Evidence for spontaneous breaking of a continuous symmetry at a non-conformal quantum critical point in one dimension

TL;DR

This paper provides evidence that a one-dimensional quantum spin chain can exhibit spontaneous continuous symmetry breaking at a critical point, defying typical expectations, with detailed analysis of its critical behavior and phase transition.

Contribution

It demonstrates spontaneous continuous symmetry breaking in a 1D quantum critical point, supported by matrix product state methods and renormalization group analysis, revealing a novel non-perturbative fixed point.

Findings

Finite perpendicular magnetization observed despite 1D constraints

Correlation functions exhibit true long-range order

Dynamical structure factor shows Bragg peak and gapless modes

Abstract

In this work, we present evidence for the spontaneous breaking of a continuous symmetry in a nearest-neighbour interacting spin-1 chain tuned to a quantum critical point at $T=0$ between two XY quasi-long-range order phases differing by the spontaneous breaking of a $\mathbb{Z}_2$ symmetry. Despite the one-dimensional nature of the system, which typically prevents such a continuous symmetry breaking due to the Hohenberg-Mermin-Wagner theorem, the presence of a Berry phase term in the quantum model allows us to observe, using matrix product state methods, a finite perpendicular magnetization. Moreover, the quasi-long-range decay of the correlation function becomes truly long-range order, and the dynamical structure factor displays a characteristic Bragg peak together with sharp gapless modes. Our results imply the quantum phase transition has an anomalous dimension of $\eta \simeq 1$ together with the dynamical critical exponent $z\simeq 3/2$, known from the Kardar-Parisi-Zhang universality class in one dimension. We perform a perturbative renormalization group calculation about the upper critical dimension $d_c=2$ that we could close at second loop order. We find an interacting fixed point with critical exponents distinct from the Ising ones. Together, our findings suggest the nature of the fixed point to be non-perturbative. We propose a field-theory that we believe to improve the quantitative results.