Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions
Abstract
The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetry remains unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-1/2 and spin-$1$ chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as ν= 0.60 ± 0.02, distinct from the Gaussian value 1/2 but consistent with the perturbative renormalization-group value. We further estimate the dynamical critical exponent to be z = 1.986 ± 0.005 from the lowest neutral excitation gap and z = 1.955 ± 0.021 from the longitudinal spin correlations. The results z < 2 are incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.
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BibTeX
@misc{shimomura2026interacting,
title = {{Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions}},
author = {Mutsumi Shimomura and Kohei Kawabata},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06682},
eprint = {2610.06682},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06682},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions
AU - Mutsumi Shimomura
AU - Kohei Kawabata
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.06682
UR - https://arxiv.org/abs/2610.06682
AB - The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetry remains unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-1/2 and spin-$1$ chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as ν= 0.60 ± 0.02, distinct from the Gaussian value 1/2 but consistent with the perturbative renormalization-group value. We further estimate the dynamical critical exponent to be z = 1.986 ± 0.005 from the lowest neutral excitation gap and z = 1.955 ± 0.021 from the longitudinal spin correlations. The results z < 2 are incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.
ER -