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Title: Excitations in the Yang–Gaudin Bose gas

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:
Report Number(s):
BNL-203499-2018-JAAM
Journal ID: ISSN 1742-5468
Grant/Contract Number:
SC0012704
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
Research Org:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
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
OSTI Identifier:
1433966