Quantum simulation of non-trivial topology

TL;DR

This paper introduces methods to simulate quantum many-body systems on manifolds with non-trivial topology using synthetic lattices, enabling exploration of topological effects in quantum physics.

Contribution

It presents novel designs for creating synthetic lattices with complex topologies, such as tori and M"obius strips, for quantum simulation.

Findings

Realization of Hubbard model on non-Euclidean manifolds

Conversion of open chains into closed topological structures

Topological changes affect quantum system behavior

Abstract

We propose several designs to simulate quantum many-body systems in manifolds with a non-trivial topology. The key idea is to create a synthetic lattice combining real-space and internal degrees of freedom via a suitable use of induced hoppings. The simplest example is the conversion of an open spin-ladder into a closed spin-chain with arbitrary boundary conditions. Further exploitation of the idea leads to the conversion of open chains with internal degrees of freedom into artificial tori and M\"obius strips of different kinds. We show that in synthetic lattices the Hubbard model on sharp and scalable manifolds with non-Euclidean topologies may be realized. We provide a few examples of the effect that a change of topology can have on quantum systems amenable to simulation, both at the single-particle and at the many-body level.