Bosonization of fermion interaction

In this paper, we investigate the quantum coherence of Bose–Fermi mixtures of ultracold dipolar particles trapped in a three-site Bose–Fermi–Hubbard model. We show that the interplay between the boson–boson on-site interaction, boson–fermion on-site interaction, and boson–fermion inter-site dipole–dipole interaction (DDI) results in interesting coherence characters. When boson–boson on-site interaction is present, the resonance character of coherence against both boson–fermion DDI and boson–fermion on-site interaction emerges, the coherence of the system can be enhanced at certain values of boson–fermion on-site interaction and boson–fermion DDI. DDI of fermion–fermion affects the coherence weak and the phase coherence decreases monotonically for all the values of fermion–fermion DDI. The obtained coherent characters are further confirmed within the variational analyzing of the ground state energy.In this paper, we investigate the quantum coherence of Bose–Fermi mixtures of ultracold dipolar particles trapped in a three-site Bose–Fermi–Hubbard model. We show that the interplay between the boson–boson on-site interaction, boson–fermion on-site interaction, and boson–fermion inter-site dipole–dipole interaction (DDI) results in interesting coherence characters. When boson–boson on-site interaction is present, the resonance character of coherence against both boson–fermion DDI and boson–fermion on-site interaction emerges, the coherence of the system can be enhanced at certain values of boson–fermion on-site interaction and boson–fermion DDI. DDI of fermion–fermion affects the coherence weak and the phase coherence decreases monotonically for all the values of fermion–fermion DDI. The obtained coherent characters are further confirmed within the variational analyzing of the ground state energy.

Modern Physics Letters BFeb 25, 20140 citations

Bosonization of Weyl Fermions

Eduardo C. Marino

Bulletin of the American Physical SocietyMar 17, 20160 citations

Microscopic foundation of the interacting boson model

Cheng-Li Wu, D.H. Feng, Jin-Quan Chen +1 more

An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.

Physical Review CJul 1, 19822 citations

Composite-fermionization of bosons in rapidly rotating atomic traps

Chia‐Chen Chang, Nicolas Regnault, Th. Jolicœur +1 more

The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect for bosons interacting with a short range interaction. Motivated by the composite fermion theory of the fractional Hall effect of electrons, we test the idea that the interacting bosons map into non-interacting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $\nu=n/(n+1)$ with non-interacting fermions at $\nu^*=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$ , but interactions between fermions become increasingly important with $n$ . At $\nu=1$ , which is obtained in the limit $n\rightarrow \infty$ , the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect for bosons interacting with a short range interaction. Motivated by the composite fermion theory of the fractional Hall effect of electrons, we test the idea that the interacting bosons map into non-interacting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $\nu=n/(n+1)$ with non-interacting fermions at $\nu^*=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$, but interactions between fermions become increasingly important with $n$. At $\nu=1$, which is obtained in the limit $n\rightarrow \infty$, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.

Jan 1, 20051 citation

\nu=n/(n+1)

with non-interacting fermions at

\nu^*=n

for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small

n

, but interactions between fermions become increasingly important with

n

. At

\nu=1

, which is obtained in the limit

n\rightarrow \infty

, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.