Universität zu Köln

Kastoryano, Michael J., Lucia, Angelo ORCID: 0000-0003-1709-1220 and Perez-Garcia, David ORCID: 0000-0003-2990-791X (2019). Locality at the Boundary Implies Gap in the Bulk for 2D PEPS. Commun. Math. Phys., 366 (3). S. 895 - 927. NEW YORK: SPRINGER. ISSN 1432-0916

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Abstract

Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showing two results: first, we identify an approximate factorization condition on the boundary state of rectangular subregions that is sufficient to prove that the parent Hamiltonian of the bulk 2D PEPS has a constant gap in the thermodynamic limit; second, we then show that Gibbs state of a local, finite-range Hamiltonian satisfy such condition. The proof applies to the case of injective and MPO-injective PEPS, employs the martingale method of nearly commuting projectors, and exploits a result of Araki (Commun Math Phys 14(2):120-157, 1969) on the robustness of one dimensional Gibbs states. Our result provides one of the first rigorous connections between boundary theories and dynamical properties in an interacting many body system.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kastoryano, Michael J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Lucia, Angelo UNSPECIFIED orcid.org/0000-0003-1709-1220 UNSPECIFIED Perez-Garcia, David UNSPECIFIED orcid.org/0000-0003-2990-791X UNSPECIFIED
URN:	urn:nbn:de:hbz:38-155037
DOI:	10.1007/s00220-019-03404-9
Journal or Publication Title:	Commun. Math. Phys.
Volume:	366
Number:	3
Page Range:	S. 895 - 927
Date:	2019
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0916
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ENTANGLED PAIR STATES; MATRIX PRODUCT STATES; SPECTRAL GAP; QUANTUM Multiple languages Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/15503