Off-Diagonal Density Profiles and Conformal Invariance

TL;DR

This paper uses conformal methods to calculate off-diagonal density profiles at the critical point for various boundary conditions, aiding the study of critical behavior in finite systems.

Contribution

It provides a conformal field theory approach to compute off-diagonal density profiles for different boundary conditions at criticality, validated by Ising model results.

Findings

Conformal profiles match direct calculations for the 2D Ising model.

Profiles help eliminate regular contributions in finite-size scaling.

Method applies to various boundary conditions.

Abstract

Off-diagonal profiles of local densities (e.g. order parameter or energy density) are calculated at the bulk critical point, by conformal methods, for different types of boundary conditions (free, fixed and mixed). Such profiles, which are defined by a non-vanishing matrix element of the appropriate operator between the ground state and the corresponding lowest excited state of the strip Hamiltonian, enter into the expression of two-point correlation functions on a strip. They are of interest in the finite-size scaling study of bulk and surface critical behaviour since they allow the elimination of regular contributions. The conformal profiles, which are obtained through a conformal transformation of the correlation functions from the half-plane to the strip, are in agreement with the results of a direct calculation, for the energy density of the two-dimensional Ising model.