Divide and conquer method for proving gaps of frustration free Hamiltonians
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Divide and conquer method for proving gaps of frustration free Hamiltonians. / Kastoryano, Michael J.; Lucia, Angelo.
I: Journal of Statistical Mechanics: Theory and Experiment, Bind 2018, 033105, 2018, s. 1-23.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Divide and conquer method for proving gaps of frustration free Hamiltonians
AU - Kastoryano, Michael J.
AU - Lucia, Angelo
N1 - 26 pages, 3 figures
PY - 2018
Y1 - 2018
N2 - 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 $\epsilon$.
AB - 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 $\epsilon$.
KW - math-ph
KW - math.MP
KW - quant-ph
U2 - 10.1088/1742-5468/aaa793
DO - 10.1088/1742-5468/aaa793
M3 - Journal article
VL - 2018
SP - 1
EP - 23
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
SN - 1742-5468
M1 - 033105
ER -
ID: 189701211