Finite size effects in the XXZ and sine-Gordon models with two boundaries

Changrim Ahn; Rafael I. Nepomechie

doi:10.1016/j.nuclphysb.2003.11.012

Finite size effects in the XXZ and sine-Gordon models with two boundaries

Changrim Ahn, Rafael I. Nepomechie

Department of Physics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

We compute the boundary energy and the Casimir energy for both the spin-1/2 XXZ quantum spin chain and (by means of the light-cone lattice construction) the massive sine-Gordon model with both left and right boundaries. We also derive a nonlinear integral equation for the ground state of the sine-Gordon model on a finite interval. These results, which are based on a recently-proposed Bethe ansatz solution, are for general values of the bulk coupling constant, and for both diagonal and nondiagonal boundary interactions. However, the boundary parameters are restricted to obey one complex (two real) constraints.

Original language	English
Pages (from-to)	637-658
Number of pages	22
Journal	Nuclear Physics, Section B
Volume	676
Issue number	3
DOIs	https://doi.org/10.1016/j.nuclphysb.2003.11.012
State	Published - 12 Jan 2004

Bibliographical note

Funding Information:
We are grateful to F. Ravanini for providing us with sample code for numerical solution of the nonlinear integral equation; and to O. Alvarez for his help in preparing a figure. This work was supported in part by the Korea Research Foundation 2002-070-C00025 (C.A.); and by the National Science Foundation under Grants PHY-0098088 and PHY-0244261, and by a UM Provost Award (R.N.).

Access to Document

10.1016/j.nuclphysb.2003.11.012

Cite this

@article{16c8bfb942a44ec2a42df6e931466915,

title = "Finite size effects in the XXZ and sine-Gordon models with two boundaries",

abstract = "We compute the boundary energy and the Casimir energy for both the spin-1/2 XXZ quantum spin chain and (by means of the light-cone lattice construction) the massive sine-Gordon model with both left and right boundaries. We also derive a nonlinear integral equation for the ground state of the sine-Gordon model on a finite interval. These results, which are based on a recently-proposed Bethe ansatz solution, are for general values of the bulk coupling constant, and for both diagonal and nondiagonal boundary interactions. However, the boundary parameters are restricted to obey one complex (two real) constraints.",

author = "Changrim Ahn and Nepomechie, {Rafael I.}",

note = "Funding Information: We are grateful to F. Ravanini for providing us with sample code for numerical solution of the nonlinear integral equation; and to O. Alvarez for his help in preparing a figure. This work was supported in part by the Korea Research Foundation 2002-070-C00025 (C.A.); and by the National Science Foundation under Grants PHY-0098088 and PHY-0244261, and by a UM Provost Award (R.N.).",

year = "2004",

month = jan,

day = "12",

doi = "10.1016/j.nuclphysb.2003.11.012",

language = "English",

volume = "676",

pages = "637--658",

journal = "Nuclear Physics, Section B",

issn = "0550-3213",

publisher = "Elsevier",

number = "3",

}

TY - JOUR

T1 - Finite size effects in the XXZ and sine-Gordon models with two boundaries

AU - Ahn, Changrim

AU - Nepomechie, Rafael I.

N1 - Funding Information: We are grateful to F. Ravanini for providing us with sample code for numerical solution of the nonlinear integral equation; and to O. Alvarez for his help in preparing a figure. This work was supported in part by the Korea Research Foundation 2002-070-C00025 (C.A.); and by the National Science Foundation under Grants PHY-0098088 and PHY-0244261, and by a UM Provost Award (R.N.).

PY - 2004/1/12

Y1 - 2004/1/12

N2 - We compute the boundary energy and the Casimir energy for both the spin-1/2 XXZ quantum spin chain and (by means of the light-cone lattice construction) the massive sine-Gordon model with both left and right boundaries. We also derive a nonlinear integral equation for the ground state of the sine-Gordon model on a finite interval. These results, which are based on a recently-proposed Bethe ansatz solution, are for general values of the bulk coupling constant, and for both diagonal and nondiagonal boundary interactions. However, the boundary parameters are restricted to obey one complex (two real) constraints.

AB - We compute the boundary energy and the Casimir energy for both the spin-1/2 XXZ quantum spin chain and (by means of the light-cone lattice construction) the massive sine-Gordon model with both left and right boundaries. We also derive a nonlinear integral equation for the ground state of the sine-Gordon model on a finite interval. These results, which are based on a recently-proposed Bethe ansatz solution, are for general values of the bulk coupling constant, and for both diagonal and nondiagonal boundary interactions. However, the boundary parameters are restricted to obey one complex (two real) constraints.

UR - http://www.scopus.com/inward/record.url?scp=0347530076&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2003.11.012

DO - 10.1016/j.nuclphysb.2003.11.012

M3 - Article

AN - SCOPUS:0347530076

SN - 0550-3213

VL - 676

SP - 637

EP - 658

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -

Finite size effects in the XXZ and sine-Gordon models with two boundaries

Abstract

Bibliographical note

Access to Document

Fingerprint

Cite this