Spatial reflection and renormalization group flow of quantum many-body systems with matrix product state representation

TL;DR

This paper explores how spatial reflection properties and renormalization group flows in quantum many-body systems can be understood and characterized using matrix product state representations, revealing conservation rules and fixed point behaviors.

Contribution

It introduces a conservation rule for reflectional MPS pairs under RG transformations and analyzes fixed points, extending the understanding of symmetry in quantum many-body systems.

Findings

Conservation rule for reflectional MPS pairs under RG

Properties of fixed points in RG flows

Existence of similar reflection rules in DMRG target states

Abstract

The property of quantum many-body systems under spatial reflection and the relevant physics of renormalization group (RG) procedure are revealed. By virtue of the matrix product state (MPS) representation, various attributes for translational invariant systems associated with spatial reflection are manifested. We demonstrate subsequently a conservation rule of the conjugative relation for reflectional MPS pairs under RG transformations and illustrate further the property of the fixed points of RG flows. Finally, we show that a similar rule exists with respect to the target states in the density matrix renormalization group algorithm.