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Classifying quantum phases using MPS and PEPS

Schuch, Norbert and Pérez García, David and Cirac, Ignacio (2010) Classifying quantum phases using MPS and PEPS. (Submitted)


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We apply the framework of Matrix Product States (MPS) and Projected Entangled Pair States
(PEPS) and their associated parent Hamiltonians to the classification of quantum phases in one and
higher dimensions, where we define two systems to be in the same phase if they can be connected
via a path of gapped Hamiltonians. In one dimension, we prove that any two Hamiltonians with
MPS ground states are in the same phase if and only if they have the same ground state degeneracy.
Subsequently, we extend our framework to the classification of two-dimensional quantum phases
in the neighborhood of a number of important cases, such as systems with unique ground states,
local symmetry breaking, and topological order. As a central tool in our derivation, we introduce
the isometric form of MPS and PEPS. Isometric forms are renormalization fixed points both for
MPS and for relevant classes of PEPS, and are connected to the original MPS via a gapped path in
Hamiltonian space. Our construction thus yields a way to implement renormalization flows locally,
this is, without actual renormalization.

Item Type:Article
Uncontrolled Keywords:Teoría cuántica, Quantum Physics, Strongly Correlated Electrons
Subjects:Sciences > Physics > Quantum theory
ID Code:12153
Deposited On:02 Feb 2011 16:47
Last Modified:06 Feb 2014 09:18

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