Back to Search
Start Over
Locality at the Boundary Implies Gap in the Bulk for 2D PEPS.
- Source :
- Communications in Mathematical Physics; Mar2019, Vol. 366 Issue 3, p895-926, 32p
- Publication Year :
- 2019
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- MARTINGALES (Mathematics)
MATHEMATICS
PROBLEM solving
Subjects
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 366
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 135478170
- Full Text :
- https://doi.org/10.1007/s00220-019-03404-9