Scaling of geometric phase versus band structure in cluster-Ising models

Abstract

We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be ordinary phases with local order parameter or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z = 1 or z = 2 are found. Quantum phase transitions are analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. In particular, we quantify the scaling behavior of the geometric phase in relation with the topology and low energy properties of the band structure of the system.

References in corpus (6)

• Quantum Criticality
• Geometric phases and criticality in spin chain systems
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Floquet engineering of long-range p-wave superconductivity
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Experimental implementation of adiabatic passage between different topological orders

Cited by in corpus (12)

• Geometry of quantum phase transitions
• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• Mesoscopic Vortex-Meissner currents in ring ladders
• Topological pumping of quantum correlations
• Decoherence and relaxation of topological states in extended quantum Ising models
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• The global phase diagram of the cluster-XY spin chain with dissipation
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Quantum cluster kink and ring frustration
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions