Critical exponents of block-block mutual information in one-dimensional infinite lattice systems

TL;DR

This paper investigates the critical behavior of block-block mutual information in one-dimensional infinite lattice quantum systems, revealing its relation to phase transitions, conformal field theory, and universality classes through numerical analysis.

Contribution

It introduces a numerical method to analyze the critical exponents of block-block mutual information in 1D quantum lattice models, connecting mutual information behavior to conformal field theory and universality classes.

Findings

Mutual information exhibits singular behavior at quantum critical points.

Logarithmic scaling of mutual information yields the central charge of the CFT.

Critical exponents of mutual information depend on universality class and block size.

Abstract

We study the mutual information between two lattice-blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum $q$-state Potts model and transverse field spin-$1/2$ XY model are considered numerically by using the infinite matrix product state (iMPS) approach. As a system parameter varies, block-block mutual informations exhibit a singular behavior that enables to identify critical points for quantum phase transition. As happens with the von Neumann entanglement entropy of a single block, at the critical points, the block-block mutual information between the two lattice-blocks of $\ell$ contiguous sites equally partitioned in a lattice-block of $2\ell$ contiguous sites shows a logarithmic leading behavior, which yields the central charge $c$ of the underlying conformal field theory. As the separation between the two lattice-blocks increases, the mutual information reveals a consistent power-law decaying behavior for various truncation dimensions and lattice-block sizes. The critical exponent of block-block mutual information in the thermodynamic limit is estimated by extrapolating the exponents of power-law decaying regions for finite truncation dimensions. For a given lattice-block size $\ell$, the critical exponents for the same universality classes seem to have very close values each other. Whereas the critical exponents have different values to a degree of distinction for different universality classes. As the lattice-block size becomes bigger, the critical exponent becomes smaller.