Trap effects and continuum limit of the Hubbard model in the presence of a harmonic potential

Abstract

We give a prescription to perform the continuum limit of the $d$-dimensional Hubbard model in the presence of a harmonic trap at zero temperature. We perform the continuum limit at fixed number of particles. In $d\ge 3$ the lattice system of spin-1/2 particles is mapped into a non-interacting two-component Fermi gas in a harmonic trap. In $d=1$ and $d=2$ the particles with opposite spin interact via a Dirac delta interaction. We show that the properties of this continuum limit can be put in correspondence with those derived applying the Trap-Size scaling (TSS) formalism to the confined Hubbard model in the so called Dilute Regime (fixed number of particles and weak confinement). The correspondence in $d=1$ and $d=2$ has been tested comparing the numerical results obtained for lattice system with those of the continuum limit in the case of two-particle and in absence of spin-polarization ($N=2$,$N_{\uparrow }=N_{\downarrow }=1$).

References in corpus (4)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

Cited by in corpus (4)

• Coherent and dissipative dynamics at quantum phase transitions
• Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases