Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking
arXiv:1408.1691 · doi:10.1016/j.aop.2015.07.008
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.
41 pages, 3 figures, published version
References in corpus (7)
- Counting rule for Nambu-Goldstone modes in nonrelativistic systems
- Effects of symmetry breaking in finite quantum systems
- Counting rule of Nambu-Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach
- Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry
- Dispersion relations of Nambu-Goldstone modes at finite temperature and density
- On the relation between decoherence and spontaneous symmetry breaking
- Nambu-Goldstone bosons and the Higgs mechanism without Lorentz invariance: Analysis based on constrained-system theory
Cited by in corpus (9)
- An Introduction to Spontaneous Symmetry Breaking
- Spontaneous symmetry breaking and Nambu-Goldstone modes in open classical and quantum systems
- The Tower of States and the Entanglement Spectrum in a Coplanar Antiferromagnet
- Effective field theory and the scattering process for magnons in the ferromagnet, antiferromagnet, and ferrimagnet
- Interpolating relativistic and non-relativistic Nambu-Goldstone and Higgs modes
- Spontaneous breaking of U(1) symmetry at zero temperature in one dimension
- Stability and Absence of a Tower of States in Ferrimagnets
- Magnon-induced long-range correlations and their neutron-scattering signature in quantum magnets
- Spontaneous continuous-symmetry breaking and tower of states in a comb chain