Thermodynamic limit and boundary energy of the su(3) spin chain with non-diagonal boundary fields

Fakai Wen,Tao Yang,Zhanying Yang,Junpeng Cao,Kun Hao,Wen-Li Yang

doi:10.1016/j.nuclphysb.2016.12.003

Abstract

We investigate the thermodynamic limit of the su(n)-invariant spin chain models with unparallel boundary fields. It is found that the contribution of the inhomogeneous term in the associated T–Q relation to the ground state energy does vanish in the thermodynamic limit. This fact allows us to calculate the boundary energy of the system. Taking the su(2) (or the XXX) spin chain and the su(3) spin chain as concrete examples, we have studied the corresponding boundary energies of the models. The method used in this paper can be generalized to study the thermodynamic properties and boundary energy of other high rank models with non-diagonal boundary fields.

Highlights

Solvable models have played essential roles in many areas of physics, such as ultracold atoms [1], condensed matter physics [2, 3], the AdS/CFT correspondence [4, 5], equilibrium and non-equilibrium statistical physics [6, 7, 8, 9, 10, 11]
The thermodynamic properties of these models, for example, the specific heat, susceptibility and elementary excitations, which can be obtained by using the thermodynamic Bethe ansatz (TBA) [12], have attracted a great attention due to the analytical results can be compared with experimental data directly [1, 2, 12, 13, 14, 15]
We study the thermodynamic limit of the su(n)-invariant spin chain models with unparallel boundary fields by taking the XXX spin-1/2 chain and the su(3)-invariant chain with unparallel boundary fields [16, 17] as concrete examples

Summary

Introduction

Solvable models have played essential roles in many areas of physics, such as ultracold atoms [1], condensed matter physics [2, 3], the AdS/CFT correspondence [4, 5], equilibrium and non-equilibrium statistical physics [6, 7, 8, 9, 10, 11]. The corresponding Bethe Ansatz equations (BAEs) obtained by using the ODBA method have much complicated structure due to the inhomogeneous term in the T -Q relation, which makes the direct employment of the TBA method to approach the thermodynamic limit of those models very involved [16, 28, 29]. Comparison of the boundary energy from the analytic expressions with that from the Hamiltonian by the extrapolation method shows that they coincide with each other very well This further demonstrates that the neglected inhomogeneous term does not affect the physical properties of the studied system in the thermodynamic limit.

Contribution of the inhomogeneous term to the ground state energy

Boundary energy

Contribution of the inhomogeneous term

Conclusions