# An exactly solvable model for Dynamic Nuclear polarization

## TL;DR

This paper presents an exactly solvable model demonstrating how the localization transition in driven disordered fermionic systems enhances hyperpolarization of nuclear spins, revealing a critical point where maximal polarization occurs.

## Contribution

The study introduces a solvable fermionic model that links Anderson localization transition to hyperpolarization in driven disordered magnets, highlighting the role of multifractal correlations.

## Key findings

- Maximal hyperpolarization occurs near the localization transition.
- Hyperpolarization is enhanced by multifractal correlations at criticality.
- The model provides exact insights into the role of localization in dynamic nuclear polarization.

## Abstract

We introduce a solvable model of driven fermions that elucidates the role of the localization transition in driven disordered magnets, as used in the context of dynamic nuclear polarization. Instead of spins, we study a set of non-interacting fermions that are coupled locally to nuclear spins and tend to hyperpolarize them. The induced hyperpolarization is a fingerprint of the driven steady state of the fermions, which undergo an Anderson Localization (AL) transition upon increasing the disorder. Our central result is that the maximal hyperpolarization level is always found close to the localization transition. In the limit of small nuclear moments the maximum is pinned to the transition, and the hyperpolarization is strongly enhanced by multi-fractal correlations in the critical state of the nearly localized driven system, its magnitude reflecting multi-fractal scaling.