Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries

被引:145
作者
Essler, FHL
Rittenberg, V
机构
[1] Physikalisches Institut, Universität Bonn, 53115 Bonn
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1996年 / 29卷 / 13期
关键词
D O I
10.1088/0305-4470/29/13/013
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are injected and extracted. By means of the method of Derrida et al the stationary probability measure can be expressed as a matrix-product state involving two matrices forming a Fock-like representation of a general quadratic algebra. We obtain the representations of this algebra, which were unknown in the mathematical literature and use the two-dimensional one to derive exact expressions for the density profile and correlation functions. Using the correspondence between the stochastic model and a quantum spin chain, we obtain exact correlation functions for a spin-1/2 Heisenberg XXZ chain with non-diagonal boundary terms. Generalizations to other reaction-diffusion models are discussed.
引用
收藏
页码:3375 / 3407
页数:33
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