Limit cycles in quantum theories

TL;DR

This paper explores the occurrence of renormalization group limit cycles in quantum Hamiltonians, presenting a simple, analytically solvable model that exhibits such cycles, contrasting with the fixed points common in classical critical phenomena.

Contribution

It introduces the simplest known quantum Hamiltonian model that displays renormalization group limit cycles, expanding understanding of quantum critical behavior.

Findings

Identifies a discrete Hamiltonian with two couplings exhibiting limit cycles.

Provides an analytical solution for the non-perturbative renormalization group.

Connects the discrete model to a previously proposed continuum Hamiltonian.

Abstract

Renormalization group limit cycles may be a commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience to date with classical models of critical points, where fixed points are far more common. We discuss the simplest model Hamiltonian identified to date that exhibits a renormalization group limit cycle. The model is a discrete Hamiltonian with two coupling constants and a non-perturbative renormalization group that involves changes in only one of these couplings and is soluble analytically. The Hamiltonian is the discrete analog to a continuum Hamiltonian previously proposed by us.