Spontaneous breaking of U(1) symmetry at zero temperature in one dimension

Abstract

The Hohenberg--Mermin--Wagner theorem states that there is no spontaneous breaking of continuous symmetries in spatial dimensions $d\le 2$ at finite temperature. At zero temperature, the classical/quantum mapping further implies the absence of continuous symmetry breaking in one dimension, which is also known as Coleman's theorem in the context of relativistic quantum field theories. Except for the classic example of the Heisenberg ferromagnet and its variations, there has been no known counterexample to the theorem. In this Letter, we discuss new examples that display spontaneous breaking of a U(1) symmetry at zero temperature, although the order parameter does not commute with the Hamiltonian unlike the Heisenberg ferromagnet. We argue that a more general condition for this behavior is that the Hamiltonian is frustration-free.

5 pages, 1 figure + Supplementary Material (16 pages and 3 figures)

References in corpus (5)

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• Spectral statistics in constrained many-body quantum chaotic systems
• Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions
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Cited by in corpus (8)

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• Quasi-local Frustration-Free Free Fermions
• Frustration-free free fermions and beyond
• Spontaneous continuous-symmetry breaking and tower of states in a comb chain
• Exact steady states and fragmentation-induced relaxation in the no-passing asymmetric simple exclusion process