Proves LTQO for AKLT models on hexagonal and Lieb lattices by modifying the 1988 polymer representation to obtain uniform exponential decay of boundary effects.
Lie-Schwinger block-diagonalization and gapped quantum chains
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling constant, the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.
citation-role summary
background 1
citation-polarity summary
fields
math-ph 1years
2026 1verdicts
UNVERDICTED 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices
Proves LTQO for AKLT models on hexagonal and Lieb lattices by modifying the 1988 polymer representation to obtain uniform exponential decay of boundary effects.