Bloch Theory for Periodic Block Spin Transformations

TL;DR

This paper develops a Bloch/Floquet framework to analyze operators arising in block spin renormalization group methods, aiding the study of symmetry breaking in weakly interacting many Boson systems on lattices.

Contribution

It introduces a novel Bloch/Floquet approach tailored for bounding translation-invariant operators on sublattices in the context of block spin transformations.

Findings

Constructed a Bloch/Floquet framework for these operators

Provided bounds for operators acting on sublattices

Enhanced understanding of symmetry breaking mechanisms

Abstract

Block spin renormalization group is the main tool used in our program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It generates operators, like the fluctuation integral covariance, that act on some lattice but are translation invariant only with respect to a proper sublattice. This paper constructs a Bloch/Floquet framework that is appropriate for bounding such operators.