Matrix coordinate Bethe Ansatz: applications to XXZ and ASEP models

被引：37

作者：

Crampe, N. ^{[1
,2
]}

Ragoucy, E. ^{[3
,4
]}

Simon, D. ^{[5
]}

机构：

[1] Univ Montpellier 2, UMR 5221, Lab Charles Coulomb, F-34095 Montpellier, France

[2] CNRS, Lab Charles Coulomb, UMR 5221, F-34095 Montpellier, France

[3] CNRS, Lab Phys Theor LAPTH, F-74941 Annecy Le Vieux, France

[4] Univ Savoie, F-74941 Annecy Le Vieux, France

[5] Univ Paris 06, LPMA, F-75252 Paris 05, France

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2011年 / 44卷 / 40期

关键词：

ASYMMETRIC EXCLUSION PROCESS; BOUNDARY K-MATRICES; SPIN CHAIN; FUNCTIONAL RELATIONS; QUADRATIC ALGEBRA; XYZ-SPIN; REPRESENTATIONS; DIFFUSION;

D O I：

10.1088/1751-8113/44/40/405003

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present the construction of the full set of eigenvectors of the open asymmetric simple exclusion process (ASEP) and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This 'matrix coordinate Bethe Ansatz' can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in the matrix Ansatz.

引用

页数：17

共 36 条

[1] Exact solutions of exactly integrable quantum chains by a matrix product ansatz [J].

Alcaraz, FC ;

Lazo, MJ .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (14) :4149-4182

[2] The Bethe ansatz as a matrix product ansatz [J].

Alcaraz, FC ;

Lazo, MJ .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (01) :L1-L7

[3]

BASEILHAC P, 2007, P RAQIS07 ANN VIEUX

[4] Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory [J].

Baseilhac, Pascal ;

Koizumi, Kozo .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2007,

[5]

Belitsky V, 2002, EL J PROB, V7, P1

[6] Metal theory [J].

Bethe, H. .

ZEITSCHRIFT FUR PHYSIK, 1931, 71 (3-4) :205-226

[7] A matrix ansatz for the diffusion of an impurity in the asymmetric exclusion process [J].

Boutillier, C ;

François, P ;

Mallick, K ;

Mallick, S .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (46) :9703-9730

[8] Exact solution of XXZ spin chain with unparallel boundary fields [J].

Cao, JP ;

Lin, HQ ;

Shi, KJ ;

Wang, YP .

NUCLEAR PHYSICS B, 2003, 663 (03) :487-519

[9] The Matrix Ansatz, orthogonal polynomials, and permutations [J].

Corteel, Sylvie ;

Josuat-Verges, Matthieu ;

Williams, Lauren K. .

ADVANCES IN APPLIED MATHEMATICS, 2011, 46 (1-4) :209-225

[10] Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions [J].

Crampe, N. ;

Ragoucy, E. ;

Simon, D. .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2010,

← 1 2 3 4 →