Quantum simulation of the Haldane phase using open shell molecules

TL;DR

This paper proposes a method to simulate the Haldane phase using open shell molecules in optical traps, demonstrating the phase's robustness and discussing experimental feasibility with specific molecules.

Contribution

It introduces a novel approach to realize spin-1 quantum magnetic Hamiltonians with $^2\Sigma$ molecules and analyzes the stability of the Haldane phase via tensor network methods.

Findings

The Haldane phase exists in the proposed molecular system.

The phase remains stable despite SU(3) symmetry-breaking terms.

Feasibility of experimental realization with MgF molecules is discussed.

Abstract

Dipolar molecules in optical traps are a versatile platform for studying many-body phases of quantum matter in the presence of strong and long-range interactions. The dipolar interactions in such setups can be enabled by microwave driving opposite parity rotational levels of the molecules. We find that the regime where the $N=0,J=1/2,F=1$ state is coupled to the $N=1,J=3/2,F=2$ manifold with circularly polarized microwaves, in the presence of a small magnetic field, can lead to spin-1 quantum magnetic Hamiltonians, due to the decoupling between electron spin and orbit, that is unique to the $^2\Sigma$ ground state molecules. We demonstrate that in one dimension, the phase diagram associated with this Hamiltonian, computed via tensor network methods, hosts the celebrated Haldane phase. We find that the Haldane phase persists even in the presence of SU(3) correction terms that break the SU(2) algebra of the Hamiltonian. We discuss the feasibility of the proposed scheme for $^2\Sigma$ molecules with large rotational constants such as the directly laser cooled molecule MgF for future experiments.