Excitations in the Yang–Gaudin Bose gas

Journal Article · Thu Jun 01 00:00:00 EDT 2017 · Journal of Statistical Mechanics

DOI:https://doi.org/10.1088/1742-5468/aa6f46· OSTI ID:1433966

Robinson, Neil J. ^[1]; Konik, Robert M. ^[1]

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1. Brookhaven National Lab. (BNL), Upton, NY (United States)

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.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0012704
• OSTI ID: 1433966
• Report Number(s): BNL-203499-2018-JAAM
• Journal Information: Journal of Statistical Mechanics, Vol. 2017, Issue 6; ISSN 1742-5468
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
integrable quantum field theory
quantum integrability (bethe Ansatz)
quantum gases