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Spectral gaps of Affleck-Kennedy-Lieb-Tasaki Hamiltonians using tensor network methods

Autor(en)

Artur Garcia-Saez, Valentin Murg, Tzu-Chieh Wei

Abstrakt

Using exact diagonalization and tensor network techniques, we compute

the gap for the Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian in one

and two spatial dimensions. Tensor network methods are used to extract

physical properties directly in the thermodynamic limit, and we support

these results using finite-size scalings from exact diagonalization.

Studying the AKLT Hamiltonian perturbed by an external field, we show

how to obtain an accurate value of the gap of the original AKLT

Hamiltonian from the field value at which the ground state verifies e0<0,

which is a quantum critical point. With the tensor network

renormalization group methods we provide direct evidence of a finite gap

in the thermodynamic limit for the AKLT models in the one-dimensional

chain and two-dimensional hexagonal and square lattices. This method can

be applied generally to Hamiltonians with rotational symmetry, and we

also show results beyond the AKLT model.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

State University of New York, Stony Brook

Journal

Physical Review B

Band

Anzahl der Seiten

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.88.245118

Publikationsdatum

12-2013

Peer-reviewed

ÖFOS 2012

103026 Quantenoptik

Schlagwörter

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