Application of Uniform Matrix Product State to Quantum Phase Transition with a Periodicity Change

TL;DR

This paper introduces a novel application of uniform matrix product states with incommensurate periodicity to detect quantum phase transitions involving changes in periodicity, demonstrating its effectiveness on spin chain models.

Contribution

The study develops a method using incommensurate MPS generated by local-spin rotations to identify phase transitions with periodicity change, extending the applicability of MPS techniques.

Findings

Successfully detected ferro to perfect ferro phase transition in S=1/2 Heisenberg model.

Calculated critical exponent of magnetization curve at the phase transition.

Analyzed periodicity change in spin-spin correlations in S=1 Heisenberg model.

Abstract

As a method beyond the mean-field analysis, a matrix product state (MPS) with incommensurate periodicity is applied to detect phase transitions accompanied with periodicity change, where the incommensurate MPS is generated by acting local-spin-rotation operators with the incommensurate periodicity on a uniform MPS. As a commensurate/commensurate change, we calculate the partial ferro -- perfect ferro phase transition in the $S=1/2$ Heisenberg model and its critical exponent of the magnetization curve. As a commensurate/incommensurate change, we calculate the S=1 Heisenberg model with bilinear and biquadratic interactions which has periodicity change in the spin-spin correlation function.