Study of entanglement and quantum information in condensed matter systems.

The quantum computer is a hypothetical computer that utilizes the superposition principle of quantum mechanics to perform certain computational tasks much faster than any classical computer can. Entanglement is one of the most curious phenomena in Nature, which involves the collapse of the quantum mechanical wave function over arbitrarily long distances. Over the last decade it has been understood that entanglement is a crucial requirement for a quantum computer to take the computational power needed. Hen ce understanding entanglement is necessary to be able to construct a quantum computer in the future. Furthermore, an implementation of a quantum computer is likely to be a condensed matter system, that is some solid state that can be effectively describe d by a low-dimensional quantum model. Therefore, we choose to focus the study on entanglement in condensed matter systems such as spin chains and quantum Hall systems. In particular, the project will study the entanglement properties of one-dimensional s pin chains, which are very complex when the system is critical, and which may serve as a useful toy model as well as a realistic quantum wire. Further, the project will study phase properties of exotic fermion states which may serve as phase reference sta tes like coherent states (such as found in a laser beam) do with bosons. These reference states will very likely be characterized by their entanglement, and will open for new quantum information processing. Moreover, the project will inevitably need to a ddress entanglement properties of the ground state, and therefore it is natural to try to understand how entanglement properties can be used in order to construct the ground state efficiently. Existing techniques to construct the ground state fails whenev er there is too much entanglement present, and thus it is reasonable to believe that comprehension of the entanglement properties will be essential to be able to conceive such a method.