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.

arXiv comment22 pages; 4 tables; 7 figures

References in corpus (26)

• An Area Law for One Dimensional Quantum Systems
• Lieb-Schultz-Mattis in Higher Dimensions
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
• The spectral gap for some spin chains with discrete symmetry breaking
• Rigorous RG algorithms and area laws for low energy eigenstates in 1D
• Local gap threshold for frustration-free spin systems
• The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
• An area law for 2D frustration-free spin systems
• Spectral gaps of frustration-free spin systems with boundary
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Improved spectral gaps for random quantum circuits: large local dimensions and all-to-all interactions
• Correlation length in random MPS and PEPS
• Improved bounds on the spectral gap above frustration free ground states of quantum spin chains
• A class of two-dimensional AKLT models with a gap
• AKLT models on decorated square lattices are gapped
• Improved local spectral gap thresholds for lattices of finite dimension
• Spectral Gaps and Incompressibility in a $\nu =1/3$ Fractional Quantum Hall System
• Computing spectral bounds of the Heisenberg ferromagnet from geometric considerations
• 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
• Gapped PVBS models for all species numbers and dimensions
• The AKLT model on a hexagonal chain is gapped

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