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:2512.21732 · Physical review. B./Physical review. B

Bethe-ansatz study of the Bose-Fermi mixture

Soham Chandak, Aleksandra Petković, Zoran Ristivojević

Published Apr 6, 2026• 0 citations
arXivHTMLPDF

Abstract

We consider a one-dimensional mixture of bosons and spinless fermions with contact interactions. In this system, the elementary excitations at low energies are described by four linearly dispersing modes characterized by two excitation velocities. Here we study the velocities in a system with equal interaction strengths and equal masses of bosons and fermions. The resulting model is integrable and admits an exact Bethe-ansatz solution. We analyze it and analytically derive various exact results, which include the Drude weight matrix. We show that the excitation velocities can be calculated from the knowledge of the matrices of compressibility and the Drude weights, as their squares are the eigenvalues of the product of the two matrices. The elements of the Drude weight matrix obey certain sum rules as a consequence of Galilean invariance. Our results are consistent with the presence of a momentum-momentum coupling term between the two subsystems of bosons and fermions in the effective low-energy Hamiltonian. The analytical method developed in the present study can be extended to other models that possess a nested Bethe-ansatz structure.

DOI
10.1103/5kqv-f1vt

Related papers

Mixture of interacting supersymmetric spinless fermions and bosons in a one-dimensional trap

P. Schlottmann

We consider a gas mixture consisting of spinless fermions and bosons in one dimension interacting via a repulsive [Formula: see text]-function potential. Bosons and fermions are assumed to have equal masses and the interaction strength between bosons and among bosons and fermions is the same. Using the Bethe ansatz solution of the model, we study the ground state properties, the dressed energy potentials for the two bands of rapidities, the elementary particle and hole excitations, the thermodynamics, the finite size corrections to the ground state energy leading to the conformal towers, and the asymptotic behavior at large distances of some relevant correlation functions. The low-energy excitations of the system form a two-component Luttinger liquid. In an elongated optical trap the gas phase separates as a function of the distance from the center of the trap.

Modern Physics Letters B•Sep 15, 2016•2 citations

Threshold singularities in the one-dimensional supersymmetric boson–fermion gas mixture

P. Schlottmann

A one-dimensional gas mixture consisting of bosons and fermions without spin interacting via a repulsive [Formula: see text]-function potential is considered. The model is integrable and soluble via two nested Bethe ansatz, if all particles are assumed to have equal masses and the interaction strength between the bosons and among the bosons and fermions is the same. The low energy excitation spectrum is a two-component Luttinger liquid and can be parametrized by a conformal field theory with conformal charges c = 1. In the low-energy limit, where the band curvature terms in the dispersion can be neglected, the linear dispersion of a Luttinger liquid is asymptotically exact. The spectral function, however, displays deviations from the Luttinger behavior for higher energy excitations. In the neighborhood of the single-particle (hole) energy, the spectral function is represented by an effective X-ray edge type model. Expressions of the critical exponents for the single-hole Green’s function are obtained using the Bethe ansatz solution in the limit of the bosonic gas. The results could be of relevance in the context of ultracold atoms confined to an elongated optical trap.

International Journal of Modern Physics B•Jul 16, 2018•4 citations

Exactly solvable case of a one-dimensional Bose–Fermi mixture

Adilet Imambekov, Eugene Demler

We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.

arXiv:cond-mat/0505632•Physical Review A•Feb 24, 2006•90 citations

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

Shi-Jian Gu, Junpeng Cao, Shu Chen +1 more

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.

arXiv:0907.4410•Nuclear Physics B•Jun 9, 2009•0 citations

Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures

F. Deuretzbacher, D. Becker, J. Bjerlin +2 more

Strongly interacting one-dimensional (1D) Bose--Fermi mixtures form a tunable $XXZ$ spin chain. Within the spin-chain model developed here, all properties of these systems can be calculated from states representing the ordering of the bosons and fermions within the atom chain and from the ground-state wave function of spinless noninteracting fermions. We validate the model by means of an exact diagonalization of the full few-body Hamiltonian in the strongly interacting regime. Using the model, we explore the phase diagram of the atom chain as a function of the boson-boson (BB) and boson-fermion (BF) interaction strengths and calculate the densities, momentum distributions, and trap-level occupancies for up to 17 particles. In particular, we find antiferromagnetic (AFM) and ferromagnetic (FM) order and a demixing of the bosons and fermions in certain interaction regimes. We find, however, no demixing for equally strong BB and BF interactions, in agreement with earlier calculations that combined the Bethe ansatz with a local-density approximation.

arXiv:1611.04418•Physical Review A•Apr 21, 2017•34 citations

Yang-Yang thermodynamics of a Bose-Fermi mixture

Xiangguo Yin, Shu Chen, Yunbo Zhang

We investigate theoretically the behavior of a one-dimensional interacting Bose-Fermi mixture with equal masses and equal repulsive interactions between atoms at finite temperature in the scheme of thermodynamic Bethe ansatz. Combining the Yang-Yang thermodynamic formalism with local-density approximation in a harmonic trap, we calculate the density distribution of bosons and fermions numerically by treating the radially and axially excited states as discrete and continuous ones, respectively. Our result from exactly solvable solutions may be used as a touchstone for one-dimensional interacting Bose-Fermi mixture for experimental data fitting where mean-field theoretical approaches fail.

arXiv:0902.2028•Physical Review A•May 5, 2009•23 citations
We consider a one-dimensional mixture of bosons and spinless fermions with contact interactions. In this system, the elementary excitations at low energies are described by four linearly dispersing modes characterized by two excitation velocities. Here we study the velocities in a system with equal interaction strengths and equal masses of bosons and fermions. The resulting model is integrable and admits an exact Bethe-ansatz solution. We analyze it and analytically derive various exact results, which include the Drude weight matrix. We show that the excitation velocities can be calculated from the knowledge of the matrices of compressibility and the Drude weights, as their squares are the eigenvalues of the product of the two matrices. The elements of the Drude weight matrix obey certain sum rules as a consequence of Galilean invariance. Our results are consistent with the presence of a momentum-momentum coupling term between the two subsystems of bosons and fermions in the effective low-energy Hamiltonian. The analytical method developed in the present study can be extended to other models that possess a nested Bethe-ansatz structure.
We consider a gas mixture consisting of spinless fermions and bosons in one dimension interacting via a repulsive [Formula: see text]-function potential. Bosons and fermions are assumed to have equal masses and the interaction strength between bosons and among bosons and fermions is the same. Using the Bethe ansatz solution of the model, we study the ground state properties, the dressed energy potentials for the two bands of rapidities, the elementary particle and hole excitations, the thermodynamics, the finite size corrections to the ground state energy leading to the conformal towers, and the asymptotic behavior at large distances of some relevant correlation functions. The low-energy excitations of the system form a two-component Luttinger liquid. In an elongated optical trap the gas phase separates as a function of the distance from the center of the trap.
A one-dimensional gas mixture consisting of bosons and fermions without spin interacting via a repulsive [Formula: see text]-function potential is considered. The model is integrable and soluble via two nested Bethe ansatz, if all particles are assumed to have equal masses and the interaction strength between the bosons and among the bosons and fermions is the same. The low energy excitation spectrum is a two-component Luttinger liquid and can be parametrized by a conformal field theory with conformal charges c = 1. In the low-energy limit, where the band curvature terms in the dispersion can be neglected, the linear dispersion of a Luttinger liquid is asymptotically exact. The spectral function, however, displays deviations from the Luttinger behavior for higher energy excitations. In the neighborhood of the single-particle (hole) energy, the spectral function is represented by an effective X-ray edge type model. Expressions of the critical exponents for the single-hole Green’s function are obtained using the Bethe ansatz solution in the limit of the bosonic gas. The results could be of relevance in the context of ultracold atoms confined to an elongated optical trap.
We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.
The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.
Strongly interacting one-dimensional (1D) Bose--Fermi mixtures form a tunable XXZXXZXXZ spin chain. Within the spin-chain model developed here, all properties of these systems can be calculated from states representing the ordering of the bosons and fermions within the atom chain and from the ground-state wave function of spinless noninteracting fermions. We validate the model by means of an exact diagonalization of the full few-body Hamiltonian in the strongly interacting regime. Using the model, we explore the phase diagram of the atom chain as a function of the boson-boson (BB) and boson-fermion (BF) interaction strengths and calculate the densities, momentum distributions, and trap-level occupancies for up to 17 particles. In particular, we find antiferromagnetic (AFM) and ferromagnetic (FM) order and a demixing of the bosons and fermions in certain interaction regimes. We find, however, no demixing for equally strong BB and BF interactions, in agreement with earlier calculations that combined the Bethe ansatz with a local-density approximation.
We investigate theoretically the behavior of a one-dimensional interacting Bose-Fermi mixture with equal masses and equal repulsive interactions between atoms at finite temperature in the scheme of thermodynamic Bethe ansatz. Combining the Yang-Yang thermodynamic formalism with local-density approximation in a harmonic trap, we calculate the density distribution of bosons and fermions numerically by treating the radially and axially excited states as discrete and continuous ones, respectively. Our result from exactly solvable solutions may be used as a touchstone for one-dimensional interacting Bose-Fermi mixture for experimental data fitting where mean-field theoretical approaches fail.