Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915043403104256 |
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| author | Schneider, Benedikt Burkard, Ruben Olmos, Beatriz Lesanovsky, Igor Sbierski, Björn |
| author_facet | Schneider, Benedikt Burkard, Ruben Olmos, Beatriz Lesanovsky, Igor Sbierski, Björn |
| contents | Quantum spin models with a large number of interaction partners per spin are frequently used to describe modern many-body quantum optical systems like arrays of Rydberg atoms, atom-cavity systems or trapped ion crystals. For theoretical analysis the mean-field (MF) ansatz is routinely applied. However, besides special cases of all-to-all or strong long range interactions, the MF ansatz provides only approximate results. Here we present a systematic correction to MF theory based on diagrammatic perturbation theory for quantum spin correlators in thermal equilibrium. Our analytic results are universally applicable for any lattice geometry and spin-length S. We provide pre-computed and easy-to-use building blocks for Ising, Heisenberg and transverse field Ising models in the symmetry-unbroken regime. We showcase the quality and simplicity of the method by computing magnetic phase boundaries and excitations gaps. We also treat the Dicke-Ising model of ground-state superradiance where we show that corrections to the MF phase boundary vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18156 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins Schneider, Benedikt Burkard, Ruben Olmos, Beatriz Lesanovsky, Igor Sbierski, Björn Quantum Gases Strongly Correlated Electrons Quantum spin models with a large number of interaction partners per spin are frequently used to describe modern many-body quantum optical systems like arrays of Rydberg atoms, atom-cavity systems or trapped ion crystals. For theoretical analysis the mean-field (MF) ansatz is routinely applied. However, besides special cases of all-to-all or strong long range interactions, the MF ansatz provides only approximate results. Here we present a systematic correction to MF theory based on diagrammatic perturbation theory for quantum spin correlators in thermal equilibrium. Our analytic results are universally applicable for any lattice geometry and spin-length S. We provide pre-computed and easy-to-use building blocks for Ising, Heisenberg and transverse field Ising models in the symmetry-unbroken regime. We showcase the quality and simplicity of the method by computing magnetic phase boundaries and excitations gaps. We also treat the Dicke-Ising model of ground-state superradiance where we show that corrections to the MF phase boundary vanish. |
| title | Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins |
| topic | Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2407.18156 |