Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble

Abstract

We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functions, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non-degenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.

17 pages, 4 figures. Cross-references added. For associated code and data repository see: https://github.com/DelMaestroGroup/CanonicalEnsembleTheory-paper-code

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Cited by in corpus (21)

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• Multi-charged moments of two intervals in conformal field theory
• Page curve and symmetries
• Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, grand canonical and canonical ensembles
• Quadratic Scaling Bosonic Path Integral Molecular Dynamics
• Symmetry-resolved entanglement in fermionic systems with dissipation
• One-body reduced density-matrix functional theory for the canonical ensemble
• A Stable, Recursive Auxiliary Field Quantum Monte Carlo Algorithm in the Canonical Ensemble: Applications to Thermometry and the Hubbard Model
• Accelerated free energy estimation in ab initio path integral Monte Carlo simulations
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
• Thermodynamic symmetry resolved entanglement entropies in integrable systems
• A projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles
• Equilibration of Non-interacting Photons and Quantum Signatures of Chaos
• Wick rotation derivation for weak values of the density and time-dependent density functional theory
• In-Medium Similarity Renormalization Group at Finite Temperature
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice