Entanglement quantifiers and phase transitions
arXiv:quant-ph/0510132 · doi:10.1088/1367-2630/8/10/260
Abstract
By the topological argument that the identity matrix is surrounded by a set of separable states follows the result that if a system is entangled at thermal equilibrium for some temperature, then it presents a phase transition (PT) where entanglement can be viewed as the order parameter. However, analyzing different entanglement measures in the 2-qubit context, we see that different entanglement quantifiers can indicate different orders for the same PT. Examples are given for different Hamiltonians. Moving to the multipartite context we show necessary and sufficient conditions for a family of entanglement monotones to attest quantum phase transitions.
4 pages, 7 figures. v2: references, text, and figures improved. v3: references added, 5 pages, 7 figures, text improved
References in corpus (21)
- The logarithmic negativity: A full entanglement monotone that is not convex
- Quantum Phase Transitions and Bipartite Entanglement
- Entanglement versus Correlations in Spin Systems
- Diverging Entanglement Length in Gapped Quantum Spin Systems
- Detecting Genuine Multipartite Entanglement with Two Local Measurements
- Sudden Death of Entanglement: Classical Noise Effects
- Sudden Death of Entanglement of Two Jaynes-Cummings Atoms
- Localizable Entanglement
- Quantifying Entanglement with Witness Operators
- Direct measurement of finite-time disentanglement induced by a reservoir
- Studying quantum spin systems through entanglement estimators
- High Temperature Macroscopic Entanglement
- All entangled states are useful for information processing
- Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
- Entanglement Scaling in the One-Dimensional Hubbard Model at Criticality
- Entanglement flow in multipartite systems
- Are all maximally entangled states pure?
- Equilibrium entanglement vanishes at finite temperature
- Entanglement in thermal equilibrium states
- Entanglement as a quantum order parameter
- Spectral Conditions on the State of a Composite Quantum System Implying its Separability