2025/05/13 by Ángelo Lucia, David Pérez-Garcı́a, Lucia, Angelo +3 · 3 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2505.08991
openalex publication_date 2025/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from an arbitrary full-rank state of a lattice quantum spin system, we define a "canonical purified Hamiltonian" and characterize its spectral gap in terms of a spatial mixing condition (or correlation decay) of the state. When the state considered is a Gibbs state of a local, commuting Hamiltonian at positive temperature, we show that the spectral gap of the canonical purified Hamiltonian provides a lower bound to the spectral gap of a large class of reversible generators of quantum Markov semigroup, including local and ergodic Davies generators. As an application of our construction, we show that the mixing condition is always satisfied for any finite-range 1D model, as well as by Kitaev's quantum double models.