Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2003.09421 · Physical Review A

Mixture of scalar bosons and two-color fermions in one dimension: Superfluid-insulator transitions

Richard Giovanni Avella, Juan José Mendoza-Arenas, R. Franco, Jereson Silva-Valencia

Published Sep 30, 2020• 8 citations
arXivHTMLPDF

Abstract

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 $n$ 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.

DOI
10.1103/physreva.102.033341

Related papers

Insulator phases of a mixture of spinor fermions and hard-core bosons

Richard Giovanni Avella, Juan José Mendoza-Arenas, R. Franco +1 more

We study numerically a one-dimensional mixture of spin-$\frac{1}{2}$ fermions and scalar bosons in the hard-core limit. Considering repulsive fermion-fermion and boson-fermion interactions, we find superfluid and insulator states, and determine the boundaries between them calculating several phase diagrams. We determine that, given a fermionic density ${\ensuremath{\rho}}_{F}$, the insulator states are located at the bosonic densities ${\ensuremath{\rho}}_{B}=1\ensuremath{-}{\ensuremath{\rho}}_{F}$ and $1\ensuremath{-}\frac{1}{2}{\ensuremath{\rho}}_{F}$, and emerge even in the absence of fermion-fermion coupling. In addition, the boson-fermion repulsion drives quantum phase transitions inside the insulator lobes with ${\ensuremath{\rho}}_{B}=1/2$. Our predictions could be observed in current cold-atom experimental platforms.

arXiv:1905.05029•Physical Review A•Dec 9, 2019•8 citations

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

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

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.

arXiv:2309.05594•SciPost Physics Core•Jan 21, 2025•2 citations

Spin-selective insulators in Bose-Fermi mixtures

Ramon Guerrero-Suarez, Juan José Mendoza-Arenas, R. Franco +1 more

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.

arXiv:2008.01893•Physical Review A•Feb 3, 2021•5 citations

Mean-field phase diagram of the Bose-Fermi Hubbard model

Marin Bukov, Lode Pollet

We analyze the ground-state properties of mixtures consisting of scalar bosons and spin-$\frac{1}{2}$ 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 $s$-, extended ${s}^{\ensuremath{-}}$-, $d$-, and $p$-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)].

arXiv:1311.7148•Physical Review B•Mar 4, 2014•28 citations

Ground state of a mixture of SU(3) fermions and scalar bosons

Jereson Silva-Valencia, Juan José Mendoza-Arenas

We explore a system composed of scalar bosons and $\mathrm{SU}(3)$ fermions in one dimension. Considering only local intra- and interspecies interactions, the system is described by the Bose-Fermi-Hubbard Hamiltonian, which is studied using the density-matrix renormalization-group method. In addition to the common gapless and mixed-Mott-insulator phases, we identify unknown gapped states, in which bosons couple with some or all flavors of fermions. We unveil different flavor-selective states characterized by itinerant fermions that coexist with an insulator state in which the bosons connect with only one- or two-flavor fermions. The states reported here could be implemented in cold-atom experiments.

arXiv:2407.15991•Physical Review A•May 27, 2025•1 citation

Quantum phases of atomic boson-fermion mixtures in optical lattices

Robert Roth, Keith R. Burnett

The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in a one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as functions of the strength of the repulsive boson-boson and the boson-fermion interactions. In addition to the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.

arXiv:cond-mat/0310114•Physical Review A•Feb 26, 2004•83 citations
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 \ensuremathρB\ifmmode±\else\textpm\fi\ensuremathρF=n{\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\rho}}_{F}=n\ensuremathρB​\ifmmode±\else\textpm\fi\ensuremathρF​=n and \ensuremathρB\ifmmode±\else\textpm\fi12\ensuremathρF=n{\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}\frac{1}{2}{\ensuremath{\rho}}_{F}=n\ensuremathρB​\ifmmode±\else\textpm\fi21​\ensuremathρF​=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 study numerically a one-dimensional mixture of spin-12\frac{1}{2}21​ fermions and scalar bosons in the hard-core limit. Considering repulsive fermion-fermion and boson-fermion interactions, we find superfluid and insulator states, and determine the boundaries between them calculating several phase diagrams. We determine that, given a fermionic density ${\ensuremath{\rho}}_{F}$, the insulator states are located at the bosonic densities ${\ensuremath{\rho}}_{B}=1\ensuremath{-}{\ensuremath{\rho}}_{F}$ and $1\ensuremath{-}\frac{1}{2}{\ensuremath{\rho}}_{F}$, and emerge even in the absence of fermion-fermion coupling. In addition, the boson-fermion repulsion drives quantum phase transitions inside the insulator lobes with ${\ensuremath{\rho}}_{B}=1/2$. Our predictions could be observed in current cold-atom experimental platforms.
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.
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 explore a system composed of scalar bosons and SU(3)\mathrm{SU}(3)SU(3) fermions in one dimension. Considering only local intra- and interspecies interactions, the system is described by the Bose-Fermi-Hubbard Hamiltonian, which is studied using the density-matrix renormalization-group method. In addition to the common gapless and mixed-Mott-insulator phases, we identify unknown gapped states, in which bosons couple with some or all flavors of fermions. We unveil different flavor-selective states characterized by itinerant fermions that coexist with an insulator state in which the bosons connect with only one- or two-flavor fermions. The states reported here could be implemented in cold-atom experiments.
The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in a one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as functions of the strength of the repulsive boson-boson and the boson-fermion interactions. In addition to the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.