Quantitatively improved finite-size criteria for spectral gaps

Abstract

Finite-size criteria have emerged as an effective tool for deriving spectral gaps in higher-dimensional frustration-free quantum spin systems. We quantitatively improve the existing finite-size criteria by introducing a novel subsystem weighting scheme. The approach applies to Euclidean lattices of any dimension, the honeycomb lattice, and the triangular lattice.

22 pages; 4 tables; 7 figures

References in corpus (5)

• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• An area law for 2D frustration-free spin systems
• Gaplessness is not generic for translation-invariant spin chains
• The spectral gap of a fractional quantum Hall system on a thin torus
• Random translation-invariant Hamiltonians and their spectral gaps

Cited by in corpus (9)

• Quadratic dispersion relations in gapless frustration-free systems
• Random translation-invariant Hamiltonians and their spectral gaps
• On the critical finite-size gap scaling for frustration-free Hamiltonians
• Rigorous lower bound on dynamical exponents in gapless frustration-free systems
• Rigorous lower bound of the dynamical critical exponent of the Ising model
• A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems
• Frustration-free free fermions and beyond
• Frustration-free free fermions
• Quasi-local Frustration-Free Free Fermions