The Small Field Parabolic Flow for Bosonic Many-body Models: Part 1 - Main Results and Algebra

TL;DR

This paper analyzes the algebraic structure of the small field parabolic flow in weakly interacting bosonic systems, revealing symmetry breaking phenomena and setting the stage for further renormalization group analysis.

Contribution

It introduces the algebraic framework for the small field parabolic flow and details the initial algebraic step in the renormalization group process for bosonic models.

Findings

Identification of the algebraic structure of the flow

First algebraic step in renormalization group analysis

Insights into symmetry breaking in bosonic systems

Abstract

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Here we state the main result of this analysis, outline the strategy of the proof, which uses a renormalization group flow, and perform the first, algebraic, part of a renormalization group step.