Spectral Gap Bounds for Quantum Markov Semigroups via Correlation Decay
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912374581100544 |
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| author | Lucia, Angelo Pérez-García, David Pérez-Hernández, Antonio |
| author_facet | Lucia, Angelo Pérez-García, David Pérez-Hernández, Antonio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Gap Bounds for Quantum Markov Semigroups via Correlation Decay Lucia, Angelo Pérez-García, David Pérez-Hernández, Antonio Quantum Physics Statistical Mechanics Mathematical Physics 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. |
| title | Spectral Gap Bounds for Quantum Markov Semigroups via Correlation Decay |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2505.08991 |