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We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in non-trivial quantum spin models. The result is also novel: in spite of presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation. This shows existence of a gapless but short range spin liquid. An unusual, all energy scale fractionization of a spin -flip quanta, into two infinitely massive π-fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.PACS numbers: 75.10.jm, 03.67.Lx, 71.10.Pm In the field of quantum computers and quantum communications, practical realizations of qubits that are robust and escape decoherence is a foremost challenge [1]. In this context Kitaev proposed[2] certain emergent topological excitations in strongly correlated quantum many body systems as robust qubits. In a fault tolerant quantum computation scheme [2,3,4], Kitaev constructed a non-trivial and exactly solvable 2-dimensional spin model [2] and illustrated basic ideas. In some limit it also becomes the celebrated 'toric code' Hamiltonian. The Kitaev model has come closer to reality, after recent proposals for experimental realizations [5,6] and schemes for manipulation and detection [7]. In initialisation, error correction and read out operations, it is 'spins' rather than emergent topological degrees of freedom that are directly accessed from outside. Thus an understanding of dynamic spin correlations is of paramount importance.We present certain exact analytical results for time dependent spin correlation functions, in arbitrary eigenstates of the Kitaev Model. Our results are non-trivial and novel, with possible implications for new quantum computational schemes. Further our result is unique in the sense that it is the first exact result for equilibrium dynamical spin correlation functions in a non trivial 2D quantum spin model.We show that dynamical two spin correlation functions are short ranged and vanish identically beyond nearest neighbor sites for all time t, for all values of the coupling constants J x , J y and J z , even in the domain of J's where the model is gapless. Our result shows rigorously that it is a short range quantum spin liquid and long range spin order is absent. We obtain a compact form for the time dependence, which makes the physics transparent.Kitaev Model is known to support dynamical Majorana fermions and static π-flux eigen-excitations. We show how fractionization [8, 9] of a local spin-flip quanta into a bound pair of static π-flux excitations and a free Majorana fermion occurs.In the present paper we have restricted our calculation to dynamical correlation functions for time independent Hamiltonians, in arbitrary eigen-states and thermal states. In actual quantum computations, key manipulat...

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A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.

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