Random translation-invariant Hamiltonians and their spectral gaps

Author:

Jauslin Ian1,Lemm Marius2

Affiliation:

1. Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA

2. Department of Mathematics, University of Tübingen, 72076 Tübingen, Germany

Abstract

We consider random translation-invariant frustration-free quantum spin Hamiltonians on ZD in which the nearest-neighbor interaction in every direction is randomly sampled and then distributed across the lattice. Our main result is that, under a small rank constraint, the Hamiltonians are automatically frustration-free and they are gapped with a positive probability. This extends previous results on 1D spin chains to all dimensions. The argument additionally controls the local gap. As an application, we obtain a 2D area law for a cut-dependent ground state via recent AGSP methods of Anshu-Arad-Gosset.

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Area law for steady states of detailed-balance local Lindbladians;Journal of Mathematical Physics;2024-05-01

2. Entropic relations for indistinguishable quantum particles;Journal of Statistical Mechanics: Theory and Experiment;2024-04-09

3. Typical Correlation Length of Sequentially Generated Tensor Network States;PRX Quantum;2023-08-31

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