Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method

The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one- and multi-particle reduced density matrices in terms of cluster functions which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.Comment: 21 pages, 10 figure

Ferromagnetism of cold fermions loaded into a decorated square lattice

We investigate two-component ultracold fermions loaded into a decorated square lattice, which are described by the Hubbard model with repulsive interactions and nearest neighbor hoppings. By combining the real-space dynamical mean-field theory with the numerical renormalization group method, we discuss how a ferromagnetically ordered ground state in the weak coupling regime, which originates from the existence of a dispersionless band, is adiabatically connected to a Heisenberg ferrimagnetic state in the strong coupling limit. The effects of level splitting and hopping imbalance are also addressed.Comment: 8 pages, 7 figure

Half-Quantum Vortices in Thin Film of Superfluid 3^3He

Stability of a half-quantum vortex (HQV) in superfluid $^3$He has been discussed recently by Kawakami, Tsutsumi and Machida in Phys. Rev. B {\bf 79}, 092506 (2009). We further extend this work here and consider the A$_2$ phase of superfluid $^3$He confined in thin slab geometry and analyze the HQV realized in this setting. Solutions of HQV and singly quantized singular vortex are evaluated numerically by solving the Ginzburg-Landau (GL) equation and respective first critical angular velocities are obtained by employing these solutions. We show that the HQV in the A$_2$ phase is stable near the boundary between the A$_2$ and A$_1$ phases. It is found that temperature and magnetic field must be fixed first in the stable region and subsequently the angular velocity of the system should be increased from zero to a sufficiently large value to create a HQV with sufficiently large probability. A HQV does not form if the system starts with a fixed angular velocity and subsequently the temperature is lowered down to the A$_2$ phase. It is estimated that the external magnetic field with strength on the order of 1 T is required to have a sufficiently large domain in the temperature-magnetic field phase diagram to have a stable HQV.Comment: 5 pages, 5 figure

Oscillatory Spin Polarization and Magneto-Optic Kerr Effect in Fe3O4 Thin Films on GaAs(001)

The spin dependent properties of epitaxial Fe3O4 thin films on GaAs(001) are studied by the ferromagnetic proximity polarization (FPP) effect and magneto-optic Kerr effect (MOKE). Both FPP and MOKE show oscillations with respect to Fe3O4 film thickness, and the oscillations are large enough to induce repeated sign reversals. We attribute the oscillatory behavior to spin-polarized quantum well states forming in the Fe3O4 film. Quantum confinement of the t2g states near the Fermi level provides an explanation for the similar thickness dependences of the FPP and MOKE oscillations.Comment: to appear in Phys. Rev. Let

Supersolid state in fermionic optical lattice systems

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by combining the real-space dynamical mean-field theory with a two-site impurity solver. By calculating the local particle density and the pair potential in the systems with different clusters, we discuss the stability of a supersolid state, where an s-wave superfluid coexists with a density-wave state of checkerboard pattern. It is clarified that a confining potential plays an essential role in stabilizing the supersolid state. The phase diagrams are obtained for several effective particle densities.Comment: 7 pages, 5 figures, Phys. Rev. A in pres