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Quantum physics in connected worlds
Joseph Tindall1,2, Amy Searle3, Abdulla Alhajri3,4
1Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY, 10010, USA. jtindall@flatironinstitute.org.
Nature Communications
|December 2, 2022
Summary
Complex many-body quantum systems behave as a single collective spin on general graphs. Exceptional geometries are key for complex physics, with inhomogeneity signaling emergent complexity via entanglement.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Theoretical research on many-body quantum systems typically focuses on regular structures with limited interactions.
- Advances in controlling pairwise interactions in quantum simulators motivate exploring more general system architectures.
Purpose of the Study:
- To determine the behavior of spin systems on arbitrary graphs, moving beyond regular structures.
- To understand the conditions under which complex many-body physics emerges.
Main Methods:
- Analysis of spin systems on general, arbitrary graphs.
- Mathematical proofs concerning system behavior in the thermodynamic limit.
- Identification of specific graph properties (inhomogeneity) that lead to complex behavior.
Main Results:
- Spin systems on general graphs behave as a single collective spin in the thermodynamic limit.
- Complex many-body physics emerges only in specific, geometrically constrained structures.
- Inhomogeneous dense graphs exhibit exceptions, with entanglement and non-uniform correlations heralding complexity.
Conclusions:
- The emergence of complex quantum many-body physics is critically dependent on specific geometric constraints.
- Inhomogeneity in dense graphs can lead to novel complex phases of matter.
- This research opens avenues for discovering and utilizing new geometries for exotic quantum phenomena.
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