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Register a new userPhase diagram of a Bose-Fermi mixture in a one-dimensional optical lattice in terms of fidelity and entanglement
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We study the ground-state phase diagram of a Bose-Fermi mixture loaded in a one-dimensional optical lattice by computing the ground-state fidelity and quantum entanglement. We find that the fidelity is able to signal quantum phase transitions between the Luttinger liquid phase, the density-wave phase, and the phase separation state of the system; and the concurrence can be used to signal the transition between the density-wave phase and the Ising phase.
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We investigate the effect of the anisotropy between the s-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the 2$k_F$ atomic density waves fluctuations of the three species. At small enough densities or strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally our results are discussed in light of a recent experiment on $^{6}$Li atoms.
We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless Bosons and spin-polarized Fermions with nearest neighbor intra-species interaction and on-site inter-species repulsion in an optical lattice at half-filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are a) supersolid Bosons coexisting with Fermions in the Mott state, b) Mott state of Bosons coexisting with Fermions in a metallic or charge-density wave state, c) a metallic Fermionic state coexisting with superfluid phase of Bosons, and d) Mott insulating state of Fermions and Bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transition between these phases are generically first order with the exception of that between the supersolid and the Mott states which is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent $z$ for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.
We study the properties of a one-dimensional (1D) gas of fermions trapped in a lattice by means of the density matrix renormalization group method, focusing on the case of unequal spin populations, and strong attractive interaction. In the low density regime, the system phase-separates into a well defined superconducting core and a fully polarized metallic cloud surrounding it. We argue that the superconducting phase corresponds to a 1D analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of tightly bound bosonic pairs with a finite center-of-mass momentum that scales linearly with the magnetization. In the large density limit, the system allows for four phases: in the core, we either find a Fock state of localized pairs or a metallic shell with free spin-down fermions moving in a fully filled background of spin-up fermions. As the magnetization increases, the Fock state disappears to give room for a metallic phase, with a partially polarized superconducting FFLO shell and a fully polarized metallic cloud surrounding the core.
A model of a mixture of spinless fermions and spin-zero hardcore bosons, with filling fractions $rho_F$ and $rho_B$, respectively, on a two-dimensional square lattice with {em composite} hopping $t$ is presented. In this model, hopping swaps the locations of a fermion and a boson at nearest-neighbor sites. When $rho_F+rho_B=1$, the fermion hopping amplitude $phi$ and boson superfluid amplitude $psi$ are calculated in the ground state within a mean-field approximation. The Fermi sector is insulating ($phi=0$) and the Bose sector is normal ($psi=0$) for $0 le rho_F < rho_c$. The model has {em coupled first-order} transitions at $rho_F = rho_c simeq 0.3$ where both $phi$ and $psi$ are discontinuous. The Fermi sector is metallic ($phi>0$) and the Bose sector is superfluid ($psi>0$) for $rho_c < rho_F < 1$. At $rho_F=1/2$, fermion density of states $rho$ has a van Hove singularity, the bulk modulus $kappa$ displays a cusp-like singularity, the system has a density wave (DW) order, and $phi$ and $psi$ are maximum. At $rho_F=rho_{kappa} simeq 0.81$, $kappa$ vanishes, becoming {em negative} for $rho_{kappa}<rho_F<1$. The role of composite hopping in the evolution of Fermi band dispersions and Fermi surfaces as a function of $rho_F$ is highlighted. The estimate for BEC critical temperature is in the subkelvin range for ultracold atom systems and several hundred kelvins for possible solid-state examples of the model.
Systems of two coupled bosonic species are studied using Mean Field Theory and Quantum Monte Carlo. The phase diagram is characterized both based on the mobility of the particles (Mott insulating or superfluid) and whether or not the system is magnetic (different populations for the two species). The phase diagram is shown to be population balanced for negative spin-dependent interactions, regardless of whether it is insulating or superfluid. For positive spin-dependent interactions, the superfluid phase is always polarized, the two populations are imbalanced. On the other hand, the Mott insulating phase with even commensurate filling has balanced populations while the odd commensurate filling Mott phase has balanced populations at very strong interaction and polarizes as the interaction gets weaker while still in the Mott phase.
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