Divide and conquer method for proving gaps of frustration free Hamiltonians
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the ground state space is sufficient to obtain such a bound. We furthermore show that such a condition is necessary and equivalent to a constant spectral gap. Thanks to this equivalence, we can prove that for gapless models in any dimension, the spectral gap on regions of diameter $n$ is at most $o\left(\frac{\log(n)^{2+\epsilon}}{n}\right)$ for any positive $\epsilon$.
Originalsprog | Engelsk |
---|---|
Artikelnummer | 033105 |
Tidsskrift | Journal of Statistical Mechanics: Theory and Experiment |
Vol/bind | 2018 |
Sider (fra-til) | 1-23 |
ISSN | 1742-5468 |
DOI | |
Status | Udgivet - 2018 |
- math-ph, math.MP, quant-ph
Forskningsområder
Links
- https://arxiv.org/abs/1705.09491
Accepteret manuskript
ID: 189701211