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.

arXiv comment21 pages, 3 figures

References in corpus (45)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• On the Integrability of the Rabi Model
• Chaos and the Quantum Phase Transition in the Dicke Model
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Macroscopic quantum self-trapping and Josephson oscillations of exciton-polaritons
• Exact solvability of the quantum Rabi models within Bogoliubov operators
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Critical Quantum metrology with a finite-component quantum phase transition
• Universal scaling and critical exponents of the anisotropic quantum Rabi model
• Quantum critical metrology
• Quantum Phase Transition in the Finite Jaynes-Cummings Lattice Systems
• Critical and strong-coupling phases in one- and two-bath spin-boson models
• Some remarks on 'superradiant' phase transitions in light-matter systems
• Quantum phase transition in the Dicke model with critical and non-critical entanglement
• Quantum entanglement and fixed-point bifurcations
• Unified Superradiant phase transitions
• Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
• Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
• Signature of Chaos and Delocalization in a Periodically Driven Many Body System : An Out-of-Time-Order Correlation Study
• The Ising model in a light-induced quantized transverse field
• Emergent Universality in a Quantum Tricritical Dicke Model
• Chaos and quantum scars in a coupled top model
• Frustrated Superradiant Phase Transition
• Frequency-renormalized multipolaron expansion for the quantum Rabi model
• Criticality-Enhanced Quantum Sensing with a Parametric Superconducting Resonator
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• 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
• Rich phase diagram of quantum phases in the anisotropic subohmic spin-boson model
• Quantum phase transitions in the spin-boson model without the counterrotating terms
• 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
• Quantum Phase Transitions in a Generalized Dicke Model
• Dynamical phase transitions in $XY$ model: a Monte Carlo and mean-field theory study