title: Correlation Length versus Gap in Frustration-Free Systems.
abstract: Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap ε has correlation length ξ upper bounded as ξ=O(1/ε). In general this bound cannot be improved. Here we study the scaling of the correlation length as a function of the spectral gap in frustration-free local Hamiltonians, and we prove a tight bound ξ=O(1/sqrt[ε]) in this setting. This highlights a fundamental difference between frustration-free and frustrated systems near criticality. The result is obtained using an improved version of the combinatorial proof of correlation decay due to Aharonov, Arad, Vazirani, and Landau.
authors.affiliation: Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.|Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: David
authors.initials: D
authors.lastname: Gosset
authors.affiliation: Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Yichen
authors.initials: Y
authors.lastname: Huang