Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation

Abstract

The finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation often breaks symmetries of the underlying many-body Hamiltonian. Restricting the calculation of the HFB partition function to a subspace with good quantum numbers through projection after variation restores some of the correlations lost in breaking these symmetries, although effects of the broken symmetries such as sharp kinks at phase transitions remain. However, the most general projection after variation formula in the finite-temperature HFB approximation is limited by a sign ambiguity. Here, we extend the Pfaffian formula for the many-body traces of HFB density operators introduced by L. M. Robledo in Ref. [1] to eliminate this sign ambiguity and evaluate the more complicated many-body traces required in projection after variation in the most general HFB case. We validate our method through a proof-of-principle calculation of the particle-number-projected HFB thermal energy in a simple model.

arXiv comment6 pages, 1 figure

References in corpus (9)

• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• The sign of the overlap of HFB wave functions
• Symmetry restoration in Hartree-Fock-Bogoliubov based theories
• Hartree-Fock-Bogoliubov Theory of Dipolar Fermi Gases
• Pairing and specific heat in hot nuclei
• Benchmarking mean-field approximations to level densities
• Quantum number projection at finite temperature via thermofield dynamics
• Particle-number projection in the finite-temperature mean-field approximation
• Thermodynamics of small superconductors with fixed particle number

Cited by in corpus (2)

• Symmetry restoration in mean-field approaches
• Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL