Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
Abstract
We study the entanglement spectrum (ES) of a finite XXZ spin\frac{1}{2} chain in the limit Δ → 1^{+} for both open and periodic boundary conditions. At Δ = 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 socalled ‘symmetric sector’ is an equal weight superposition of all possible spin configurations. In the gapless phase at Δ > 1 this property is progressively lost as one moves away from the Δ = 1 point. We investigate how the ES obtained from the states in this manifold reflects this change, using exact diagonalization and Bethe ansatz calculations. We find that in the limit Δ → 1^{+} most of the ES levels show divergent behavior. Moreover, while at Δ = 1 the ES contains no information about the boundaries, for Δ > 1 it depends dramatically on the choice of boundary conditions. For both open and periodic boundary conditions the ES exhibits an elegant multiplicity structure for which we conjecture a combinatorial formula. We also study the entanglement eigenfunctions, i.e. the eigenfunctions of the reduced density matrix. We find that the eigenfunctions corresponding to the nondiverging levels mimic the behavior of the state wavefunction, whereas the others show intriguing polynomial structures. Finally we analyze the distribution of the ES levels as the system is detuned away from Δ = 1.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 August 2012
 DOI:
 10.1088/17425468/2012/08/P08011
 arXiv:
 arXiv:1206.0131
 Bibcode:
 2012JSMTE..08..011A
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 21 pages, 8 figures. Minor corrections, references added. Published version