Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems

TL;DR

This paper demonstrates that continuous symmetry breaking can occur in one-dimensional quantum systems with long-range interactions, revealing a new universality class and providing insights relevant to ion-trap experiments.

Contribution

The study identifies conditions for continuous symmetry breaking in 1D long-range interacting systems and uncovers a new universality class for the phase transition.

Findings

CSB occurs for decay exponent α less than a critical value.

The phase transition is mediated by conformal symmetry breaking.

Numerical results agree with analytical predictions.

Abstract

Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with $U(1)$ symmetry and power-law interactions $V(r)\sim1/r^\alpha$, directly relevant to ion-trap experiments. Using bosonization and renormalization group theory, we find CSB for $\alpha$ smaller than a critical exponent $\alpha_c(\le 3)$ depending on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal symmetry due to long-range interactions, and is described by a new universality class akin to the Berezinskii-Kosterlitz-Thouless transition. Our analytical findings are in good agreement with a numerical calculation. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.