A new kind of symmetry, called Supersymmetry, is introduced in t-J model and its corresponding Supersymmetric Formulation is constructed. The new formulation unifies the so-called slave-fermion and slave-boson formulations to the model in a single framework and is able to incorporate the advantage of the two approaches. The formulation is analysed at mean-field level where we found that antiferromagnetism described by slave-fermion-like state is stable at low doping regime, and the slave-boson-like d-wave RVB superconducting state becomes favorable at optimal doping. The global phase diagram is determined. To remedy the relaxation of non-double-occupancy constraint in a simple mean-field theory, the Gutzwiller's approximation is applied. Surprisingly the resulting phase diagram is in rather close agreement with experiment. Several physical quantities such as spin-spin correlation lengths, electron spectral functions, magnetic dynamical structure factors and spin susceptibilities are also calculated at the mean-field level where the new effect coming from finite spin and charge excitations of opposite statistics allowed by supersymmetry is pointed out. Finally, future research direction of the formulation is discussed.
We find a mapping between the attractive Fermi-Hubbard model and the repulsive Bose-Hubbard model at finite temperature and at imaginary chemical potential
μ=iθ. We show, by using a large
N-expansion, that the partition functions of the two models are related by a simple shift
θ→θ+π. This condition maps the BCS--BEC crossover of attractive fermions to a Bose--Fermi crossover (fermion-like occupation) of repulsive bosons. Central feature of this correspondence plays the thermal kernel
g(βE,ϕ), whose analytic continuation
gB(βE,ϕ)=gF(βE,ϕ+π) governs the bosonic and fermionic sectors. Interestingly, we are able to find that the special angles
ϕ=2π/3,4π/3 for fermions correspond to
ϕ=π/3,5π/3 for bosons, marking the boundaries of a universal thermal window. We further argue that the present mechanism shows that fermionization can occur at finite interaction strength through a thermodynamic effect induced by the imaginary chemical potential. This suggests that it is a new way of fermionization (not a change in statistics but a fermion-like behaviour) unlike the Tonks--Girardeau limit, where fermionization arises from an infinite repulsive interaction and anyonic or Floquet-engineered systems where transmutation emerges from modified statistics or dynamics. Essentially, the phase
ϕ is a statistical parameter; by twisting the thermal phase, it generates fermion-like behaviour without hard-core constraints or infinite repulsion but only by using thermodynamics. We derive the gap equation and number equation for the bosonic model, highlighting the role of the imaginary chemical potential as a statistical regulator. Our results provide a unified framework for understanding crossovers in interacting lattice systems.
A ground state energy variational calculation of anyon gas with Hamiltonian included the interaction of spins of particles with anyon vector potential induced, i.e. statistical, magnetic field exhibits exact cancelation of terms connected with fractional statistics. This leads to bosonization of anyons due to coupling of their spins with statistical magnetic field. We presume that at the dense gas fluctuations of effective spins destroy the coupling and bosons become anyons. At the assumption that pseudogap (PG) boundary is temperature independent and when anyons are fermions we use this model to interpret experimental phase diagrams of Tallon and Loram hole and electron doped High-T_c superconductors below PG energy E_g and find the qualitative and quantitative agreement. We do the hypothesis that phase transition (PT) of bosons into Bose-Einstein condensate is not of second order, but of first order, close to second one, PG regime is meta stable phase of bosons, and E_g=0 is the critical point of this PT. Bosons undergo PT into fermions on PG boundary. Described in the literature non-Fermi quasi-particles might be related to bosons with effective spins.