Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point

@article{Alba2012EntanglementSO,
  title={Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point},
  author={Vincenzo Alba and Masudul Haque and Andreas M. Laeuchli},
  journal={arXiv: Strongly Correlated Electrons},
  year={2012}
}
We study the entanglement spectrum (ES) of a finite XXZ spin 1/2 chain in the limit \Delta -> -1^+ for both open and periodic boundary conditions. At \Delta=-1 (ferromagnetic point) the model is equivalent to the Heisenberg ferromagnet and its degenerate ground state manifold is the SU(2) multiplet with maximal total spin. Any state in this so-called "symmetric sector" is an equal weight superposition of all possible spin configurations. In the gapless phase at \Delta>-1 this property is… 

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References

SHOWING 1-10 OF 65 REFERENCES
Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their
Permutation operators, entanglement entropy, and the XXZ spin chain in the limit \Delta \to-1^+
In this paper we develop a new approach to the investigation of the bi-partite entanglement entropy in integrable quantum spin chains. Our method employs the well-known replica trick, thus taking a
Nonlocal order in gapless systems: entanglement spectrum in spin chains.
We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high "entanglement energy" levels, from a
Entanglement spectra of complex paired superfluids.
TLDR
This work shows how the entanglement gap diverges as a model pairing function is approached, and using the Bardeen-Cooper-Schrieffer (BCS) form of the ground-state wave function on a cylinder, allows a simple and explicit exact solution for the ES.
Entanglement spectrum of one-dimensional extended Bose-Hubbard models
The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the blocklike nature of the reduced density matrix in number sectors and the
Entanglement gap and a new principle of adiabatic continuity.
We give a complete definition of the entanglement gap separating low-energy, topological levels from high-energy, generic ones, in the "entanglement spectrum" of fractional quantum Hall (FQH) states.
Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model
Recent studies have shown that logarithmic divergence of entanglement entropy as a function of the size of a subsystem is a signature of criticality in quantum models. We demonstrate that the
General relationship between the entanglement spectrum and the edge state spectrum of topological quantum states.
TLDR
This paper provides a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state, using the tools of boundary conformal field theory.
Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states.
TLDR
It is proposed that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order and is compared with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions.
Correlation length and unusual corrections to entanglement entropy
We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite
...
1
2
3
4
5
...