We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those that can not be simulated. Whereas for general spin systems no finite universal set of generatin...

We study the magnetic interactions in Mott-Hubbard systems with partially filled t_{2g} levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an e...

A general mapping between the energy of pertinent magnetic solutions and the diagonal terms of the spin Hamiltonian in a local representation provides the first general framework to extract accurate values for the many body terms of extended spin Hamiltonians from periodic first-principle calculations. Estimates of these terms for La2CuO4, the paradigm of high-Tc superconductor parent compounds...

The entanglement properties of some novel quantum systems are studied that are inspired by recent developments in cold-atom technology. A triangular optical lattice of two atomic species can be employed to generate a variety of spin-1/2 Hamiltonians including effective three-spin interactions. A variety of one or two dimensional systems can thus be realized that possess multi-degenerate ground ...

It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speedup of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a CNOT (controlled NOT) gate for free fermions, using...

Why do we not experience a violation of macroscopic realism in everyday life. Normally, no violation can be seen either because of decoherence or the restriction of coarse-grained measurements, transforming the time evolution of any quantum state into a classical time evolution of a statistical mixture. We find the sufficient condition for these classical evolutions for spin systems under coars...