NLIE and finite size effects of the spin-1/2 XXZ and sine-Gordon models with two boundaries revisited

Murgan, Rajan

doi:10.1007/s13130-010-0528-2

Cited by 2 publications

(3 citation statements)

References 47 publications

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“…Among others, its finite size properties of ground and excited states have received much attention over the years. This lattice model has also been used to study the ground and excited states of the corresponding field theoretical model i.e., the sine-Gordon (SG) model with boundaries [16], let it be with Dirichlet or general integrable boundary conditions [14], [17]- [28]. As for the periodic case [29]- [31], NLIEs have also been derived from the corresponding Bethe ansatz solutions of the open spin-1/2 XXZ chains with nondiagonal boundary terms [9]- [13], [15] and used in such investigations [14,22,26,27,28], in particular, in studies involving the crucial ultraviolet (UV) and infrared (IR) limits.…”

Section: Introductionmentioning

confidence: 99%

On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms

Murgan

2011

J. High Energ. Phys.

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Starting from the T -Q equations of the open spin-1 XXZ quantum spin chain with general integrable boundary terms, for values of the boundary parameters which satisfy a certain constraint, we derive a set of nonlinear integral equations (NLIEs) for the inhomogeneous open spin-1 XXZ chain. By taking the continuum limit of these NLIEs, and working in analogy with the open spin-1 XXZ chain with diagonal boundary terms, we compute the boundary and the Casimir energies of the corresponding supersymmetric sine-Gordon (SSG) model. We also present an analytical result for the effective central charge in the ultraviolet (UV) limit. 1 email: rmurgan@gustavus.edufor the open spin-1 XXZ spin chain with general integrable boundary terms are reviewed. This is followed by the derivation of a set of NLIEs for the inhomogeneous open spin-1 XXZ chain in section 3. We then give a brief review of the SSG model following [41]. Proceeding by analogy with the SG model with general integrable boundary conditions [14,27] and the SSG model with Dirichlet boundary conditions [46], we consider the continuum limit of the NLIEs in section 4. In section 5, we compute the boundary and Casimir energies for the ground state. We analyze the UV limit of the Casimir energy and give an analytical result for the effective central charge in section 6. Finally, we conclude the paper with a brief discussion of our results and some open problems in section 7.

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Section: Introductionmentioning

confidence: 99%

On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms

Murgan

2011

J. High Energ. Phys.

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“…These models have thus been widely studied over the years [1]- [39]. Studies conducted have covered various aspects of these models, with much of them focusing on the nondiagonal boundary interactions such as in [4,5,6] and [18]- [39]. In particular, progress made in finding solutions of the open spin- 1 2 XXZ quantum spin chain with nondiagonal boundary terms such as that given in [20,21,22,24] has motivated further studies of these models [23,25,39].…”

Section: Introductionmentioning

confidence: 99%

“…Open spin- 1 2 XXZ quantum spin chains and boundary sine-Gordon (bsG) models have applications in statistical mechanics and condensed matter physics. These models have thus been widely studied over the years [1]- [39]. Studies conducted have covered various aspects of these models, with much of them focusing on the nondiagonal boundary interactions such as in [4,5,6] and [18]- [39].…”

Section: Introductionmentioning

confidence: 99%

A note on a boundary sine-Gordon model at the free-Fermion point

Murgan¹

2018

J. Stat. Mech.

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We investigate the free-Fermion point of a boundary sine-Gordon model with nondiagonal boundary interactions for the ground state using auxiliary functions obtained from T − Q equations of a corresponding inhomogeneous open spin-1 2 XXZ chain with nondiagonal boundary terms. In particular, we obtain the Casimir energy. Our result for the Casimir energy is shown to agree with the result from the TBA approach. The analytical result for the effective central charge in the ultraviolet (UV) limit is also verified from the plots of effective central charge for intermediate values of volume.1 email:rmurgan@svsu.edu 1 See [24] next. In Section 3, the T − Q equations of the corresponding inhomogeneous open spin-1 2 XXZ chain are reviewed. This is followed by derivations of crucial auxiliary functions at the free-Fermion point. Utilizing the auxiliary functions and the analyticity of the transfer matrix eigenvalues, we present the derivation of the Casimir energy at the free-Fermion point in Section 4 and compare our result for the Casimir energy of bsG model at the free-Fermion point with that of the TBA approach given in [16]. We then examine the result in the UV limit. The computation of the effective central charge in the UV limit is indeed a new result. We find it to be independent of the boundary parameters. We remark here that the approach using T − Q equations can be viewed as an alternative way (to the elegant TBA approach employed in [16]) of arriving at the ground state Casimir energy. In [16], the authors pointed out some of the technical difficulties encountered during the computations of the K matrices which are indeed crucial in the ground state Casimir energy calculation. Computations of K matrices there required complex analytic continuations. Nevertheless, this was carried out successfully in [16] to yield the desired results. Finally, plots of effective central charge for intermediate volume values are presented to support the analytical results obtained earlier for the UV limit. We conclude with a brief discussion of our results and some open problems in Section 5.

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NLIE and finite size effects of the spin-1/2 XXZ and sine-Gordon models with two boundaries revisited

Cited by 2 publications

References 47 publications

On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms

On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms

A note on a boundary sine-Gordon model at the free-Fermion point

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