Entanglement in extended Hubbard models and quantum phase transitions

Abstract

The role of two-point and multipartite entanglement at quantum phase transitions (QPTs) in correlated electron systems is investigated. We consider a bond-charge extended Hubbard model exactly solvable in one dimension which displays various QPTs, with two (qubit) as well as more (qudit) on-site degrees of freedom involved. The analysis is carried out by means of appropriate measures of bipartite/multipartite quantum correlations. It is found that all transitions ascribed to two-point correlations are characterized by an entanglement range which diverges at the transition points. The exponent coincides with that of the correlation length at the transitions. We introduce the correlation ratio, namely, the ratio of quantum mutual information and single-site entanglement. We show that at T=0, it captures the relative role of two-point and multipartite quantum correlations at transition points, generalizing to qudit systems the entanglement ratio. Moreover, a finite value of quantum mutual information between infinitely distant sites is seen to quantify the presence of off-diagonal long-range order induced by multipartite entanglement.

14 pages, 8 figures, 2 tables

References in corpus (31)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• A computable measure of entanglement
• Entanglement in quantum critical phenomena
• Distributed Entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• General Monogamy Inequality for Bipartite Qubit Entanglement
• On the quantum, classical and total amount of correlations in a quantum state
• Quantum Phase Transitions and Bipartite Entanglement
• Quantum Entanglement in Fermionic Lattices
• Entanglement and quantum phase transition in the extended Hubbard model
• Local entanglement and quantum phase transition in the Hubbard model
• A potential multipartide entanglement measure
• A comparison of the entanglement measures negativity and concurrence
• Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
• Studying quantum spin systems through entanglement estimators
• Quantum phase transitions and quantum fidelity in free fermion graphs
• High Temperature Macroscopic Entanglement
• Entanglement Scaling in the One-Dimensional Hubbard Model at Criticality
• Divergence of the entanglement range in low dimensional quantum systems
• Linking entanglement and quantum phase transitions via density functional theory
• Two-Point Versus Multipartite Entanglement in Quantum Phase Transitions
• Superconductivity in an exactly solvable Hubbard model with bond-charge interaction
• Single-Site Entanglement of Fermions at a Quantum Phase Transition
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Anomalous flux quantization in a Hubbard ring with correlated hopping
• Multipartite Entanglement Measure
• Single-site entanglement at superconductor-insulator transition in the Hirsch model
• Entanglement of eta-pairing state with off-diagonal long-range order
• Finite-temperature properties of the Hubbard chain with bond-charge interaction
• Spin-fermion mappings for even Hamiltonian operators

Cited by in corpus (22)

• Dzyaloshinskii-Moriya Interaction and Anisotropy effects on the Entanglement of Heisenberg Model
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems
• Floquet dynamical phase transition and entanglement spectrum
• Quantum discord and classical correlations in the bond-charge Hubbard model: quantum phase transitions, ODLRO and violation of the monogamy property for discord
• Incommmensurability and unconventional superconductor to insulator transition in the Hubbard model with bond-charge interaction
• Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model
• Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
• Thermal entanglement witness for materials with variable local spin lengths
• Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model
• Machine Learning Phase Diagram in the Half-filled One-dimensional Extended Hubbard Model
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Momentum-space analysis of multipartite entanglement at quantum phase transitions
• Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states
• Phase separation in fermionic systems with particle-hole asymmetry
• Quantum phase transition and entanglement in Li atom system
• The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field
• Characterization of photoexcited states in the half-filled one-dimensional extended Hubbard model assisted by machine learning
• Anderson-Mott transition in a disordered Hubbard model with correlated hopping
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Quantum phase transitions in the Kondo-necklace model: Perturbative continuous unitary transformation approach
• Exploring Entanglement Spectrum and Phase Diagram in multi-electron Quantum Dot Chains