Onsager reaction terms for quantum many-body systems: Application to antiferromagnetic and superconducting order in the Hubbard model
- Department of Physics, Joseph Henry Laboratories, Jadwin Hall, Princeton University, Princeton, New Jersey 08544 (US)
We demonstrate that an expansion in powers of the strength of the interaction, of the free energy at {ital fixed} order parameter, can be used to generate and correct mean-field theories for interacting quantum many-body systems. The first two terms in the expansion generally yield ordinary Hartree-Fock mean-field theory and the next term gives an Onsager reaction field'' correction to Hartree-Fock theory. This method can be used to directly generate expansions for {ital inverse} susceptibilities. We illustrate the method for the one- and two-dimensional Hubbard model, for which we consider corrections to mean-field theories of antiferromagnetism for the repulsive-{ital U} half-filled case and superconductivity in the attractive-{ital U} case. These corrections give a quantitative account superior to that of the random-phase approximation (RPA) for the correlation energy at small and intermediate values of {ital U}. For susceptibilities, we recover from the first two terms in the expansion the usual RPA results, while higher-order terms give systematic corrections to the RPA susceptibilities. For the case of superconductivity in the repulsive-{ital U} Hubbard model, we show that the higher-order terms in the expansion must be considered to determine whether or not an instability exists. We find that there is no superconducting instability in the repulsive-{ital U} case, at least towards ordinary singlet or triplet pairing. We also find no evidence for a superconducting instability driven by a coexisting antiferromagnetic order.
- OSTI ID:
- 5751920
- Journal Information:
- Physical Review, B: Condensed Matter; (USA), Journal Name: Physical Review, B: Condensed Matter; (USA) Vol. 43:4; ISSN 0163-1829; ISSN PRBMD
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
656100 -- Condensed Matter Physics-- Superconductivity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANTIFERROMAGNETIC MATERIALS
CRYSTAL MODELS
MAGNETIC MATERIALS
MAGNETIC PROPERTIES
MAGNETIC SUSCEPTIBILITY
MATERIALS
MATHEMATICAL MODELS
MEAN-FIELD THEORY
ONE-DIMENSIONAL CALCULATIONS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
RANDOM PHASE APPROXIMATION
SUPERCONDUCTORS
TWO-DIMENSIONAL CALCULATIONS