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arXiv:cond-mat/0610435 · Europhysics Letters (EPL)

Paired state in an integrable spin-1 boson model

Junpeng Cao, Yuzhu Jiang, Yupeng Wang

Published Jul 18, 2007• 28 citations
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Abstract

An exactly solvable model describing the low-density limit of the spin-1 bosons in a one-dimensional optical lattice is proposed. The exact Bethe ansatz solution shows that the low-energy physics of this system is described by a quantum liquid of spin singlet bound pairs. Motivated by the exact results, a mean-field approach to the corresponding three-dimensional system is carried out. Condensation of singlet pairs and coexistence with ordinary Bose-Einstein condensation are predicted.

DOI
10.1209/0295-5075/79/30005

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An exactly solvable model describing the low-density limit of the spin-1 bosons in a one-dimensional optical lattice is proposed. The exact Bethe ansatz solution shows that the low-energy physics of this system is described by a quantum liquid of spin singlet bound pairs. Motivated by the exact results, a mean-field approach to the corresponding three-dimensional system is carried out. Condensation of singlet pairs and coexistence with ordinary Bose-Einstein condensation are predicted.
We consider a model of one-dimensional spin-1 bosons with repulsive density–density interactions and antiferromagnetic exchange. We show that the low energy effective field theory is given by a spin–charge separated theory of a Tomonaga–Luttinger Hamiltonian and the O(3) non-linear sigma model describing collective charge and spin excitations respectively. At a particular ratio of the density–density to spin–spin interaction the model is integrable, and we use the exact solutions to provide an independent derivation of the low energy effective theory. The system is in a superfluid phase made of singlet pairs of bosons, and we calculate the long-distance asymptotics of certain correlation functions.
We investigate magnetism and quantum phase transitions in a one-dimensional system of integrable spin-1 bosons with strongly repulsive density-density interaction and antiferromagnetic spin-exchange interaction via the thermodynamic Bethe ansatz method. At zero temperature, the system exhibits three quantum phases: (i) a singlet phase of boson pairs when the external magnetic field HHH is less than the lower critical field Hc1{H}_{c1}Hc1​; (ii) a ferromagnetic phase of atoms in the hyperfine state ∣F=1, mF=1⟩|F=1,\text{ }{m}_{F}=1⟩∣F=1, mF​=1⟩ when the external magnetic field exceeds the upper critical field Hc2{H}_{c2}Hc2​; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region Hc1<H<Hc2{H}_{c1}<H<{H}_{c2}Hc1​<H<Hc2​. At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired mF=1{m}_{F}=1mF​=1 bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime.
We analyze paired phases of cold bosonic atoms with spin S=1S=1S=1 and with an attractive interaction. We derive mean-field self-consistent equations for the matrix order parameter describing such paired bosons on an optical lattice. The possible solutions are classified according to their symmetries. In particular, we find that the self-consistent equations for the SO(3) symmetric phase are of the same form as those for scalar bosons with attractive interactions. This singlet phase may exhibit either the BCS-type pairing instability (BCS phase) or the Bose-Einstein condensation (BEC) quasiparticle condensation together with the BCS-type pairing (BEC phase) for an arbitrary attraction U0{U}_{0}U0​ in the singlet channel of the two-body interaction. We show that both condensate phases become stable if a repulsion U2{U}_{2}U2​ in the quintet channel is above a critical value, which depends on U0{U}_{0}U0​ and other thermodynamic parameters.
A t–J1–J2 model is constructed to describe the spin-1 bosons in optical lattices in the strong correlation limit. In the parameter region of J1<J2, with the slave-boson-mean-field approach, it is found that two kinds of condensed phases may exist: a condensate with spin singlet pairs and a condensate with ferro-quadruple long range order coexisting with singlet pairs. A first-order quantum phase transition occurs at the point J1 = 0. The finite-temperature phase transition in a cubic optical lattice was also discussed.
We combine model mapping, exact spectral bounds, and a quantum Monte Carlo method to study the ground state phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional optical lattice. The exact boundary of the boson-demixing transition is obtained from the Bethe Ansatz solution of the standard Hubbard model. We prove that along a symmetry plane in the parameter space, the boson-fermion mixed phase is stable at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. The static density correlations are studied in these two limits and shown to have markedly different features.
Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two-dimensional model of bosons with correlated hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single-particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed.