|title||"Trapped-Ion Quantum Simulations of Spin Systems at Non-Vanishing Temperature"|
Quantum simulations in trapped ions are prosperous candidates for the solution of otherwise intractable quantum many-body problems. A prominent focus of such efforts is the simulation of quantum spin systems. Thus far, these are restricted to investigations at vanishing temperature or far from equilibrium. In this thesis, we study how trapped-ion quantum simulations of spin systems may be extended to non-vanishing temperature, ultimately allowing probes of the thermal phase diagram. For this, we introduce a noise modulated coupling between the qubits and a subset of the vibrational modes of the ions. We investigate analytically how this may provide an effective bath for the pseudo-spins. Subsequently, we numerically study the phase diagram of a variable-range Ising model with a transverse field. This model can both be readily implemented in trapped-ion quantum simulations as well as offer a phase diagram strongly varying on the chosen range of interaction. We put special focus on a comparison between the thermal phase diagram of an ideally thermalised system and that which may be achieved in a trapped-ion spin chain with the effective bath. This proposal may open the way to a crucial missing piece for the investigation of quantum many-body spin models in trapped ions.