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 $\nu =0.60\pm 0.02$, distinct from the Gaussian value $1/2$ but consistent with the perturbative renormalization-group value. We further estimate the dynamical critical exponent to be $z=1.986\pm 0.005$ from the lowest neutral excitation gap and $z=1.955\pm 0.021$ 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.

arXiv comment22 pages, 7 figures, 4 tables