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arXiv:2508.17908 · Physical review. B./Physical review. B

Finite temperature single-particle Green's function in the Lieb-Liniger model

Riccardo Senese, Fabian H. L. Eßler

Published Mar 30, 2026• 2 citations
arXivHTMLPDF

Abstract

We develop a Monte Carlo sampling algorithm to numerically evaluate the Lehmann representation for the finite temperature single-particle Green's function in the repulsive Lieb-Liniger model. This allows us to determine the spectral function in the full range of temperatures and interactions, as well as in generalized Gibbs ensembles. We test our results against known results for dynamics at infinite interaction strength and static correlators, and find excellent agreement.

DOI
10.1103/8qtr-dm7g

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Abstract. The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb-Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is welladapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case. One-particle dynamical correlations in the one-dimensional Bose gas 2 1.
We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional, strongly correlated system: the integrable one-dimensional Bose gas with a repulsive $\ensuremath{\delta}$-function interaction (the Lieb-Liniger model). Focusing on the dynamical density-density function, we present a Bethe ansatz-based method allowing for its accurate evaluation in finite but large systems, over broad ranges of momenta, frequencies, temperatures, and interaction parameters which are difficult to access using other methods. This allows us to quantify the reshaping of the zero-temperature critical behavior by thermal fluctuations, in experimentally accessible regimes.
We have developed a Monte Carlo algorithm to explore the equilibrium and out-of-equilibrium properties of the Lieb-Liniger model. This Monte Carlo Bethe-ansatz (MCBA) algorithm has enabled us to successfully reconstruct statistical ensembles for equilibrium or postquench dynamics, thereby facilitating the calculation of macroscopic quantities of integrable models. Our results substantiate the validity of the (quench) thermodynamic Bethe-ansatz equation from the perspective of first-principles statistical physics. Additionally, we have employed this method to study the generalized Gibbs ensemble in relation to the postquench dynamics of the Lieb-Liniger model. Furthermore, we have demonstrated the MCBA algorithm's capacity to calculate correlations using Bethe-ansatz wave functions. Our approach offers an efficient methodology for the investigation of the equilibrium and out-of-equilibrium properties of integrable systems.