Quantum simulation of spin ordering with nuclear spins in a solid state lattice

An experiment demonstrating the quantum simulation of a spin-lattice Hamiltonian is proposed. Dipolar interactions between nuclear spins in a solid state lattice can be modulated by rapid radio-frequency pulses. In this way, the effective Hamiltonian of the system can be brought to the form of an antiferromagnetic Heisenberg model with long range interactions. Using a semiconducting material with strong optical properties such as InP, cooling of nuclear spins could be achieved by means of optical pumping. An additional cooling stage is provided by adiabatic demagnetization in the rotating frame (ADRF) down to a nuclear spin temperature at which we expect a phase transition from a paramagnetic to antiferromagnetic phase. This phase transition could be observed by probing the magnetic susceptibility of the spin-lattice. Our calculations suggest that employing current optical pumping technology, observation of this phase transition is within experimental reach.Comment: 11 pages, 3 figues; Published versio

Efficiency of free energy calculations of spin lattices by spectral quantum algorithms

Quantum algorithms are well-suited to calculate estimates of the energy spectra for spin lattice systems. These algorithms are based on the efficient calculation of the discrete Fourier components of the density of states. The efficiency of these algorithms in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size.Comment: 9 pages, 4 figures; corrected typographical and minor mathematical error