Entanglement of quantum spin systems: a valence-bond approach
arXiv:1011.6530 · doi:10.1142/S0217984911026620
Abstract
In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.
Proceedings of StatPhys 24 satellite conference in Hanoi; submitted for a special issue of Modern Physics Letters B
References in corpus (25)
- Concentrating Partial Entanglement by Local Operations
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- Quantum Noise as an Entanglement Meter
- Entanglement entropy of random quantum critical points in one dimension
- Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
- Boundary effects in the critical scaling of entanglement entropy in 1D systems
- Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
- Spin nematic correlations in bilinear-biquadratic S=1 spin chains
- Spin nematics in the bilinear-biquadratic S=1 spin chain
- Entanglement spectra of quantum Heisenberg ladders
- General Relation between Entanglement and Fluctuations in One Dimension
- Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
- Entanglement in a Valence-Bond-Solid State
- Ground state projection of quantum spin systems in the valence bond basis
- The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study
- Some formal results for the valence bond basis
- Valence Bond Entanglement Entropy
- Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders
- Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model
- Valence bond entanglement entropy of frustrated spin chains
- Hardcore dimer aspects of the SU(2) Singlet wavefunction
- Definitions of entanglement entropy of spin systems in the valence-bond basis
- Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain