By using unbiased continuous-space quantum Monte Carlo simulations, we investigate the ground-state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas [C.-N. Yang, Phys. Rev. Lett. 19, 1312 (1967)PRLTAO0031-900710.1103/PhysRevLett.19.1312] is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model [E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)PRLTAO0031-900710.1103/PhysRevLett.20.1445], comparing two approaches to map the continuous space to the discrete-lattice model: The first is based on (noninteracting) Wannier functions and the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs and also in very shallow OLs if the interaction strength approaches the Tonks-Girardeau limit. In deep OLs we find quantitative agreement with density-matrix renormalization-group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi-long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.

One-dimensional repulsive Fermi gas in a tunable periodic potential / Pilati, S.; Barbiero, L.; Fazio, R.; Dell'Anna, L.. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - ELETTRONICO. - 96:2(2017). [10.1103/PhysRevA.96.021601]

One-dimensional repulsive Fermi gas in a tunable periodic potential

Barbiero L.;Fazio R.;Dell'Anna L.
2017

Abstract

By using unbiased continuous-space quantum Monte Carlo simulations, we investigate the ground-state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas [C.-N. Yang, Phys. Rev. Lett. 19, 1312 (1967)PRLTAO0031-900710.1103/PhysRevLett.19.1312] is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model [E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)PRLTAO0031-900710.1103/PhysRevLett.20.1445], comparing two approaches to map the continuous space to the discrete-lattice model: The first is based on (noninteracting) Wannier functions and the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs and also in very shallow OLs if the interaction strength approaches the Tonks-Girardeau limit. In deep OLs we find quantitative agreement with density-matrix renormalization-group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi-long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2971675