Local Density of States for Individual Energy Levels in Finite Quantum Wires

The local density of states in finite quantum wires is calculated as a function of discrete energies and position along the wire. By using a combination of numerical density matrix renormalization group calculations and analytical bosonization techniques, it is possible to obtain a good understanding of the local spectral weights along the wire in terms of the underlying many-body excitations.

Figure 1

Single-particle excitations on the filled Fermi sea for the noninteracting system.

Figure 2

DMRG data for the LDOS $|⟨b|{\psi }^{†}(x)|N_0⟩{|}^2$ (first row) and $|⟨a|{\psi }^{†}(x)|N_0⟩{|}^2$ for $L=78$, where $|b⟩$ and $|a⟩$ are eigenstates that have evolved from the $n=2$ states in Fig. 1 when interactions $U$ are switched on. The spectral weight is shifted towards $|b⟩$ with increasing interactions, but $|a⟩$ remains dominant.

Figure 3

DMRG data for the total LDOS of different levels $n$ for $U=1.4t$ (crosses) compared to the bosonization results in Eq. (7) with $a=0.56$ (solid line). Dots mark the LDOS from bosonization at discrete lattice points.

Figure 4

DMRG data for $U=1.8t$ and $L=78$ of the position integrated DOS $\rho (\omega )=\sum _x\rho (\omega ,x)$ for each individual state (crosses). The stars represent the sum over all nearly degenerate states at each discrete energy ${\omega }_n$, which agrees very well with the integral of Eq. (7) (circles).