Quantum Physics in Connected Worlds

TL;DR

This paper investigates how quantum spin systems on arbitrary graphs tend to behave like a collective spin in the thermodynamic limit, revealing the role of graph structure in many-body quantum physics.

Contribution

It proves that under minimal constraints, such systems exhibit collective behavior, and identifies complex phases arising from inhomogeneous dense graphs.

Findings

Systems on arbitrary graphs behave like a collective spin in the thermodynamic limit.

Regular, low-dimensional graphs lead to simple collective behavior.

Inhomogeneous dense graphs exhibit complex phases with entanglement and non-uniform correlations.

Abstract

Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in control over the pairwise interactions in many-body simulators, we determine the fate of spin systems on more general, arbitrary graphs. Placing the minimum possible constraints on the underlying graph, we prove how, with certainty in the thermodynamic limit, such systems behave like a single collective spin. We thus understand the emergence of complex many-body physics as dependent on `exceptional', geometrically constrained structures such as the low-dimensional, regular ones found in nature. Within the space of dense graphs we identify hitherto unknown exceptions via their inhomogeneity and observe how complexity is heralded in these systems by entanglement and highly non-uniform correlation functions. Our work paves the way for the discovery and exploitation of a whole class of geometries which can host uniquely complex phases of matter.