Geometric phases and quantum phase transitions

Abstract

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed so-called "criticality of geometric phase", in which geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of geometric quantities may open attractive avenues and fruitful dialog between different scientific communities.

Invited review article for IJMPB; material covered till June 2007; 10 pages

References in corpus (39)

• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Holonomic Quantum Computation
• Ground state overlap and quantum phase transitions
• Geometric quantum computation with NMR
• Geometric Manipulation of Trapped Ions for Quantum Computation
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Geometric phases for mixed states in interferometry
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Local entanglement and quantum phase transition in the Hubbard model
• Entanglement and quantum phase transition in the extended Hubbard model
• Implementation of universal quantum gates based on nonadiabatic geometric phases
• Kinematic approach to the mixed state geometric phase in nonunitary evolution
• Non-Abelian Berry connections for quantum computation
• Unconventional geometric quantum computation
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Geometric phases and criticality in spin chain systems
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Transverse force on a quantized vortex in a superfluid
• Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems
• Critical Property of Geometric Phase in the Dicke Model
• Quantum Dynamical Model for Wave Function Reduction in Classical and Macroscopic Limits
• Loschmidt Echo and Berry phase of the quantum system coupled to the XY spin chain: Proximity to quantum phase transition
• Measurement of geometric phase for mixed states using single photon interferometry
• Berry phase in a composite system
• Nonadiabatic noncyclic geometric phase of a spin-1/2 particle subject to an arbitrary magnetic field
• Nonadiabatic noncyclic geometric phase and ensemble average spectrum of conductance in disordered mesoscopic rings with spin-orbit coupling
• Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition
• Geometric phases induced in auxiliary qubits by many-body systems near its critical points
• Quantum Critical Dynamics of A Qubit Coupled to An Isotropic Lipkin-Meshkov-Glick Bath
• Geometric Phase and Quantum Phase Transition in the Lipkin-Meshkov-Glick model
• Entanglement of a qubit coupled to a resonator in the adiabatic regime
• Vanishing environment-induced decoherence
• Berry Phases and Quantum Phase Transitions

Cited by in corpus (26)

• Geometry of quantum phase transitions
• Experimental Observation of Tensor Monopoles with a Superconducting Qudit
• Quantum Fidelity and Thermal Phase Transitions
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Geometric phases and quantum phase transitions in open systems
• Geometric phase and quantum phase transition in an inhomogeneous periodic XY spin-1/2 model
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Spin crossover: the quantum phase transition induced by high pressure
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Identifying non-Hermitian critical points with quantum metric
• Classical analog of the quantum metric tensor
• Operator Quantum Geometric Tensor and Quantum Phase Transitions
• Geometric Phase and Quantum Phase Transition : Two-Band Model
• Finite-Temperature Scaling of Magnetic Susceptibility and Geometric Phase in the XY Spin Chain
• Non-Markovian dynamics of mixed-state geometric phase of dissipative qubits
• Exact scaling of geometric phase and fidelity susceptibility and their breakdown across the critical points
• Measuring geometric phases with a dynamical quantum Zeno effect in a Bose-Einstein condensate
• Path dependent scaling of geometric phase near a quantum multi-critical point
• Quantum phase transition without gap opening
• Geometric phases and cyclic isotropic cosmologies
• Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
• Geometric phase in the Kitaev honeycomb model and scaling behavior at critical points
• Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Quantum Geometry of Finite XY Chains: A Comparison of Neveu-Schwarz and Ramond Sectors