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Register a new userPhases and collective modes of hardcore Bose-Fermi mixture in an optical lattice
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Added by
Krishnendu Sengupta
Publication date
2008
fields
Physics
and research's language is
English
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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.
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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.
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