Generalized mean field description of entanglement in dimerized spin systems

Abstract

We discuss a generalized self-consistent mean field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin 1/2 systems with anisotropic ferromagnetic-type XY and XYZ couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single spin MF. Its phase diagram differs significantly from that of the latter, exhibiting (Sz) parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration, the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.

arXiv comment13 pages, 9 figures. Final version

References in corpus (41)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Area laws for the entanglement entropy - a review
• Entanglement of a Pair of Quantum Bits
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement in a simple quantum phase transition
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• A class of quantum many-body states that can be efficiently simulated
• Matrix product states represent ground states faithfully
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Continuum variational and diffusion quantum Monte Carlo calculations
• Renormalization and tensor product states in spin chains and lattices
• Quantum Spin Dimers from Chiral Dissipation in Cold-Atom Chains
• Quantum and classical criticality in a dimerized quantum antiferromagnet
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• Theory of ground state factorization in quantum cooperative systems
• Separability and ground state factorization in quantum spin systems
• New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
• Correlated cluster mean-field theory for spin systems
• Entanglement of finite cyclic chains at factorizing fields
• Thermally activated Peierls dimerization in ferromagnetic spin chains
• Ground-state factorization and quantum phase transition in dimerized spin chains
• Factorization and entanglement in general XYZ spin arrays in non-uniform transverse fields
• Variational ground states of 2D antiferromagnets in the valence bond basis
• Exact results on spin dynamics and multiple quantum dynamics in alternating spin-1/2 chains with XY-Hamiltonian at high temperatures
• In-plane dipole coupling anisotropy of a square ferromagnetic Heisenberg monolayer
• Separability and entanglement in finite dimer-type chains in general transverse fields
• Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz
• Description of thermal entanglement with the static path plus random-phase approximation
• The dimerized ferromagnetic Heisenberg chain
• Evaluation of ground state entanglement in spin systems with the random phase approximation
• Exact Solution of a Yang-Baxter Spin-1/2 Chain Model and Quantum Entanglement
• Spin systems with dimerized ground states
• Evaluation of pairwise entanglement in translationally invariant systems with the random phase approximation
• Dimensionality induced entanglement in macroscopic dimer systems

Cited by in corpus (5)

• Dimerized ground states in spin-S frustrated systems
• Non-transverse factorizing fields and entanglement in finite spin systems
• Quantum correlated cluster mean-field theory applied to the transverse Ising model
• Pair entanglement in dimerized spin-s chains
• Quantum Covariance Scalar Products and Efficient Estimation of Max-Ent Projections