Geometric phases and criticality in spin systems

Abstract

A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study regions of criticality without having to undergo a quantum phase transition. As a concrete example a spin-1/2 chain with XY interactions is presented and the corresponding geometric phases are analyzed. The generalization of these results to the case of an arbitrary spin system provides an explanation for the existence of such a relation.

12 pages, 4 figures

References in corpus (9)

• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Counterflow Superfluidity of Two-Species Ultracold Atoms in a Commensurate Optical Lattice
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Geometric phases and criticality in spin chain systems
• Entanglement entropy and the Berry phase in solid states
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Effective three-body interactions in triangular optical lattices
• Optimal Topological Test for Degeneracies of Real Hamiltonians

Cited by in corpus (18)

• Geometry of quantum phase transitions
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Geometric phases and quantum phase transitions in open systems
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Quantum Information Metric and Berry Curvature from a Lagrangian Approach
• Spin crossover: the quantum phase transition induced by high pressure
• A Geometrical Approach towards Entanglement
• Geometric Phase and Quantum Phase Transition : Two-Band Model
• Geometric Phases and Critical Phenomena in a Chain of Interacting Spins
• Finite-Temperature Scaling of Magnetic Susceptibility and Geometric Phase in the XY Spin Chain
• Path dependent scaling of geometric phase near a quantum multi-critical point
• Dynamics of geometric phase in the adiabatic limit of quantum phase transition
• An Interplay of Topology and Quantized Geometric Phase for two Different Symmetry-Class Hamiltonians
• The geometric phase and the dynamics of quantum phase transition induced by a linear quench
• Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench
• Geometric phase and multipartite entanglement of Rydberg atom chains
• Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems
• Quantum phases and dynamics of geometric phase in a quantum spin chain system under linear quench