Competing symmetry breaking and topology in quantum spin chains
Abstract
We investigate how spontaneous symmetry breaking and symmetry-protected topology compete and cooperate in one-dimensional quantum spin-1/2 systems. We introduce two families of local Hamiltonians with ℤ 2×ℤ 2×ℤT2 symmetry which host a zoo of broken-symmetry phases with and without gapless boundary spins, namely, six long-range-ordered gapped phases that differ by their ℤ 2-symmetry-breaking patterns (FM x,y,z and Neel x,y,z), their partner symmetry-protected topological phases (FMSPTx,y and NeelSPTx,y), and two gapless phases (gFM z and gNeel z) with incommensurate ℤT2-breaking magnetic long-range order and central charge c=1. Direct transitions between competing gapped phases can be continuous or weakly first order. We demonstrate that continuous phase transition lines have exotic critical properties. For example, a line of deconfined quantum critical points (between the Neel x and Neel y phases) described by Tomonaga-Luttinger liquid theory is terminated by the gFM z phase at a Lifshitz tricritical point which exhibits spontaneous breaking of the continuous U(1) symmetry despite the locality and one-dimensionality of the Hamiltonian, contrary to a naive expectation from the Hohenberg-Mermin-Wagner-Coleman theorem. Furthermore, critical lines between symmetry-protected topological phases with different ℤ 2-symmetry breaking (e.g., NeelSPTx and NeelSPTy) additionally retain low-energy boundary degrees of freedom, realizing symmetry-enriched criticality (or a gapless SPT phase). Our results reveal unconventional mechanisms by which competing symmetry breaking and topology generate ordered critical phases and multicriticality.
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BibTeX
@misc{rey2026competing,
title = {{Competing symmetry breaking and topology in quantum spin chains}},
author = {Anthony Rey and Ömer M. Aksoy and Claudio Chamon and Akira Furusaki and Christopher Mudry},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10694},
eprint = {2610.10694},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10694},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Competing symmetry breaking and topology in quantum spin chains
AU - Anthony Rey
AU - Ömer M. Aksoy
AU - Claudio Chamon
AU - Akira Furusaki
AU - Christopher Mudry
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10694
UR - https://arxiv.org/abs/2610.10694
AB - We investigate how spontaneous symmetry breaking and symmetry-protected topology compete and cooperate in one-dimensional quantum spin-1/2 systems. We introduce two families of local Hamiltonians with ℤ^ _2×ℤ^ _2×ℤ^T_2 symmetry which host a zoo of broken-symmetry phases with and without gapless boundary spins, namely, six long-range-ordered gapped phases that differ by their ℤ^ _2-symmetry-breaking patterns (FM^ _x,y,z and Neel^ _x,y,z), their partner symmetry-protected topological phases (FM^SPT_x,y and Neel^SPT_x,y), and two gapless phases (gFM^ _z and gNeel^ _z) with incommensurate ℤ^T_2-breaking magnetic long-range order and central charge c=1. Direct transitions between competing gapped phases can be continuous or weakly first order. We demonstrate that continuous phase transition lines have exotic critical properties. For example, a line of deconfined quantum critical points (between the Neel^ _x and Neel^ _y phases) described by Tomonaga-Luttinger liquid theory is terminated by the gFM^ _z phase at a Lifshitz tricritical point which exhibits spontaneous breaking of the continuous U(1) symmetry despite the locality and one-dimensionality of the Hamiltonian, contrary to a naive expectation from the Hohenberg-Mermin-Wagner-Coleman theorem. Furthermore, critical lines between symmetry-protected topological phases with different ℤ^ _2-symmetry breaking (e.g., Neel^SPT_x and Neel^SPT_y) additionally retain low-energy boundary degrees of freedom, realizing symmetry-enriched criticality (or a gapless SPT phase). Our results reveal unconventional mechanisms by which competing symmetry breaking and topology generate ordered critical phases and multicriticality.
ER -