Yang–Baxter integrable models in experiments: from condensed matter to ultracold atoms

Abstract

The Yang-Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article we provide an introductory overview of the impact of Yang-Baxter integrable models on experiments in condensed matter physics and ultracold atoms. A number of prominent examples are mentioned, including the hard-hexagon model, the Heisenberg spin chain, the transverse quantum Ising chain, a spin ladder model, the Lieb-Liniger Bose gas, the Gaudin-Yang Fermi gas and the two-site Bose-Hubbard model. The review concludes by pointing to some other recent developments with promise for further progress.

In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas

“…The fermions do not interact among each each other due to the Pauli exclusion principle. The system is solvable by the Bethe ansatz, which is a common start- * dhuber@theorie.ikp.physik.tu-darmstadt.de † hammer@theorie.ikp.physik.tu-darmstadt.de ing point for analyzing cold atom systems in 1D geometries [28][29][30]. In Section IV, we go on to discuss effective models for describing two impurities in a medium and benchmark them against the Bethe ansatz results.…”

One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction

“…Here the two alternative contributions ±2k F to the excitation momentum k = ±2k F − q − q result from c band momentum shifts 2πΦ 0 c = ±π in Eq. (11), such that 2π At zero spin density, m = 0, the transitions under one-fermion addition lead to excited energy eigenstates associated with the two-parametric processes whose number deviations relative to those of the initial ground state are given by,…”

“…That the latter is the simplest condensed-matter toy model for the description of the role of correlations in the exotic properties of 1D and quasi-1D lattice condensed matter systems [8,9] justifies why for several decades it had attracted more attention than its continuous cousin, the fermionic gas with repulsive delta-function interaction. This refers both to its metallic and Mott-Hubbard insulator phases [10], the latter not existing in the case of the continuous 1D repulsive fermion model.However, in the last years the interest in that Yang-Baxter integrable model has been renewed by its new found impact on experiments in both condensed matter physics and ultra-cold atomic gases [11]. The latter have provided new opportunities for studying 1D systems of spin-1/2 fermions with repulsive interaction [12,13].…”

“…The latter have provided new opportunities for studying 1D systems of spin-1/2 fermions with repulsive interaction [12,13]. The present model can indeed be implemented with ultra-cold atoms [11][12][13][14][15][16][17]. Ultra-cold Fermi gases trapped inside a tight atomic waveguide offer for instance the opportunity to measure the spin-drag relaxation rate that controls the broadening of a spin packet.…”

Traces of integrability in scattering of one-dimensional dimers on a barrier

“…The last two decades are marked by a revival of interest in Bethe Ansatz integrable particle systems [1][2][3][4][5][6][7], inspired by the emerged experimental relevance of the former in both many-body [8][9][10][11] and few-body [12,13] cold-atom systems (see [14] for a review). Integrability, besides providing a way to produce theoretical predictions, also induces new empirically observable integrals of motion.…”