Incommensurate Matrix Product State for Quantum Spin Systems

TL;DR

This paper introduces an incommensurate matrix product state (MPS) that incorporates spin rotations to better capture incommensurate correlations in quantum spin chains, breaking translational and rotational symmetries.

Contribution

The authors develop a novel incommensurate MPS method by applying site-dependent spin rotations, improving the description of incommensurate correlations in quantum spin systems.

Findings

Reduces variational energy compared to uniform MPS

Captures incommensurate properties of spin correlations

Breaks translational and rotational symmetries in optimized states

Abstract

We introduce a matrix product state (MPS) with an incommensurate periodicity by applying the spin-rotation operator of each site to a uniform MPS in the thermodynamic limit. The spin rotations decrease the variational energy with accompanying translational symmetry breaking and the rotational symmetry breaking in the spin space even if the Hamiltonian has the both symmetries. The optimized pitch of rotational operator reflects the commensurate/incommensurate properties of spin-spin correlation functions in the $S=1/2$ Heisenberg chain and the $S=1/2$ ferro-antiferro zigzag chain.