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arXiv:1106.4971 · Physical Review A

Equilibrium thermodynamic properties of interacting two-component bosons in one dimension

Antoine Klauser, Jean-Sébastien Caux

Published Sep 2, 2011• 20 citations
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Abstract

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 ansatz and obtain the equation of state as a function of temperature and of the interaction strength, the relative chemical potential, and either the total chemical potential or a fixed number of particles, allowing quantification of the full crossover behavior of the system between its low-temperature ferromagnetic and high-temperature unpolarized regime, and from the low coupling decoherent regime to the fermionization regime at high interaction.

DOI
10.1103/physreva.84.033604

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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 ansatz and obtain the equation of state as a function of temperature and of the interaction strength, the relative chemical potential, and either the total chemical potential or a fixed number of particles, allowing quantification of the full crossover behavior of the system between its low-temperature ferromagnetic and high-temperature unpolarized regime, and from the low coupling decoherent regime to the fermionization regime at high interaction.
We study the interplay of quantum statistics, strong interactions, and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities, and local density correlation numerically as a function of all physical parameters (interaction, temperature, and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single component, Lieb-Liniger gas, nonmonotonic behavior of the local density correlation as a function of temperature is observed.
On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and δ-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin "ferromagnetic" state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like T at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.
On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and δδδ-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin "ferromagnetic" state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like TTT at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.
In this paper we solve one-dimensional trapped SU (2) bosons with repulsive δ-function interaction by means of the Bethe-ansatz method. The features of ground state and low-lying excited states are studied by numerical and analytic methods. We show that the ground state is an isospin `ferromagnetic' state which differs from spin-½ fermion systems. There exist three quasi-particles in the excitation spectra, and both holon-antiholon and holon-isospinon excitations are gapless for large systems. The equilibrium thermodynamics of the system at finite temperature is studied using the thermodynamic Bethe ansatz. The thermodynamic quantities, such as specific heat, etc, are obtained for the case of the strong coupling limit.
The one-dimensional system interacting via a delta-function interparticle interaction is a very important one in cold atomic systems and has fundamental importance in many-body physics. In one dimension, due to the geometric confinement induced quantum correlations and quantum fluctuations, there may exist a number of unusual phenomena, such as spin-charge separation, effective fermionization and quantum criticality. This paper studies the basic properties of a uniform one-dimensional Gaudin-Yang model for fermions by solving the thermodynamic Bethe-ansatz equations by a numerical method. Numerically, we use the many-variable Newton’s method to solve the coupled equations. We analyze the physical properties, including density, interaction, temperature and entropy at a given temperature and a given interaction, separately. We know that a lot of researches are limited to zero temperature. However, we cannot reach the absolute zero temperature in the real cold atomic experiment. So it is important to deal with the finite temperature problems. We study the density and entropy as a function of the chemical potential, temperature and interaction and, then give the phase diagrams, respectively. We found that there is a quantum critical zone in the phase diagram of entropy, including the high temperature zone with thermal fluctuations and the Luttinger liquid zone with quantum fluctuations. For a given temperature and low chemical potential, the thermal fluctuations are the main factor in the entropy. With the increase of chemical potential, the system enters the quantum critical zone where the competitive effect between the thermal fluctuations and the quantum fluctuations exists. When the chemical potential is large enough, the quantum fluctuations become the main factor in the system’s entropy, and we get the Luttinger liquid phase. Our results can be further used in the finite temperature density-functional theory and to analyze the collective phenomena at a finite temperature.
We investigate the low-temperature behavior of the integrable one-dimensional two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility, and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat ${c}_{v}\ensuremath{\sim}{T}^{1∕2}$ and the susceptibility $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.