# Treelike interactions and fast scrambling with cold atoms

## TL;DR

This paper introduces a cold atom quantum spin model with tunable geometry that transitions from linear to treelike structures, enabling the study of fast scrambling and entanglement dynamics in different geometries.

## Contribution

It presents a feasible experimental setup for observing emergent geometries and fast information spreading in quantum many-body systems.

## Key findings

- Peak entanglement at the transition point
- Exponential quantum information spreading in treelike regime
- Observable geometry transition in quench dynamics

## Abstract

We propose an experimentally realizable quantum spin model that exhibits fast scrambling, based on non-local interactions which couple sites whose separation is a power of 2. By controlling the relative strengths of deterministic, non-random couplings, we can continuously tune from the linear geometry of a nearest-neighbor spin chain to an ultrametric geometry in which the effective distance between spins is governed by their positions on a tree graph. The transition in geometry can be observed in quench dynamics, and is furthermore manifest in calculations of the entanglement entropy. Between the linear and treelike regimes, we find a peak in entanglement and exponentially fast spreading of quantum information across the system. Our proposed implementation, harnessing photon-mediated interactions among cold atoms in an optical cavity, offers a test case for experimentally observing the emergent geometry of a quantum many-body system.