Locality at the boundary implies gap in the bulk for 2D PEPS

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Standard

Locality at the boundary implies gap in the bulk for 2D PEPS. / Kastoryano, Michael J.; Lucia, Angelo; Perez-Garcia, David.

I: Communications in Mathematical Physics, Bind 366, Nr. 3, 2019, s. 895–926.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Kastoryano, MJ, Lucia, A & Perez-Garcia, D 2019, 'Locality at the boundary implies gap in the bulk for 2D PEPS', Communications in Mathematical Physics, bind 366, nr. 3, s. 895–926. https://doi.org/10.1007/s00220-019-03404-9

APA

Kastoryano, M. J., Lucia, A., & Perez-Garcia, D. (2019). Locality at the boundary implies gap in the bulk for 2D PEPS. Communications in Mathematical Physics, 366(3), 895–926. https://doi.org/10.1007/s00220-019-03404-9

Vancouver

Kastoryano MJ, Lucia A, Perez-Garcia D. Locality at the boundary implies gap in the bulk for 2D PEPS. Communications in Mathematical Physics. 2019;366(3):895–926. https://doi.org/10.1007/s00220-019-03404-9

Author

Kastoryano, Michael J. ; Lucia, Angelo ; Perez-Garcia, David. / Locality at the boundary implies gap in the bulk for 2D PEPS. I: Communications in Mathematical Physics. 2019 ; Bind 366, Nr. 3. s. 895–926.

Bibtex

@article{bbe7ec98b62247b983137b05e296648a,
title = "Locality at the boundary implies gap in the bulk for 2D PEPS",
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 that if the boundary state of any rectangular subregion is a quasi-local Gibbs state of the virtual indices, then the parent Hamiltonian of the bulk 2D PEPS has a constant gap in the thermodynamic limit. The proof employs the martingale method of nearly commuting projectors, and exploits a result of Araki 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. We show that the proof can be extended to MPO-injective PEPS, and speculate that the assumption on the locality of the boundary Hamiltonian follows from exponential decay of correlations in the bulk.",
keywords = "quant-ph, math-ph, math.MP",
author = "Kastoryano, {Michael J.} and Angelo Lucia and David Perez-Garcia",
year = "2019",
doi = "10.1007/s00220-019-03404-9",
language = "English",
volume = "366",
pages = "895–926",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Locality at the boundary implies gap in the bulk for 2D PEPS

AU - Kastoryano, Michael J.

AU - Lucia, Angelo

AU - Perez-Garcia, David

PY - 2019

Y1 - 2019

N2 - 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 that if the boundary state of any rectangular subregion is a quasi-local Gibbs state of the virtual indices, then the parent Hamiltonian of the bulk 2D PEPS has a constant gap in the thermodynamic limit. The proof employs the martingale method of nearly commuting projectors, and exploits a result of Araki 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. We show that the proof can be extended to MPO-injective PEPS, and speculate that the assumption on the locality of the boundary Hamiltonian follows from exponential decay of correlations in the bulk.

AB - 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 that if the boundary state of any rectangular subregion is a quasi-local Gibbs state of the virtual indices, then the parent Hamiltonian of the bulk 2D PEPS has a constant gap in the thermodynamic limit. The proof employs the martingale method of nearly commuting projectors, and exploits a result of Araki 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. We show that the proof can be extended to MPO-injective PEPS, and speculate that the assumption on the locality of the boundary Hamiltonian follows from exponential decay of correlations in the bulk.

KW - quant-ph

KW - math-ph

KW - math.MP

U2 - 10.1007/s00220-019-03404-9

DO - 10.1007/s00220-019-03404-9

M3 - Journal article

VL - 366

SP - 895

EP - 926

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -

ID: 189701270