Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems

Abstract

The pairwise entanglement, measured by concurrence and geometric phase in $d=2,3$-dimensional free-fermion lattice systems have been studied for the ground state in this paper. Their derivation with respect to the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-fermion model that both concurrence and geometric phase shows the intimate connection with the correlation functions. The possible relation between concurrence and geometric phase has been also discussed.

7+pages, EPJD style

References in corpus (35)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Quantum Communication Through an Unmodulated Spin Chain
• Ground state overlap and quantum phase transitions
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Quantum Entanglement in Fermionic Lattices
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Geometric phases and criticality in spin chain systems
• Magnetic Susceptibility as a Macrosopic Entaglement Witness
• Entanglement entropy and the Berry phase in solid states
• Generalized Jordan-Wigner Transformations
• Spin Hall effect and Berry phase in two dimensional electron gas
• Entanglement and Quantum Phase Transition Revisited
• Algebraic Approach to Interacting Quantum Systems
• Quantum information and physics: some future directions
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Demonstration of Quantum Error Correction using Linear Optics
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Bose-Fermi Transformation In Three Dimensional Space
• Conserved Spin and Orbital Angular Momentum Hall Current in a Two-Dimensional Electron System with Rashba and Dresselhaus Spin-orbit Coupling
• The effect of in-plane magnetic field on the spin Hall effect in Rashba-Dresselhaus system
• Entanglement induced in spin-1/2 particles by a spin chain near its critical points
• Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition
• Geometric phases and quantum phase transitions
• Degeneracy and Consistency Condition of Berry phases: Gap Closing under the Twist
• Quantum information storage and state transfer based on spin systems
• Geometric phases and criticality in spin systems
• Geometric Phase and Quantum Phase Transition in the Lipkin-Meshkov-Glick model
• Entanglement and quantum phase transitions
• Topological quantum phase transition and the Berry phase near the Fermi surface in hole-doped quantum wells
• Geometric Phase and Quantum Phase Transition : Two-Band Model
• Quantumness without quantumness: entanglement as classical correlations in higher dimensions

Cited by in corpus (2)

• Geometry of quantum phase transitions
• Quantum renormalization group approach to geometric phases in spin chains