Uniform Matrix Product State in the Thermodynamic Limit

TL;DR

This paper investigates the use of uniform matrix product states to accurately model classical and quantum spin chains in the thermodynamic limit, emphasizing the importance of translational symmetry and periodicity for precise magnetization calculations.

Contribution

It introduces a method to incorporate translational symmetry in uniform matrix product states, improving the modeling of ground state periodicity and magnetization in spin chains.

Findings

Eigenvalues of the transfer matrix reflect ground state periodicity.

The approach reduces finite-size errors in magnetization calculations.

It is particularly effective for magnetic plateau problems.

Abstract

We study a uniform matrix product state as a variational state for classical and quantum spin chains in the thermodynamic limit. Under a careful treatment of the translational symmetry, eigen values of the transfer matrix defined in the calculation of expectation values can reflect the periodicity of the ground state and indicate optimum periodicity of the matrix product state. We discuss the relation between the periodicity and accuracy of magnetization curves. This approach is free from the error due to finite system size, which works well especially for the magnetic plateau problem.