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 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.
Additional Information
© Springer-Verlag GmbH Germany, part of Springer Nature 2019. Received: 12 December 2017 / Accepted: 30 January 2019 / First Online: 09 March 2019. Communicated by M. M. Wolf. We thank Albert Werner and Wojciech De Roeck for fruitful discussions. M. J. K. was supported by the VILLUM FONDEN Young Investigator Program. A. L. acknowledges financial support from the European Research Council (ERC Grant Agreement No. 337603), the Danish Council for Independent Research (Sapere Aude), VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059), the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY-1733907). D. P. G. acknowledges support from MINECO (Grant MTM2014-54240-P), Comunidad de Madrid (Grant QUITEMAD+-CM, ref. S2013/ICE-2801), and Severo Ochoa project SEV-2015-556. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 648913).Attached Files
Submitted - 1709.07691.pdf
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Additional details
- Eprint ID
- 93692
- Resolver ID
- CaltechAUTHORS:20190311-132254669
- 10059
- Villum Fonden
- 337603
- European Research Council (ERC)
- Danish Council for Independent Research
- Walter Burke Institute for Theoretical Physics, Caltech
- MTM2014-54240-P
- Ministerio de Economía y Competitividad (MINECO)
- S2013-ICE2801
- Comunidad de Madrid
- 648913
- European Research Council (ERC)
- PHY-1733907
- NSF
- Sherman Fairchild Foundation
- Institute for Quantum Information and Matter (IQIM)
- SEV-2015-556
- Severo Ochoa
- Created
-
2019-03-11Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter