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

The Hohenberg-Mermin-Wagner theorem is the no-go theorem for the spontaneous breaking of continuous symmetries in spatial dimensions d>1 at finite temperature. The classical/quantum mapping implies the absence of continuous symmetry breaking in one dimension at zero temperature, 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 work, 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 the Hamiltonian being frustration-free.

*The work of H.W. is supported by JSPS KAKENHI Grant No.JP20H01825 and JP21H01789. The work of H.K. is supported by JSPS KAKENHI Grand No.JP23H01093, No.JP23H01093, and MEXT KAKENHI Grant-in-Aid for Transformative Research Areas A "Extreme Universe" (KAKENHI Grant No. JP21H05191). The work of J.Y.L is supported by a faculty startup grant at the University of Illinois, Urbana-Champaign. This work was initiated in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452.

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Bulletin of the American Physical Society

2024 APS March Meeting

Monday–Friday, March 4–8, 2024; Minneapolis & Virtual

Session M14: Nonergodic and Anomalous Quantum Dynamics

Abstract: M14.00013 : Spontaneous breaking of U(1) symmetry at zero temperature in one dimension*

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