### 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.- 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

```
Robinson, Neil J., and Konik, Robert M..
```*Excitations in the Yang–Gaudin Bose gas*. United States: N. p.,
Web. doi:10.1088/1742-5468/aa6f46.

```
Robinson, Neil J., & Konik, Robert M..
```*Excitations in the Yang–Gaudin Bose gas*. United States. doi:10.1088/1742-5468/aa6f46.

```
Robinson, Neil J., and Konik, Robert M.. 2017.
"Excitations in the Yang–Gaudin Bose gas". United States.
doi: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}

}