# Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian

## TL;DR

This paper establishes the strong unique continuation property for many-body Pauli operators with various potentials and magnetic fields, using a novel singular Carleman estimate involving fractional Laplacians.

## Contribution

It introduces a new Carleman estimate to prove unique continuation for Pauli operators with less regular potentials and magnetic fields.

## Key findings

- Proved strong unique continuation for Pauli operators with $L^p_{loc}$ potentials.
- Developed a singular Carleman estimate involving fractional Laplacians.
- Extended unique continuation results to broader classes of potentials.

## Abstract

We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p\loc(\R^d)$, and with magnetic potentials in ${L^{q}\loc(\R^d)}$, where ${p > \max(2d/3,2)}$ and ${q > 2d}$. For this purpose, we prove a singular Carleman estimate involving fractional Laplacian operators.