Short-time Spin Dynamics in Strongly Correlated Few-fermion Systems

TL;DR

This paper investigates the short-time spin dynamics of strongly correlated one-dimensional fermion systems, revealing how decay behaviors change with interaction strength, with implications for ultra-cold atom experiments.

Contribution

It provides a detailed analysis of the decay of spin oscillations in strongly interacting fermions using density-matrix renormalization-group simulations, highlighting the transition from quadratic to linear decay regimes.

Findings

Decay rate increases linearly with interaction strength in weak coupling.

Decay rate is inversely proportional to interaction strength in strong coupling.

Decay behavior transitions from quadratic to linear and back to quadratic as interactions vary.

Abstract

The non-equilibrium spin dynamics of a one-dimensional system of repulsively interacting fermions is studied by means of density-matrix renormalization-group simulations. We focus on the short-time decay of the oscillation amplitudes of the centers of mass of spin-up and spin-down fermions. Due to many-body effects, the decay is found to evolve from quadratic to linear in time, and eventually back to quadratic as the strength of the interaction increases. The characteristic rate of the decay increases linearly with the strength of repulsion in the weak-coupling regime, while it is inversely proportional to it in the strong-coupling regime. Our predictions can be tested in experiments on tunable ultra-cold few-fermion systems in one-dimensional traps.