Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model
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 Z2 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 Z2 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 Z2 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 Z2 symmetry breaking. The framework provides an ideal platform for experimentally controlling symmetries and investigating associated physical phenomena.
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