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We investigate two solvable models for Bose-Einstein condensates and extract physical information by studying the structure of the solutions of their Bethe ansatz equations. A careful observation of these solutions for the ground state of both models, as we vary some parameters of the Hamiltonian, suggests a connection between the behavior of the roots of the Bethe ansatz equations and the physical behavior of the models. Then, by the use of standard techniques for approaching quantum phase transition - gap, entanglement and fidelity - we find that the change in the scenery in the roots of the Bethe ansatz equations is directly related to a quantum phase transition, thus providing an alternative method for its detection.
Excited-state quantum phase transitions (ESQPTs) extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for ESQPTs poses however a major ch
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, scaling functio
We study the entanglement entropy and spectrum between components in binary Bose-Einstein condensates in $d$ spatial dimensions. We employ effective field theory to show that the entanglement spectrum exhibits an anomalous square-root dispersion rela
We study binary Bose-Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. Within the mean-field theory, the two types of fields have been shown to give the same vortex-lattice phase diagram. We de
Generation of different nonequilibrium states in trapped Bose-Einstein condensates is studied by numerically solving nonlinear Schrodinger equation. Inducing nonequilibrium states by shaking the trap, the following states are created: weak nonequilib