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 (8)

• 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 phase transitions and quantum fidelity in free fermion graphs
• Divergence of the entanglement range in low dimensional quantum systems
• Single-Site Entanglement of Fermions at a Quantum Phase Transition
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Multipartite Entanglement Measure

Cited by in corpus (7)

• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Incommmensurability and unconventional superconductor to insulator transition in the Hubbard model with bond-charge interaction
• Thermal entanglement witness for materials with variable local spin lengths
• Momentum-space analysis of multipartite entanglement at quantum phase transitions
• Phase separation in fermionic systems with particle-hole asymmetry
• Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states
• Quantum phase transition and entanglement in Li atom system