Aspects of Integrable Models

JUSSI TIMONEN, Yu Chen, R. Bullough

Indrani Bose

Integrable models are often constructed with real systems in mind. The exact solvability of the models leads to results which are unambiguous and provide the correct physical picture. In this review, we discuss the physical basis of some integrable spin models and their relevance in the study of real systems. The emphasis in the review is on physical understanding rather than on the mathematical aspects of integrability.

Colin Rylands, Natan Andrei

Driven by breakthroughs in experimental and theoretical techniques, the study of nonequilibrium quantum physics is a rapidly expanding field with many exciting new developments. Among the manifold ways the topic can be investigated, one-dimensional systems provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques, and experimental viability have resulted in a flurry of research activity over the past decade or so. In this review, we explore the nonequilibrium aspects of one-dimensional systems that are integrable. Through a number of illustrative examples, we discuss nonequilibrium phenomena that arise in such models, the role played by integrability, and the consequences these have for more generic systems.

R. Bullough, D. J. Pilling, JUSSI TIMONEN

Yuzhu Jiang, Yang-Yang Chen, Xi‐Wen Guan

This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb–Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe's hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb–Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang–Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb–Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability.

M. D'Ariano, RASETTI M., Arianna Montorsi