We present a diagrammatic approach for the dimer-dimer scattering problem in two or three spatial dimensions, within the resonance approximation where these dimers are in a weakly bound resonant state. This approach is first applied to the calculation of the dimer-dimer scattering length ${a}_{B}$ in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length ${a}_{F}$ , and the already known result ${a}_{B}=0.60$ ${a}_{F}$ is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate bound-state energies for three $bbb$ and four $bbbb$ resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact bound-state energies of two bosons plus one fermion $bbf$ , two bosons plus two fermions $b{f}_{\ensuremath{\uparrow}}b{f}_{\ensuremath{\downarrow}}$, and three bosons plus one fermion $bbbf$ .We present a diagrammatic approach for the dimer-dimer scattering problem in two or three spatial dimensions, within the resonance approximation where these dimers are in a weakly bound resonant state. This approach is first applied to the calculation of the dimer-dimer scattering length ${a}_{B}$ in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length ${a}_{F}$, and the already known result ${a}_{B}=0.60$ ${a}_{F}$ is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate bound-state energies for three $bbb$ and four $bbbb$ resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact bound-state energies of two bosons plus one fermion $bbf$, two bosons plus two fermions $b{f}_{\ensuremath{\uparrow}}b{f}_{\ensuremath{\downarrow}}$, and three bosons plus one fermion $bbbf$.

Physical Review AMar 24, 2006123 citations

One-Dimensional Fermions and Bosonization

Yoshio Kuramoto

Lecture notes in physicsJan 1, 20201 citation

Fermionic SPT phases in higher dimensions and bosonization

Anton Kapustin, Ryan Thorngren

We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological parameters which label such phases and the connection with higher-form symmetries. We propose a classification scheme for fermionic SPT phases in three spatial dimensions with an arbitrary finite point symmetry G. It generalizes the supercohomology of Gu and Wen. We argue that the most general such phase can be obtained from a bosonic “shadow” by condensing both fermionic particles and strings.We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological parameters which label such phases and the connection with higher-form symmetries. We propose a classification scheme for fermionic SPT phases in three spatial dimensions with an arbitrary finite point symmetry G. It generalizes the supercohomology of Gu and Wen. We argue that the most general such phase can be obtained from a bosonic “shadow” by condensing both fermionic particles and strings.

arXiv:1701.08264Journal of High Energy PhysicsOct 1, 2017190 citations

How to distinguish fermionized bosons from noninteracting fermions through one-body and two-body density

Sangita Bera, Rhombik Roy, Barnali Chakrabarti

Fermionization is what happens when repulsive interacting bosons in one spatial dimension feel infinite interaction. Due to their strong repulsion the bosons try to minimize their spatial overlap like the fermions. Fermionized bosons and noninteracting fermions resemble each other and we trace these similarities of strongly correlated one-dimensional bosonic systems and fermionic system by exploring their ground state properties using the one- and two-body density matrix in coordinate space. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. Using the one- and two-body density in momentum space, fermionized bosons can be distinguished from noninteracting fermions.Fermionization is what happens when repulsive interacting bosons in one spatial dimension feel infinite interaction. Due to their strong repulsion the bosons try to minimize their spatial overlap like the fermions. Fermionized bosons and noninteracting fermions resemble each other and we trace these similarities of strongly correlated one-dimensional bosonic systems and fermionic system by exploring their ground state properties using the one- and two-body density matrix in coordinate space. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. Using the one- and two-body density in momentum space, fermionized bosons can be distinguished from noninteracting fermions.

AIP conference proceedingsJan 1, 20195 citations

Fermion Systems in Different Dimensions

Leon N. Cooper

Springer eBooksJan 1, 19770 citations

{a}_{B}

in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length

{a}_{F}

, and the already known result

{a}_{B}=0.60

{a}_{F}

is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate bound-state energies for three

bbb

and four

bbbb

resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact bound-state energies of two bosons plus one fermion

bbf

, two bosons plus two fermions $b{f}_{\ensuremath{\uparrow}}b{f}_{\ensuremath{\downarrow}}$, and three bosons plus one fermion

bbbf