arXiv:2402.03875 · Physical Review A

Exotic superfluid with emergent flux in a one-dimensional Bose-Fermi mixture

Qi‐Wei Song, Jie Lou, Yan Chen

Published Dec 12, 2024• 1 citation

Abstract

We find a chiral superfluid (CSF) phase in a one-dimensional Bose-Fermi Hubbard model with significant mass and density imbalance between the two species. In the CSF phase, bosons condensate at nonzero momentum $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/L$ with chain length $L$. To capture the essential physics of this phenomenon, we study an alternative simplified model that only features competition between single-fermion hopping and hopping of composite particles composed of a fermion and a boson. This model captures the low-energy physics of the Hubbard model and hosts a robust CSF phase. Our numerical studies show that in the CSF phase, the local superfluid order parameter continuously rotates along the chain, indicating that time-reversal symmetry is spontaneously broken. This symmetry breaking generates an emergent flux in the background, effectively optimizing the system's ground-state energy. We provide a physical understanding at the mean-field level. Furthermore, we have explored the potential realization of this phase in cold-atom experiments.

DOI: 10.1103/physreva.110.063312

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arXiv:2402.03875 · Physical Review A

Exotic superfluid with emergent flux in a one-dimensional Bose-Fermi mixture

Qi‐Wei Song, Jie Lou, Yan Chen

Published Dec 12, 2024• 1 citation

arXiv HTML PDF

Abstract

\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/L

with chain length

L

. To capture the essential physics of this phenomenon, we study an alternative simplified model that only features competition between single-fermion hopping and hopping of composite particles composed of a fermion and a boson. This model captures the low-energy physics of the Hubbard model and hosts a robust CSF phase. Our numerical studies show that in the CSF phase, the local superfluid order parameter continuously rotates along the chain, indicating that time-reversal symmetry is spontaneously broken. This symmetry breaking generates an emergent flux in the background, effectively optimizing the system's ground-state energy. We provide a physical understanding at the mean-field level. Furthermore, we have explored the potential realization of this phase in cold-atom experiments.

DOI: 10.1103/physreva.110.063312

Related papers

Unconventional Superfluidity in a model of Fermi-Bose Mixtures

K. Sheshadri, A. Chainani

A finite-temperature ( $T>0$ ) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions $ρ_B$ and $ρ_F$ , respectively, on a two-dimensional square lattice with composite hopping $t$ is presented. The composite hopping swaps the locations of a fermion and a boson that occupy nearest-neighbor sites of the lattice. The superfluid order parameter $ψ$ , the femion hopping amplitude $ϕ$ , the chemical potential $μ$ , the free energy minimum $\tilde{F}$ and entropy $S$ are calculated in the limit $ρ_B+ρ_F=1$ within a mean-field approximation, and lead to a phase diagram in the $ρ_F - T$ plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped $T(ρ_F)$ , and insulating normal liquid and insulating normal gas phases outside the dome. These phases are separated by coupled discontinuous transitions as indicated by jumps in $ψ$ and $ϕ$ . The maximum critical transition temperature $T_c$ is observed very close to $ρ_F = 1/2$ . While $\tilde{F} (T)$ is continuous with a derivative discontinuity at $T=T_c (ρ_F)$ for $0 1/2$ (zeroth-order transition), where the entropy becomes negative for a range of temperatures below $T_c$ . The ratio of $T_c$ to Fermi band width agrees remarkably with the ratio of $T_c$ / $T_F$ (where $T_F$ is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high- $T_c$ cuprates, iron-based and hydride superconductors, that exhibit experimental values of $T_c$ spread over nine orders of magnitude from $\sim 200$ nK to $\sim 260$ K.A finite-temperature ($T>0$) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions $ρ_B$ and $ρ_F$, respectively, on a two-dimensional square lattice with composite hopping $t$ is presented. The composite hopping swaps the locations of a fermion and a boson that occupy nearest-neighbor sites of the lattice. The superfluid order parameter $ψ$, the femion hopping amplitude $ϕ$, the chemical potential $μ$, the free energy minimum $\tilde{F}$ and entropy $S$ are calculated in the limit $ρ_B+ρ_F=1$ within a mean-field approximation, and lead to a phase diagram in the $ρ_F - T$ plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped $T(ρ_F)$, and insulating normal liquid and insulating normal gas phases outside the dome. These phases are separated by coupled discontinuous transitions as indicated by jumps in $ψ$ and $ϕ$. The maximum critical transition temperature $T_c$ is observed very close to $ρ_F = 1/2$. While $\tilde{F} (T)$ is continuous with a derivative discontinuity at $T=T_c (ρ_F)$ for $0 1/2$ (zeroth-order transition), where the entropy becomes negative for a range of temperatures below $T_c$. The ratio of $T_c$ to Fermi band width agrees remarkably with the ratio of $T_c$/$T_F$ (where $T_F$ is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high-$T_c$ cuprates, iron-based and hydride superconductors, that exhibit experimental values of $T_c$ spread over nine orders of magnitude from $\sim 200$nK to $\sim 260$K.

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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)].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:1311.7148Physical Review BMar 4, 201428 citations

\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}/L

with chain length

L

A finite-temperature (

T>0

) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions

ρ_B

and

ρ_F

, respectively, on a two-dimensional square lattice with composite hopping

t

is presented. The composite hopping swaps the locations of a fermion and a boson that occupy nearest-neighbor sites of the lattice. The superfluid order parameter

ψ

, the femion hopping amplitude

ϕ

, the chemical potential

μ

, the free energy minimum

\tilde{F}

and entropy

S

are calculated in the limit

ρ_B+ρ_F=1

within a mean-field approximation, and lead to a phase diagram in the

ρ_F - T

plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped

T(ρ_F)

, and insulating normal liquid and insulating normal gas phases outside the dome. These phases are separated by coupled discontinuous transitions as indicated by jumps in

ψ

and

ϕ

. The maximum critical transition temperature

T_c

is observed very close to

ρ_F = 1/2

. While

\tilde{F} (T)

is continuous with a derivative discontinuity at

T=T_c (ρ_F)

for

0 1/2

(zeroth-order transition), where the entropy becomes negative for a range of temperatures below

T_c

. The ratio of

T_c

to Fermi band width agrees remarkably with the ratio of

T_c

T_F

(where

T_F

is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high-

T_c

cuprates, iron-based and hydride superconductors, that exhibit experimental values of

T_c

spread over nine orders of magnitude from

\sim 200

nK to

\sim 260

^{40}\mathrm{K}

and

^{87}\mathrm{Rb}

. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture,

{N}_{\mathrm{F}}

and

{N}_{\mathrm{B}}

, and by phase diagrams in the

({N}_{\mathrm{F}},{N}_{\mathrm{B}})

plane, which displays regions of symmetric and asymmetric ground states. The dynamical picture of the SSB, induced by a gradual transformation of the single-well potential into the DWP, is reported too. An analytical approximation is proposed for the case when the GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relationship between

{N}_{\mathrm{F}}

and

{N}_{\mathrm{B}}

, the TF approximation allows us to reduce the model to a single equation for the fermionic function, which includes competing repulsive and attractive nonlinear terms. The latter one directly displays the mechanism of the generation of the effective attraction in the Fermi superfluid, mediated by the bosonic component of the mixture.

{U}_{c}

. If

U<{U}_{c}

, the ground state of the system is in the superfluid phase, while if

U>{U}_{c}

, the ground state is in the insulating phase. The superfluid-insulator transition occurs at

{U}_{c}

. From the analysis of the superfluid density, the value of the critical point is determined as

{U}_{c}=2.79256

, which is larger than the

{U}_{c}=0

for the Fermi-Hubbard model and smaller than the

{U}_{c}=3.28

for the Bose-Hubbard model. The elementary excitations and effective Hamiltonian in the strong-coupling limit are also discussed.

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)].