Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry

TL;DR

This paper explores how spatial and spin symmetries influence the dynamics of a small XXZ quantum simulator in a double-ring geometry, proposing a simple measurement protocol to observe symmetry effects.

Contribution

It identifies observable consequences of symmetries on quantum dynamics and introduces a feasible experimental scheme for symmetry-based measurements in XXZ spin systems.

Findings

Symmetries determine measurement probability behaviors over time.

The number of distinct measurement outcomes is dictated by symmetry.

Collapse of the initial state can be observed in larger systems.

Abstract

We theoretically identify observable consequences of spatial and spin symmetries on the dynamics of a small XXZ quantum simulator. Our proposed protocol relies on the choice of suitable initial states, and involves the measurement scheme whose experimental implementation is the simplest. We analyze a system of $N=2n=6$ to $12$ particles, trapped in a planar geometry comprised of two rings which exhibits point group symmetry $D_{nh}$. The particles represent effective spins whose interaction is described by the XXZ or Heisenberg Hamiltonian. The system is prepared in an initial state which is sitewise-factorized and invariant under all spatial symmetries, it evolves for a given time, after which the $z$-components of all $N$ spins are measured. We show that symmetries dictate (i) the qualitative behaviour of the measurement probabilities as a function of the evolution time, and (ii) the number of measurement results with different probabilities. We highlight the role of a twofold rotation of all spins. We also demonstrate that, in larger systems, the collapse of the initial state may be observed.