The emerging closeness between correlated spin systems and error-correcting codes enables us to use coding theoretical techniques to study physical properties of manybody spin systems. This thesis illustrates the use of classical and quantum coding theory in classifying quantum phases arising in many-body spin systems via a systematic study of stabilizer Hamiltonians with translation symmetries...

We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed dynamical resonance theory, and we piece them together to obtain the total evolution. The initial state corresponding to one time-interval with constant Hamiltoni...

We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the ...

Due to non-linear structure, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast the wave-function methods, a detailed and careful analysis of such was not performed before. this work, we use two-particle density matrices investigate local spin charge correlators that quantify charge-resonance covalent characters these sol...

By considering distance-regular graphs as spin networks, first we introduce some particular spin Hamiltonians which are extended version of those of Refs.[1, 2]. Then, by using spectral analysis techniques and algebraic combinatoric structure of distanceregular graphs such as stratification introduced in [3, 4] and Bose-Mesner algebra, we give a method for finding a set of coupling constants in...

We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form H = dΓ(ω) + V acting on the bosonic Fock space Γ(h), where ω is a massive one-particle Hamiltonian acting on h and V is a Wick polynomial Wick(w) for a kernel w satisfying some decay properties at infinity. We describe the essential spectrum of H , prov...

We investigate generic Hamiltonians for confined electrons with weak inhomogeneous spin-orbit coupling. Using a local gauge transformation we show how the SU(2) Hamiltonian structure reduces to a U(1)×U(1) structure for spinless fermions in a fictitious orbital magnetic field, to leading order in the spin-orbit strength. Using an Onsager relation, we further show how the resulting spin conducta...