Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking

TL;DR

This paper establishes precise criteria under which quantum fluctuations are absent after spontaneous symmetry breaking, explaining why certain systems like ferromagnets exhibit classical groundstates with minimal quantum effects.

Contribution

It provides a detailed set of conditions that determine when quantum fluctuations are suppressed in symmetry-broken systems, extending understanding beyond the commutation of order parameters with the Hamiltonian.

Findings

The classical groundstate of a ferromagnet coincides with its quantum groundstate.

Absence of quantum fluctuations correlates with fewer Nambu-Goldstone modes.

Criteria for the absence of quantum fluctuations include conditions beyond the commutation of the order parameter with the Hamiltonian.

Abstract

The lowest-energy state of a macroscopic in which symmetry is spontaneously broken, is a very stable wavepacket centered around a spontaneously chosen, classical direction in symmetry space. However, for a Heisenberg ferromagnet the quantum groundstate is exactly the classical groundstate. This coincides with other exceptional properties of the ferromagnet, including spontaneous time-reversal symmetry breaking, a reduced number of Nambu-Goldstone modes and the absence of a thin spectrum (Anderson tower of states). Recent discoveries of other non-relativistic systems with fewer Nambu-Goldstone modes suggest these specialties apply there as well. I establish precise criteria for the absence of quantum fluctuations and all the other features. In particular, it is not sufficient that the order parameter commute with the Hamiltonian. It leads to a measurably larger coherence time of superpositions in small but macroscopic systems.