Institut für Theoretische Physik, Leibniz Universität Hannover, Germany.
J Phys Condens Matter. 2013 Jan 9;25(1):014002. doi: 10.1088/0953-8984/25/1/014002. Epub 2012 Dec 5.
We investigate the local density of states of the one-dimensional half-filled spinless fermion model with nearest-neighbour hopping t > 0 and interaction V in its Luttinger liquid phase -2t < V ≤ 2t. The bulk density of states and the local density of states in open chains are calculated over the full band width ∼4t with an energy resolution ≤0.08t using the dynamical density-matrix renormalization group (DDMRG) method. We also perform DDMRG simulations with a resolution of 0.01t around the Fermi energy to reveal the power-law behaviour D(ϵ) ∼ |ϵ - ϵ(F)|(α) predicted by the Luttinger liquid theory for bulk and boundary density of states. The exponents α are determined using a finite-size scaling analysis of DDMRG data for lattices with up to 3200 sites. The results agree with the exact exponents given by the Luttinger liquid theory combined with the Bethe Ansatz solution. The crossover from boundary to bulk density of states is analysed. We have found that boundary effects can be seen in the local density of states at all energies, even far away from the chain edges.
我们研究了一维半填充无自旋费米子模型的局域态密度，该模型具有最近邻跳跃 t > 0 和相互作用 V，处于其 Luttinger 液体相 -2t < V ≤ 2t。使用动态密度矩阵重整化群（DDMRG）方法，我们在整个带宽 ∼4t 上进行了计算，能量分辨率≤0.08t，计算了在开放链中的体密度和局域态密度。我们还在费米能附近以 0.01t 的分辨率进行了 DDMRG 模拟，以揭示 Luttinger 液体理论预测的体和边界态密度的幂律行为 D(ϵ) ∼ |ϵ - ϵ(F)|(α)。使用多达 3200 个站点的晶格的 DDMRG 数据的有限大小标度分析确定了指数 α。结果与 Luttinger 液体理论与 Bethe Ansatz 解相结合给出的精确指数一致。分析了从边界到体态密度的转变。我们发现，即使在远离链边缘的所有能量处，边界效应都可以在局域态密度中看到。
