Ground state of the Hubbard model with spin-dependent linear potential

TL;DR

This study uses DMRG simulations to analyze how a spin-dependent linear potential influences the ground state of a one-dimensional Fermi-Hubbard model, revealing three regimes of pairing and separation.

Contribution

It introduces a detailed numerical and analytical analysis of the ground state phases under spin-dependent external forces in the Hubbard model, including critical thresholds and experimental relevance.

Findings

Identified three regimes: pairing, staircase-like pair breaking, and complete spin separation.

Derived analytical estimates for critical potential gradients separating these regimes.

Confirmed staircase structure persists under harmonic confinement.

Abstract

We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a linear external potential whose gradient is opposite for the two spin components, so that each spin species sees a potential minimum at a different end of the lattice. Using density-matrix renormalization group (DMRG) simulations, we map the ground-state density distributions and the number of doubly occupied sites as a function of the potential gradient $\beta$ and interaction strength. We identify three distinct regimes separated by critical threshold gradients: (i) a small-$\beta$ regime where fermion pairing remains robust against the external potential; (ii) an intermediate-$\beta$ phase-separated regime characterized by a staircase-like decrease in the doublon number, corresponding to the successive, one-by-one breaking of bound pairs; and (iii) a large-$\beta$ regime where the two spin components are completely spatially separated. We complement the numerical results with a phenomenological model and a local-density approximation analysis, from which we derive closed-form analytical estimates for these critical threshold values. We also verify that the staircase structure persists under additional harmonic confinement. Our results are directly testable in cold-atom experiments, and demonstrate that a spin-dependent linear potential enables precise, integer-level control of the number of bound fermion pairs.