Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2011-03-17
Phys. Rev. B 83, 245134 (2011)
Physics
Condensed Matter
Strongly Correlated Electrons
13 pages, 14 figures
Scientific paper
10.1103/PhysRevB.83.245134
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 [1], an Ising-type [2], and Kitaev's toric code [3], 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.
Cirac Juan Ignacio
Poilblanc Didier
Schuch Norbert
Verstraete Frank
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