# Quench dynamics of two component dipolar fermions subject to a quasiperiodic potential

## TL;DR

This paper investigates the non-equilibrium dynamics and localization phenomena of two-component dipolar fermions in a quasiperiodic potential, revealing a phase transition and reduced spin delocalization due to long-range interactions, with implications for cold atom experiments.

## Contribution

It provides the first analysis of charge and spin localization in long-range dipolar fermions under quasiperiodic disorder, using exact diagonalization and MPS methods.

## Key findings

- Charge imbalance decay indicates a localization transition with disorder strength.
- Strong disorder reduces spin delocalization in long-range interacting fermions.
- Predictions are experimentally relevant for ultracold dipolar atom systems.

## Abstract

Motivated by recent experiments in fermionic polar gases, we study the non-equilibrium dynamics of two-component dipolar fermions subject to a quasiperiodic potential. We investigate the localization of charge and spin degrees of freedom time evolving with a long-range spin-SU(2) symmetric fermionic Hamiltonian, by calculating experimentally accessible dynamical observables. To study the non-equilibrium dynamics, we start the time evolution with two initial states at half-filling: (i) product state with doublons $|\uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow \downarrow \rangle$ and (ii) product state with singlons $|\uparrow \ \downarrow \ \uparrow \ \downarrow \ \uparrow \ \downarrow \ \uparrow \ \downarrow \ \uparrow \ \downarrow \ \rangle$. We carried out the real-time evolution via the fermionic Hamiltonian using exact diagonalization(ED) and the time-dependent variational principle (TDVP) for finite Matrix product states(MPSs), within experimentally relevant time scales. For the product state with doublons, we observe a delocalized to localized phase transition varying disorder strengths, by monitoring the decay of charge imbalance with time. For the long-range interacting Hamiltonian of our focus, and in the presence of strong enough disorder, starting the time evolution with singlons we find a strong reduction in the spin delocalization, contrary to results of previous studies using the disordered short-range (on-site) Hubbard model with SU(2) symmetry. Our predictions for localization of both charge and spin should be observable in ultra-cold experiments with fermionic dipolar atoms subject to a quasiperiodic potential.