We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LPs) with increasing attraction, in the presence of the Zeeman magnetic field ( h ) for d =2, within the spin-polarized attractive Hubbard model. The broken symmetry Hartree approximation as well as the strong coupling expansion are used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. For spin-independent hopping integrals ( t ↑ = t ↓ ), we find no stable homogeneous polarized superfluid (SC M ) state in the ground state for the strong attraction and obtain that for a two-component Fermi system on a 2D lattice with population imbalance, phase separation (PS) is favoured for a fixed particle concentration, even on the LP (BEC) side. We also examine the influence of spin-dependent hopping integrals (mass imbalance) on the stability of the SC M phase. We find a topological quantum phase transition (Lifshitz type) from the unpolarized superfluid phase (SC 0 ) to SC M and tricritical points in the h -| U | and t ↑ / t ↓ -| U | ground-state phase diagrams. We also construct the finite temperature phase diagrams for both t ↑ = t ↓ and t ↑ ≠ t ↓ and analyze the possibility of occurrence of a spin-polarized KT superfluid.
The influence of the Zeeman magnetic field (h) on the ground state evolution of superfluid properties from the weak coupling (BCS-like) to the strong coupling limit of tightly bound local pairs with increasing attraction has been studied.The analysis was carried out within the spin-polarized attractive Hubbard model, for a fixed number of particles and a d = 3 simple cubic lattice.The broken symmetry Hartree approximation was used.For strong attraction and in the dilute limit, the homogeneous magnetized superconducting phase (SC M ) was found in the h-|U | and P -|U | diagrams.
The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physics in the ground state. The methods used included: the mean field approximation (BCS-Stoner type) and the estimation of the phase coherence temperature within the Kosterlitz-Thouless (KT) scenario in two dimensions. The BCS-BEC crossover was also analyzed in three dimensions, at finite temperatures, within the spin polarized Attractive Hubbard Model (AHM), going beyond the mean field approximation. In this case, the critical temperatures of the superconducting transition were determined within the self-consistent T-matrix method. The strong coupling expansion was applied to map the spin polarized AHM onto the model of hard-core bosons on the lattice.
We investigate the superuid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic eld.We analyze the temperature and magnetic eld dependencies of the order parameter.We nd that in the two-dimensional case, the spatially homogeneous spin polarized superuidity (SC (P ̸ = 0)) is stable in the weak coupling limit, at T = 0, as opposed to the s-wave pairing symmetry case in 2D.We construct the ground state phase diagrams both for xed chemical potential and electron concentration.Furthermore, we obtain the temperature vs. magnetic eld and temperature vs. spin polarization phase diagrams.
Recent experiments with ultracold fermionic atoms in optical lattices have provided a tuneable and clean realization of the attractive Hubbard model (AHM). In view of this, several physical properties may be thoroughly studied across the crossover between weak (Bardeen-Cooper-Schrieffer, BCS) and strong (Bose-Einstein condensation, BEC) couplings. Here we report on extensive determinant Quantum Monte Carlo (DQMC) studies of the AHM on a square lattice, from which several different quantities have been calculated and should be useful as a roadmap to experiments. We have obtained a detailed phase diagram for the critical superconducting temperature,
Tc, in terms of the band filling, $\ave{n}$, and interaction strength,
U, from which we pinpoint a somewhat wide region
∣U∣/t≈5±1 (
t is the hopping amplitude) and $\ave{n} \approx 0.79 \pm 0.09$ leading to a maximum
Tc≈0.16t. Two additional temperature scales, namely pairing,
Tp, and degeneracy,
Td, have been highlighted: the former sets the scale for pair formation (believed to be closely related to the scale for the gap of spin excitations in cuprates), while the latter sets the scale for dominant quantum effects. Our DQMC data for the distribution of doubly occupied sites, for the momentum distribution function, and for the quasiparticle weight show distinctive features on both sides of the BCS-BEC crossover, being also suggestive of an underlying crossover between Fermi- and non-Fermi liquid behaviors.