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This paper establishes rigorous mathematical proofs for spontaneous symmetry breaking in gapless, frustrated quantum systems using novel "quantum bottleneck" techniques analogous to many-body WKB methods. By demonstrating robust ferromagnetism in random-bond Ising models and proving metastability in false vacuum states, the work advances a formal classification of stable gapless quantum phases without relying on local interactions. These findings provide foundational theoretical tools for understanding complex quantum magnetism and phase stability beyond standard perturbative approaches.
Robust symmetry breaking in gapless quantum magnets
arXiv:2603.13212v2 Announce Type: replace-cross Abstract: We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous symmetry breaking of a finite group at some positive temperature. Additionally, the classical model need not be local in space, as long as it satisfies a quantum analogue of the Peierls condition. As an example of our technique, we establish robust ferromagnetism in random-bond Ising models in $d= 2$ dimensions with sufficiently biased random couplings, with weak transverse field. Our mathematical technique is based on establishing quantum bottlenecks, similar to a "many-body WKB" method for evaluating tunneling rates. Using these same methods, we provide new proofs of metastability and the slow decay of the false vacuum, applicable to gapless metastable states. Our work represents a first step towards a rigorous classification of stable gapless quantum phases.
Abstract:We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous symmetry breaking of a finite group at some positive temperature. Additionally, the classical model need not be local in space, as long as it satisfies a quantum analogue of the Peierls condition. As an example of our technique, we establish robust ferromagnetism in random-bond Ising models in $d= 2$ dimensions with sufficiently biased random couplings, with weak transverse field. Our mathematical technique is based on establishing quantum bottlenecks, similar to a "many-body WKB" method for evaluating tunneling rates. Using these same methods, we provide new proofs of metastability and the slow decay of the false vacuum, applicable to gapless metastable states. Our work represents a first step towards a rigorous classification of stable gapless quantum phases.
5+28 pages, 1+2 figures. Published version
Mathematical Physics (math-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
arXiv:2603.13212 [math-ph]
(or arXiv:2603.13212v2 [math-ph] for this version)
Phys. Rev. Lett. 137, 070405 (2026)
https://doi.org/10.1103/5ntb-ggcz DOI(s) linking to related resources
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