Title
"Complementary inequality between the energy gap and fluctuation"
Tomotaka Kuwahara (The University of Tokyo)
Abstract
We investigate Hamiltonians which contain terms of up to m-body coupling with finite m. We give a complementary inequality between the energy gap just above the ground state and the fluctuation of an extensive quantity A; the energy gap is bounded from above by the fluctuation, or vice versa. By applying our inequality to systems at quantum critical points, we derive a new fundamental inequality for quantum critical exponents, which clarifies how fast the correlation decays at least in accordance with the scaling of the energy gap. We finally show that there exists a non-trivial model where the inequality gives the upper limit up to a constant coefficient.
