Excitations in the Yang–Gaudin Bose gas
Abstract
Here, we study the excitation spectrum of twocomponent deltafunction interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finitesize 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 finitemomentum rotonlike 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 multiparticle 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 multispinon 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 zerotemperature 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 twospinon bound states by numerically solving the Bethe ansatz equations with string deviations.
 Authors:

 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES)
 OSTI Identifier:
 1433966
 Report Number(s):
 BNL2034992018JAAM
Journal ID: ISSN 17425468
 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 17425468
 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. https://doi.org/10.1088/17425468/aa6f46.
Robinson, Neil J., & Konik, Robert M. Excitations in the Yang–Gaudin Bose gas. United States. https://doi.org/10.1088/17425468/aa6f46
Robinson, Neil J., and Konik, Robert M. Thu .
"Excitations in the Yang–Gaudin Bose gas". United States. https://doi.org/10.1088/17425468/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 twocomponent deltafunction interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finitesize 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 finitemomentum rotonlike 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 multiparticle 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 multispinon 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 zerotemperature 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 twospinon bound states by numerically solving the Bethe ansatz equations with string deviations.},
doi = {10.1088/17425468/aa6f46},
journal = {Journal of Statistical Mechanics},
number = 6,
volume = 2017,
place = {United States},
year = {2017},
month = {6}
}