Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction

Details Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction

2010-03-29

arxiv.org/abs/1003.5463v2

J. Phys. Soc. Jpn. 79 (2010) 073002

Physics

Condensed Matter

Statistical Mechanics

5 pages, 1 figure

Scientific paper

10.1143/JPSJ.79.073002

We study a matrix product representation of the Bethe ansatz state for the Lieb-Linger model describing the one-dimensional Bose gas with delta-function interaction. We first construct eigenstates of the discretized model in the form of matrix product states using the algebraic Bethe ansatz. Continuous matrix product states are then exactly obtained in the continuum limit with a finite number of particles. The factorizing $F$-matrices in the lattice model are indispensable for the continuous matrix product states and lead to a marked reduction from the original bosonic system with infinite degrees of freedom to the five-vertex model.

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