Spectral gaps of AKLT Hamiltonians using Tensor Network methods

Using exact diagonalization and tensor network techniques we compute the gap for the AKLT Hamiltonian in 1D and 2D spatial dimensions. Tensor Network methods are used to extract physical properties directly in the thermodynamic limit, and we support these results using finite-size scalings from exact diagonalization. Studying the AKLT Hamiltonian perturbed by an external field, we show how to obtain an accurate value of the gap of the original AKLT Hamiltonian from the field value at which the ground state verifies e_0<0, which is a quantum critical point. With the Tensor Network Renormalization Group methods we provide evidence of a finite gap in the thermodynamic limit for the AKLT models in the 1D chain and 2D hexagonal and square lattices. This method can be applied generally to Hamiltonians with rotational symmetry, and we also show results beyond the AKLT model.

Area laws and entanglement distillability of thermal states

We study the entanglement distillability properties of thermal states of many-body systems. Following the ideas presented in [D.Cavalcanti et al., arxiv:0705.3762], we first discuss the appearance of bound entanglement in those systems satisfying an entanglement area law. Then, we extend these results to other topologies, not necessarily satisfying an entanglement area law. We also study whether bound entanglement survives in the macroscopic limit of an infinite number of particles.