Quantum simulation of spin-1 XXZ Heisenberg models and the Haldane phase with dysprosium

Dysprosium atoms have proven to be a promising platform for quantum simulation due to their strong magnetic moment and high tunability of interactions. In this work, we propose dysprosium atoms for simulating the one-dimensional spin-1 XXZ Heisenberg model, which is known to have a rich phase diagram including the famous Haldane phase. To realize the model, we make use of the strong dipolar exchange interactions that naturally occur in the ground state of dysprosium due to its large electron angular momentum of J = 8. To implement spin-1 particles, we encode the spin degree of freedom into three Zeeman sublevels, which are energetically isolated by applying a magnetic field. Using the density-matrix renormalization group, we analyze the ground-state properties of the resulting effective model. We find that a chain of fermionic dysprosium atoms in a suitable magnetic field can form a Haldane state with the characteristic spin-1/2 edge modes. Furthermore, we discuss the use of AC Stark shifts and Raman-type schemes for bosonic dysprosium to isolate effective spin-1 systems and to increase the tunability of model parameters.