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:
-
- 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 = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}
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