Decay of correlations in 2D quantum systems with continuous symmetry

TL;DR

This paper proves a general theorem on the algebraic decay of correlations in 2D quantum lattice systems with continuous symmetries, with applications to several important models.

Contribution

It introduces a broad, unified proof of correlation decay for various 2D quantum models with continuous symmetry, extending previous results.

Findings

Proves algebraic decay of correlations in 2D quantum systems with continuous symmetry.

Applies the main theorem to Heisenberg, Hubbard, and t-J models.

Includes results for certain models of random loops.

Abstract

We study a large class of models of two-dimensional quantum lattice systems with continuous symmetries, and we prove a general McBryan-Spencer-Koma-Tasaki theorem concerning algebraic decay of correlations. We present applications of our main result to the Heisenberg-, Hubbard-, and t-J models, and to certain models of random loops.