Approximating Gibbs states of local Hamiltonians efficiently with projected entangled pair states

Autor(en)

Andras Molnar, Norbert Schuch, Frank Verstraete, J. Ignacio Cirac

Abstrakt

We analyze the error of approximating Gibbs states of local quantum spin Hamiltonians on lattices with projected entangled pair states (PEPS) as a function of the bond dimension (D), temperature (β-1), and system size (N). First, we introduce a compression method in which the bond dimension scales as D=eO(log22(N/ε)) if β<O(log2N). Second, building on the work of Hastings [M. B. Hastings, Phys. Rev. B 73, 085115 (2006)PRBMDO1098-012110.1103/PhysRevB.73.085115], we derive a polynomial scaling relation, D=(N/ε)O(β). This implies that the manifold of PEPS forms an efficient representation of Gibbs states of local quantum Hamiltonians. From those bounds it also follows that ground states can be approximated with D=NO(log2N) whenever the density of states only grows polynomially in the system size. All results hold for any spatial dimension of the lattice.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Max-Planck-Institut für Quantenoptik, Rheinisch-Westfälische Technische Hochschule Aachen, Ghent University

Journal

Physical Review B

Band

91

Anzahl der Seiten

11

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.91.045138

Publikationsdatum

01-2015

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie

Schlagwörter

ASJC Scopus Sachgebiete

Electronic, Optical and Magnetic Materials, Condensed Matter Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/b6232dfd-9317-4871-896e-792e6993e534