Dear group,
In case you forgot and want to hear Norbert's talk: it is starting in
a few minutes.
Regards,
Sergio
On Mon, May 16, 2011 at 3:08 PM, Sergio Boixo <sergio(a)boixo.com> wrote:
Dear group,
Title and abstract for the blackboard talk that Norbert Schuch is
giving tomorrow at 11:30 in the division room:
Entanglement spectrum and boundary theories with projected entangled-pair states
In many physical scenarios, close relations between the bulk
properties of quantum systems and theories associated to their
boundaries have been observed. In this work, we provide an exact
duality mapping between the bulk of a quantum spin system and its
boundary using Projected Entangled Pair States (PEPS). This duality
associates to every region a Hamiltonian on its boundary, in such a
way that the entanglement spectrum of the bulk corresponds to the
excitation spectrum of the boundary Hamiltonian. We study various
specific models, like a deformed AKLT, an Ising-type, and
Kitaev's toric code, both in finite ladders and infinite square
lattices. In the latter case, some of those models display quantum
phase transitions. We find that a gapped bulk phase with local order
corresponds to a boundary Hamiltonian with local interactions, whereas
critical behavior in the bulk is reflected on a diverging interaction
length of the boundary Hamiltonian. Furthermore, topologically ordered
states yield non-local Hamiltonians. As our duality also associates a
boundary operator to any operator in the bulk, it in fact provides a
full holographic framework for the study of quantum many-body systems
via their boundary.
http://arxiv.org/abs/1103.3427
Regards,
Sergio
On Thu, May 12, 2011 at 2:05 PM, Sergio Boixo <sergio(a)boixo.com> wrote:
Dear group,
Norbert Schuch will be giving a blackboard talk Tuesday at 11:30 on
the division room. Topic TBA but either
1.-Entanglement spectrum and boundary theories with projected
entangled-pair states
or
2.-The complexity of commuting Hamiltonians.
Regards,
Sergio