Improved bounds on the spectral gap above frustration free ground states of quantum spin chains

Abstract

In \cite{Nac2,Nac1} Nachtergaele obtained explicit lower bounds for the spectral gap above many frustration free quantum spin chains by using the ``martingale method''. We present simple improvements to his main bounds which allow one to obtain a sharp lower bound for the spectral gap above the spin-1/2 ferromagnetic XXZ chain. As an illustration of the method, we also calculate a lower bound for the spectral gap of the AKLT model, which is about 1/3 the size of the expected gap.

12 pages

References in corpus (2)

• Determination of the Spectral Gap for Kac's Master Equation and Related Stochastic Evolutions
• The Ferromagnetic Heisenberg XXZ chain in a pinning field

Cited by in corpus (10)

• Stability of Frustration-Free Hamiltonians
• Liquid ground state, gap and excited states of a strongly correlated spin chain
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III
• Perturbation Theory for Parent Hamiltonians of Matrix Product States
• Quantitatively improved finite-size criteria for spectral gaps
• An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory
• Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
• Spectral properties for a family of two-dimensional quantum antiferromagnets
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States