742-5468/aa6f46.
Robinson, Neil J., & Konik, Robert M. Excitations in the Yang–Gaudin Bose gas. United States. https://doi.org/10.1088/1742-5468/aa6f46
Robinson, Neil J., and Konik, Robert M. Thu . "Excitations in the Yang–Gaudin Bose gas". United States. https://doi.org/10.1088/1742-5468/aa6f46. https://www.osti.gov/servlets/purl/1433966.
@article{osti_1433966,
title = {Excitations in the Yang–Gaudin Bose gas},
author = {Robinson, Neil J. and Konik, Robert M.},
abstractNote = {Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known as $\Lambda$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $\Lambda$-string dressed energies $\epsilon_n(\lambda)$ and the dressed energy $\epsilon(k)$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $\Lambda$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $\lambda = 0$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.},
doi = {10.1088/1742-5468/aa6f46},
journal = {Journal of Statistical Mechanics},
number = 6,
volume = 2017,
place = {United States},
year = {2017},
month = {6}
}

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

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
journal, March 1931


Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
journal, June 1968


Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension
journal, July 1968


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


Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
journal, May 1963


Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
journal, December 1967


Un systeme a une dimension de fermions en interaction
journal, January 1967


Further Results for the Many-Body Problem in One Dimension
journal, January 1968


Exact results of the ground state and excitation properties of a two-component interacting Bose system
journal, February 2003


Conformal invariance, the central charge, and universal finite-size amplitudes at criticality
journal, February 1986


Universal term in the free energy at a critical point and the conformal anomaly
journal, February 1986


Conformal invariance and universality in finite-size scaling
journal, May 1984


Finite size effects in conformal field theories and non-local operators in one-dimensional quantum systems
journal, May 1990


Critical exponents for the one-dimensional Hubbard model
journal, December 1990


Critical exponents in multiparticle 1D quantum systems from finite-size effects in conformal field theories
journal, February 1991


Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories
journal, November 2016


Exact Edge Singularities and Dynamical Correlations in Spin- 1 / 2 Chains
journal, January 2008


Spectral function of spinless fermions on a one-dimensional lattice
journal, April 2009


Threshold singularities in the one-dimensional Hubbard model
journal, May 2010


Nonuniversal prefactors in the correlation functions of one-dimensional quantum liquids
journal, July 2011


Mobile impurity approach to the optical conductivity in the Hubbard chain
journal, May 2016


Quantum quenches in the Luttinger model and its close relatives
journal, June 2016


Generalized Gibbs ensemble in integrable lattice models
journal, June 2016


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

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
journal, June 2016


Equilibration properties of classical integrable field theories
journal, June 2016


Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
journal, March 2007

  • Lewenstein, Maciej; Sanpera, Anna; Ahufinger, Veronica
  • Advances in Physics, Vol. 56, Issue 2
  • DOI: 10.1080/00018730701223200

Interaction Quench in the Hubbard Model
journal, May 2008


Metastable Superfluidity of Repulsive Fermionic Atoms in Optical Lattices
journal, December 2008


Real-time evolution for weak interaction quenches in quantum systems
journal, October 2009


Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems
journal, August 2011


Quench dynamics in a model with tuneable integrability breaking
journal, April 2014


Quantum Quench and Prethermalization Dynamics in a Two-Dimensional Fermi Gas with Long-Range Interactions
journal, November 2014


On conservation laws, relaxation and pre-relaxation after a quantum quench
journal, March 2014


Prethermalization of weakly interacting bosons after a sudden interaction quench
journal, May 2015


Entanglement pre-thermalization in a one-dimensional Bose gas
journal, September 2015

  • Kaminishi, Eriko; Mori, Takashi; Ikeda, Tatsuhiko N.
  • Nature Physics, Vol. 11, Issue 12
  • DOI: 10.1038/nphys3478

Motion of a Distinguishable Impurity in the Bose Gas: Arrested Expansion Without a Lattice and Impurity Snaking
journal, April 2016


Non relativistic limit of integrable QFT and Lieb–Liniger models
journal, December 2016

  • Bastianello, Alvise; De Luca, Andrea; Mussardo, Giuseppe
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 12
  • DOI: 10.1088/1742-5468/aa4f98

Non relativistic limit of integrable QFT with fermionic excitations
journal, May 2017

  • Bastianello, Alvise; De Luca, Andrea; Mussardo, Giuseppe
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 23
  • DOI: 10.1088/1751-8121/aa6f69

Spinor Bose gases: Symmetries, magnetism, and quantum dynamics
journal, July 2013


Fermi gases in one dimension: From Bethe ansatz to experiments
journal, November 2013


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

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

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
journal, May 2016


A quantum Newton's cradle
journal, April 2006

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

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

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


Percolation transition in the Bose gas
journal, September 1993


Polarization of Interacting Bosons with Spin
journal, November 2002


Spin Waves in a One-Dimensional Spinor Bose Gas
journal, October 2005


Spin Dynamics in a One-Dimensional Ferromagnetic Bose Gas
journal, December 2007


One-Dimensional Heisenberg Model at Finite Temperature
journal, August 1971

  • Takahashi, Minoru
  • Progress of Theoretical Physics, Vol. 46, Issue 2
  • DOI: 10.1143/PTP.46.401

On form factors in nested Bethe Ansatz systems
journal, October 2012

  • Pozsgay, Balázs; van Gerven Oei, Willem-Victor; Kormos, Márton
  • Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 46
  • DOI: 10.1088/1751-8113/45/46/465007

Hydrodynamic Theory of Spin Waves
journal, December 1969


Dynamic properties of the multicomponent Bose fluid
journal, January 1975


Atomic Theory of the Two-Fluid Model of Liquid Helium
journal, April 1954


Theory of Inelastic Scattering of Cold Neutrons from Liquid Helium
journal, July 1957


Specific heat and dispersion curve for helium II
journal, September 1981

  • Donnelly, R. J.; Donnelly, J. A.; Hills, R. N.
  • Journal of Low Temperature Physics, Vol. 44, Issue 5-6
  • DOI: 10.1007/BF00117839

Colloquium : Spontaneous magnon decays
journal, January 2013


Fine structure of the Bethe ansatz for the spin-1/2 Heisenberg XXX model
journal, August 1992

  • Essler, F. H. L.; Korepin, V. E.; Schoutens, K.
  • Journal of Physics A: Mathematical and General, Vol. 25, Issue 15
  • DOI: 10.1088/0305-4470/25/15/019

Deformed strings in the Heisenberg model
journal, November 2007

  • Hagemans, Rob; Caux, Jean-Sébastien
  • Journal of Physics A: Mathematical and Theoretical, Vol. 40, Issue 49
  • DOI: 10.1088/1751-8113/40/49/001

Proof of the invariance of the Bethe-ansatz solutions under complex conjugation
journal, January 1986

  • Vladimirov, A. A.
  • Theoretical and Mathematical Physics, Vol. 66, Issue 1
  • DOI: 10.1007/BF01028945

Equilibrium thermodynamic properties of interacting two-component bosons in one dimension
journal, September 2011


Exact results in the theory of magnetic alloys
journal, January 1983


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

Quantum quenches to the attractive one-dimensional Bose gas: exact results
journal, January 2016


Non self-conjugate strings, singular strings and rigged configurations in the Heisenberg model
journal, February 2015


Thermodynamics and excitations of the one-dimensional Hubbard model
journal, July 2000


Computation of dynamical correlation functions of the spin-1 Babujan–Takhtajan chain
journal, May 2014


Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz
journal, December 2007


Polarization suppression and nonmonotonic local two-body correlations in the two-component Bose gas in one dimension
journal, December 2009

  • Caux, Jean-Sébastien; Klauser, Antoine; van den Brink, Jeroen
  • Physical Review A, Vol. 80, Issue 6
  • DOI: 10.1103/PhysRevA.80.061605

Quantum Transport through a Tonks-Girardeau Gas
journal, October 2009


Quantum dynamics of impurities in a one-dimensional Bose gas
journal, February 2012


Observation of Complex Bound States in the Spin- 1 / 2 Heisenberg X X Z Chain Using Local Quantum Quenches
journal, February 2012


Multiparticle Bound-State Formation following a Quantum Quench to the One-Dimensional Bose Gas with Attractive Interactions
journal, February 2016


Analytical inversion of symmetric tridiagonal matrices
journal, April 1996