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A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights since they are often amenable to exact methods. However, no exact solution is…

We study a one-dimensional system of two-component fermions in the limit of strong attractive particle-particle interactions. First, we analyze scattering in the corresponding few-body problem, which is analytically solvable via Bethe…

We consider a one dimensional interacting bose-fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between bose-fermi and bose-bose particles. Such a system can be realized in experiments with…

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become…

We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground…

We consider one dimensional interacting bose-fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between bose-fermi and bose-bose particles. Such a system can be realized in current experiments…

This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase transitions, universal thermodynamics,…

A growing expertise to engineer, manipulate and probe different cold-atom analogs of electronic condensed matter systems allows to probe properties of exotic pairing. We study paired states of spin-imbalanced ultracold atomic system of…

We investigate the elementary excitations of charge and spin degrees for the 1D interacting two-component Bose and Fermi gases by means of the discrete Bethe ansatz equations. Analytic results in the limiting cases of strong and weak…

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas -- the Gaudin-Yang model -- and its generalisations…

We consider two particular 1D quantum many-body systems with local interactions related to the root system $C_N$. Both models describe identical particles moving on the half-line with non-trivial boundary conditions at the origin, and they…

By the Bethe ansatz method we study the energy dispersion of a particle interacting by a local interaction with fermions (or hard core bosons) of equal mass in a one dimensional lattice. We focus on the period of the Bloch oscillations…

We introduce a new type of models for two-component systems in one dimension subject to exact solutions by Bethe ansatz, where the interspecies interactions are tunable via Feshbach resonant interactions. The applicability of Bethe ansatz…

Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the…

Quantum many-body systems in one dimension (1D) exhibit some peculiar properties. In this article, we review some of our work on strongly interacting 1D spinor quantum gas. First, we discuss a generalized Bose-Fermi mapping that maps the…

Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $\delta$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering…

We investigate the ground state properties of a one-dimensional two-component ultra-cold Fermi gas in an infinite potential well. Exact Bethe ansatz solution is used to calculate the many-body wave function of the system. Then we evaluate…

The interplay of quantum statistics, interactions and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe…

Few-atom systems play an important role in understanding the transition from few- to many-body quantum behaviors. This work introduces a new approach for determining the energy spectra and eigenstates of small harmonically trapped…