Flow Equations and Normal Ordering

TL;DR

This paper explores flow equations with adaptive normal ordering based on the Hamiltonian's one-particle energy, demonstrating convergence to stable phases and the emergence of symmetry breaking below critical temperatures.

Contribution

It introduces a method of normal ordering tailored to the Hamiltonian's one-particle energy, enhancing the analysis of phase stability and symmetry breaking in flow equations.

Findings

Flow equations with adjusted normal ordering converge to stable phases.

Symmetry breaking occurs below the critical temperature when starting from symmetric Hamiltonians.

Nearly always yields symmetry breaking, indicating robustness of the method.

Abstract

In this paper we consider flow-equations where we allow a normal ordering which is adjusted to the one-particle energy of the Hamiltonian. We show that this flow converges nearly always to the stable phase. Starting out from the symmetric Hamiltonian and symmetry-broken normal ordering nearly always yields symmetry breaking below the critical temperature.