Divide and conquer method for proving gaps of frustration free Hamiltonians
Research output: Contribution to journal › Journal article › Research › peer-review
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 $\epsilon$.
Original language | English |
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Article number | 033105 |
Journal | Journal of Statistical Mechanics: Theory and Experiment |
Volume | 2018 |
Pages (from-to) | 1-23 |
ISSN | 1742-5468 |
DOIs | |
Publication status | Published - 2018 |
Bibliographical note
26 pages, 3 figures
Links
- https://arxiv.org/abs/1705.09491
Accepted author manuscript
ID: 189701211