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 $Z_2$ 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.

21 pages, 3 figures

References in corpus (19)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Some remarks on 'superradiant' phase transitions in light-matter systems
• Quantum phase transition in the Dicke model with critical and non-critical entanglement
• Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
• Emergent Universality in a Quantum Tricritical Dicke Model
• Chaos and quantum scars in a coupled top model
• Frustrated Superradiant Phase Transition
• Criticality-Enhanced Quantum Sensing with a Parametric Superconducting Resonator
• Entanglement resonance in the asymmetric quantum Rabi model
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Dynamical route to ergodicity and quantum scarring in kicked coupled top
• Entanglement phase transitions in non-Hermitian Floquet systems
• Quantum walk on the Bloch sphere
• Using a Feedback-Based Quantum Algorithm to Analyze the Critical Properties of the ANNNI Model Without Classical Optimization
• Quantum phase transitions in the triangular coupled-top model
• Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
• Dynamical phase transitions in $XY$ model: a Monte Carlo and mean-field theory study
• Quantum Phase Transitions in a Generalized Dicke Model