Our goal is to understand the phenomena arising in optical lattice fermions at low temperature in an external magnetic field. Varying the field, the attraction between any two fermions can be made arbitrarily strong, where composite bosons form via so-called Feshbach resonances. By setting up strong-coupling equations for fermions, we find that in spatial dimension d>2 they couple to bosons which dress up fermions and lead to new massive composite fermions. At low enough temperature, we obtain the critical temperature at which composite bosons undergo the Bose–Einstein condensate (BEC), leading to BEC-dressing massive fermions. These form tightly bound pair states which are new bosonic quasi-particles producing a BEC-type condensate. A quantum critical point is found and the formation of condensates of complex quasi-particles is speculated over.Our goal is to understand the phenomena arising in optical lattice fermions at low temperature in an external magnetic field. Varying the field, the attraction between any two fermions can be made arbitrarily strong, where composite bosons form via so-called Feshbach resonances. By setting up strong-coupling equations for fermions, we find that in spatial dimension d>2 they couple to bosons which dress up fermions and lead to new massive composite fermions. At low enough temperature, we obtain the critical temperature at which composite bosons undergo the Bose–Einstein condensate (BEC), leading to BEC-dressing massive fermions. These form tightly bound pair states which are new bosonic quasi-particles producing a BEC-type condensate. A quantum critical point is found and the formation of condensates of complex quasi-particles is speculated over.

arXiv:1708.04023Nuclear Physics BSep 27, 20184 citations

Quasi-particle formulation of quantum statistics

Roger Balian, C. De Dominicis

PhysicaOct 1, 196430 citations

Quantum mechanics and quantum field theory of a fermion system

Wolfgang Bulla, K. Unterkofler

Jan 1, 19860 citations

New Transformation for Treating Pair Correlation and Microscopic Foundation of Interacting Boson Model

Yang Li-ming

For strongly pair-correlated systems, a new transformation is derived similar in form to the usual Bogoliubov-Valatin transformation, but with the transformation coefficients replaced by operators. The original fermion operators are now replaced by two sets of independent operators, the pair operators and the quasi-fermions . The transformation conserves the particle number. Among other applications, it is particularly suited for the construction of a microscopic theory of the type of the interacting boson model. The new transformation given here also serves to provide a connection between the usual ph picture of a phonon and the pp picture-of bosons in IBM. However, the boson picture that evolves from the present formulation differs from the ideal boson picture in IBM..For strongly pair-correlated systems, a new transformation is derived similar in form to the usual Bogoliubov-Valatin transformation, but with the transformation coefficients replaced by operators. The original fermion operators are now replaced by two sets of independent operators, the pair operators and the quasi-fermions . The transformation conserves the particle number. Among other applications, it is particularly suited for the construction of a microscopic theory of the type of the interacting boson model. The new transformation given here also serves to provide a connection between the usual ph picture of a phonon and the pp picture-of bosons in IBM. However, the boson picture that evolves from the present formulation differs from the ideal boson picture in IBM..

Communications in Theoretical PhysicsSep 1, 19825 citations

Two identical 1D anyons with zero-range interactions: Exchange statistics, scattering theory, and anyon-anyon mapping

Raúl Hidalgo-Sacoto, Thomas Busch, D. Blume

While elementary particles obey either bosonic or fermionic exchange statistics, generalized exchange statistics that interpolate between bosons and fermions -- applicable to quasi-particles -- constitute an intriguing topic, both from the fundamental and practical points of view. This work develops a scattering framework for two identical 1D bosonic anyons and two identical 1D fermionic anyons with zero-range contact interactions. The two-body system with zero-range interactions, both in free space and under external confinement, is used to illustrate the recently proposed bosonic-anyon -- fermionic-anyon mapping~(R. Hidalgo-Sacoto {\em{et al.}}, arXiv:2505.17669), which connects the eigenstates of bosonic anyons to those of fermionic anyons and vice versa. Performing explicit calculations for two-particle systems, the momentum distributions and the off-diagonal correlations of the single-particle density matrix for bosonic anyons and fermionic anyons are confirmed to be distinct. We also confirm the previously derived asymptotic coefficients of the momentum distribution tail at orders $k^{-2}$ and $k^{-3}$ for two harmonically confined anyons. Non-universal contributions at order $k^{-4}$ are discussed.While elementary particles obey either bosonic or fermionic exchange statistics, generalized exchange statistics that interpolate between bosons and fermions -- applicable to quasi-particles -- constitute an intriguing topic, both from the fundamental and practical points of view. This work develops a scattering framework for two identical 1D bosonic anyons and two identical 1D fermionic anyons with zero-range contact interactions. The two-body system with zero-range interactions, both in free space and under external confinement, is used to illustrate the recently proposed bosonic-anyon -- fermionic-anyon mapping~(R. Hidalgo-Sacoto {\em{et al.}}, arXiv:2505.17669), which connects the eigenstates of bosonic anyons to those of fermionic anyons and vice versa. Performing explicit calculations for two-particle systems, the momentum distributions and the off-diagonal correlations of the single-particle density matrix for bosonic anyons and fermionic anyons are confirmed to be distinct. We also confirm the previously derived asymptotic coefficients of the momentum distribution tail at orders $k^{-2}$ and $k^{-3}$ for two harmonically confined anyons. Non-universal contributions at order $k^{-4}$ are discussed.

arXiv:2505.23127May 29, 20250 citations

k^{-2}

and

k^{-3}

for two harmonically confined anyons. Non-universal contributions at order

k^{-4}

are discussed.