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Seminário do grupo de Óptica e Informação Quântica

Data: Sexta-Feira 14/12/2018, Sala A5-01, 11 am.

Palestrante: Tiago Mendes (ICTP)

Title: "DETECTING UNIVERSAL PROPERTIES OF LATTICE MODELS
WITH ENTANGLEMENT HAMILTONIANS".

Abstract:  The modular (or entanglement) Hamiltonian (EH) of a quantum 
system provides an alternative way to uniquely characterize its entanglement properties. In 
particular, an appealing fact, which can be explored in both numerical and real  experiments, is that the
ground state entanglement entropy is directly related to the  thermodynamic entropy of the
EH. However, in the context of lattice models, the explicit form of the  EH is analytically
known just for the quantum Ising model. On the other hand, a closed form  of the modular EH is provided by the Bisognano-Wichmann (BW) for quantum field theory.  Here we explore the lattice version of this theorem to construct the  entanglement Hamiltonian for a variety of lattice models, supporting diverse quantum phases and  critical points,
and scanning several universality classes, including Ising, Potts, and 
Luttinger liquids. Extensive numerical simulations based on density matrix renormalization  group, exact
diagonalization, and quantum Monte Carlo, are then used to provide a 
comparison between exact results and the lattice version of BW theorem. Our results provide  evidence that the
lattice EH is close to the BW one. In particular, we show that the  entanglement entropy obtained via the BW theorem properly decribes universal properties in  both one- and two-dimensional lattice models.