Quantum phases of matter in hyperbolic space

Quantum many-body systems on hyperbolic lattices have been a growing field of interest, with applications ranging from quantum gravity to error correction. Yet, fundamental connections between phases of matter, energetic structure, and correlations which are well-explored in Euclidean settings remain murky in the hyperbolic setting. In our work, we discuss insights gained from investigating the paradigmatic quantum transverse-field Ising model on the Cayley tree, using tensor networks as a central numerical and analytical tool. We also discuss how measurement and feedback may be able to efficiently prepare states on such lattices that have evaded constructions in Euclidean settings.