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arXiv:2309.05594 · SciPost Physics Core

Insulator phases of Bose-Fermi mixtures induced by intraspecies next-neighbor interactions

Felipe Gómez-Lozada, Roberto Franco Peñaloza, Jereson Silva-Valencia

Published Jan 21, 2025• 2 citations
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Abstract

We study a one-dimensional mixture of two-color fermions and scalar bosons at the hardcore limit, focusing on the effect that the intraspecies next-neighbor interactions have on the zero-temperature ground state of the system for different fillings of each carrier. Exploring the problem’s parameters, we observed that the nearest-neighbor interaction could favor or harm the well-known mixed Mott and spin-selective Mott insulators. We also found the emergence of three unusual insulating states with charge density wave (CDW) structures in which the orders of the carriers are out of phase between each other. For instance, the immiscible CDW appears only at half-filling bosonic density, whereas the mixed CDW state is characterized by equal densities of bosons and fermions. Finally, the spin-selective CDW couples the bosons and only one kind of fermions. Appropriate order parameters were proposed for each phase to obtain the critical parameters for the corresponding superfluid-insulator transition. Our results can inspire or contribute to understanding experiments in cold-atom setups with long-range interactions or recent reports involving quasiparticles in semiconductor heterostructures.

DOI
10.21468/scipostphyscore.8.1.007

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We study a one-dimensional mixture of two-color fermions and scalar bosons at the hardcore limit, focusing on the effect that the intraspecies next-neighbor interactions have on the zero-temperature ground state of the system for different fillings of each carrier. Exploring the problem’s parameters, we observed that the nearest-neighbor interaction could favor or harm the well-known mixed Mott and spin-selective Mott insulators. We also found the emergence of three unusual insulating states with charge density wave (CDW) structures in which the orders of the carriers are out of phase between each other. For instance, the immiscible CDW appears only at half-filling bosonic density, whereas the mixed CDW state is characterized by equal densities of bosons and fermions. Finally, the spin-selective CDW couples the bosons and only one kind of fermions. Appropriate order parameters were proposed for each phase to obtain the critical parameters for the corresponding superfluid-insulator transition. Our results can inspire or contribute to understanding experiments in cold-atom setups with long-range interactions or recent reports involving quasiparticles in semiconductor heterostructures.
Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of nontrivial insulator phases that depend on the sign of the boson-fermion interaction. These nontrivial insulator phases satisfy the conditions ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\rho}}_{F}=n$ and ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}\frac{1}{2}{\ensuremath{\rho}}_{F}=n$, with the plus (minus) sign for repulsive (attractive) interactions and nnn an integer. Far from fermionic half filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.
We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless bosons and spin-polarized fermions with nearest-neighbor intraspecies interaction and on-site interspecies 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 transitions between these phases are generically first order with the exception of that between the supersolid and the Mott states which, within mean-field theory, 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 zzz for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.
We investigate an imbalanced mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering repulsive and attractive interspecies and intraspecies interactions. The interplay between commensurability, repulsive interactions, and imbalance generates three insulating phases: a mixed Mott state and two spin-selective insulators characterized by the commensurability relations ${\ensuremath{\rho}}_{B}+{\ensuremath{\rho}}_{F}^{\ensuremath{\uparrow},(\ensuremath{\downarrow})}=1$. For an attractive coupling between fermions and bosons, we found the relations ${\ensuremath{\rho}}_{B}\ensuremath{-}{\ensuremath{\rho}}_{F}^{\ensuremath{\uparrow},(\ensuremath{\downarrow})}=0$ for the spin-selective insulators. State-of-the-art cold-atom setups constitute ideal platforms to implement these unveiled insulating states and verify their commensurability relations.
We analyze the ground-state properties of mixtures consisting of scalar bosons and spin-12\frac{1}{2}21​ fermions using a mean-field treatment of the local boson-fermion interaction on a simple cubic lattice. In the deep superfluid limit of the boson sector and the BCS regime of the fermion sector, we derive BCS-type equations to determine the phase diagram of the system. We find a competition between a charge density wave and a superconducting phase. In the opposite limit, we study the Mott-insulator-to-superfluid transition of the boson sector in the presence of a staggered density-induced alternating potential provided by the fermions, and determine the mean-field transition line. In the two-superfluids phase of the mixture, we restrict to nearest-neighbor-induced interactions between the fermions and consider the extended Hubbard model. We perform a mean-field analysis of the critical temperature for the formation of boson-assisted sss-, extended ${s}^{\ensuremath{-}}$-, ddd-, and ppp-wave pairs at fermionic half-filling. We compare our results with a recent dynamical mean-field study [P. Anders et al., Phys. Rev. Lett. 109, 206401 (2012)].
We investigate a cold-atom mixture of spinless bosons and fermions in two-dimensional optical lattices. In the presence of a nested Fermi surface, the bosons may develop a fascinating supersolid behavior characterized by a finite superfluid density as well as a spatial density wave order. Focusing on the triangular lattice geometry and combining a general Landau-Ginzburg-Wilson approach with microscopically derived mean-field theory, we find an exotic supersolid phase at a fermionic band filling of nf=3∕4{n}_{f}=3∕4nf​=3∕4 with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of 87Rb40K^{87}\mathrm{Rb}^{40}\mathrm{K}87Rb40K and 23Na6Li^{23}\mathrm{Na}^{6}\mathrm{Li}23Na6Li, we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.
The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.