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Finite quantum wires are modeled by interacting Fermions on a one-dimensional lattice with open ends. We are able to obtain the local density of states (LDOS) as a function of discrete energies and position along the chain by using the density matrix renormalization group (DMRG). We compare to results obtained by bosonization for the LDOS of individual single particle excitations in a finite Luttinger liquid with open boundary conditions.
In this way, a detailed understanding of the LDOS for each individual energy level can be obtained in both fermionic and bosonic pictures. Certain degeneracies of the Luttinger Liquid spectrum are lifted in the lattice model by band curvature and interaction effects, leading to a large number of states and energy levels in the LDOS. The results are of relevance for high resolution STM experiments on quantum wires. |
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