Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model

TL;DR

This paper explores how tuning anisotropic couplings in the coupled-top model controls symmetries and quantum phase transitions, revealing distinct critical behaviors and degeneracies associated with $Z_2$ and U(1) symmetries.

Contribution

It introduces a method to manipulate symmetries in the coupled-top model and analyzes the resulting quantum critical phenomena and degeneracies.

Findings

Mean-field phase diagram has five phases with different symmetry breakings.

U(1) symmetry breaking leads to Goldstone modes and infinite degeneracy.

Critical points exhibit diverging quantum fluctuations and entanglement entropy.

Abstract

We investigate the anisotropic coupled-top model, which describes the interactions between two large spins along both $x-$ and $y-$directions. By tuning anisotropic coupling strengths along distinct directions, we can manipulate the system's symmetry, inducing either discrete $Z_2$ or continuous U(1) symmetry. In the thermodynamic limit, the mean-field phase diagram is divided into five phases: the disordered paramagnetic phase, the ordered ferromagnetic or antiferromagnetic phases with symmetry breaking along either $x-$ or $y-$direction. This results in a double degeneracy of the spin projections along the principal direction for $Z_2$ symmetry breaking. When U(1) symmetry is broken, infinite degeneracy associated with the Goldstone mode emerges. Beyond the mean-field ansatz, at the critical points, the energy gap closes, and both quantum fluctuations and entanglement entropy diverge, signaling the onset of second-order quantum phase transitions. These critical behaviors consistently support the universality class of $Z_2$ symmetry. Contrarily, when U(1) symmetry is broken, the energy gap vanishes beyond the critical points, yielding a novel exponent of 1, rather than 1/2 for $Z_2$ symmetry breaking. The framework provides an ideal platform for experimentally controlling symmetries and investigating associated physical phenomena.