Homogeneous and domain wall topological Haldane conductors with dressed Rydberg atoms

TL;DR

This paper demonstrates that dressed Rydberg atoms in a one-dimensional optical lattice can realize topological Haldane phases, showing both metallic and superconducting states, and explores their domain wall structures and stabilization methods.

Contribution

It introduces a method to realize and analyze topological Haldane conductors using dressed Rydberg atoms, combining theoretical predictions with experimental feasibility.

Findings

Both metallic and superconducting topological Haldane states can be achieved.

Domain wall structures with finite magnetization are formed under magnetic fields.

A procedure to dynamically stabilize Haldane phases from a confined Ising state is proposed.

Abstract

The interplay between antiferromagnetic interaction and hole motion is capable of inducing intriguing conducting topological Haldane phases described by a finite non-local string order parameter. Here we show that these states of matter are captured by the one dimensional $t-J_z$ model which can be experimentally realized with dressed Rydberg atoms trapped onto a one dimensional optical lattice. In the sector with vanishing total magnetization exact Bethe ansatz calculations associated to bosonization technique allow to predict that both metallic and superconducting topological Haldane states can be achieved. With the addition of an appropriate magnetic field the system enters in a domain wall structure with finite total magnetization. In this regime conducting topological Haldane states are confined in domains separated by regions where fully polarized Luttinger liquid occurs. A procedure to dynamically stabilize such Haldane topological phases starting from a confined Ising state is also described