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arXiv · 2610.06682

Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions

Mutsumi Shimomura·Kohei Kawabata
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Abstract

The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetries remain 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 $ν= 0.60 \pm 0.02$, distinct from the Gaussian value $0.5$ but consistent with the perturbative renormalization-group prediction. We further analyze the finite-size scaling of the lowest neutral excitation gap and obtain the dynamical critical exponent $z=1.986 \pm 0.005$. The result $z < 2$ is 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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Mutsumi Shimomura, Kohei Kawabata. 2026-10-05. Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions. https://arxiv.org/abs/2610.06682

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