Entanglement entropy for the long range Ising chain
arXiv:1207.3957 · doi:10.1103/PhysRevLett.109.267203
Abstract
We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi long range order, and one dominated by the long range interaction, with long range Néel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central-charges. In the phase with quasi long range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.
5 pages, all comments welcome
References in corpus (11)
- Matrix product states represent ground states faithfully
- From density-matrix renormalization group to matrix product states
- Entanglement spectrum in one-dimensional systems
- General entanglement scaling laws from time evolution
- Applying matrix product operators to model systems with long-range interactions
- Unusual Corrections to Scaling in Entanglement Entropy
- Anomalous Behavior of Spin Systems with Dipolar Interactions
- Tensor operators: constructions and applications for long-range interaction systems
- Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
- 1D Quantum Liquids with Power-Law Interactions: a Luttinger Staircase with Polar Molecules
- Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation