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Matrix product state description of Halperin states

Author(s): Crepel, V; Estienne, B; Bernevig, Bogdan A.; Lecheminant, P; Regnault, N

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Abstract: Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.
Publication Date: 15-Apr-2018
Electronic Publication Date: 23-Apr-2018
Citation: Crepel, V, Estienne, B, Bernevig, BA, Lecheminant, P, Regnault, N. (2018). Matrix product state description of Halperin states. PHYSICAL REVIEW B, 97, doi:10.1103/PhysRevB.97.165136
DOI: doi:10.1103/PhysRevB.97.165136
ISSN: 2469-9950
EISSN: 2469-9969
Pages: 165136-1 - 165136-20
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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