We re-examine the zero-temperature phase diagram of the two-leg Hubbard ladder in the small $U$ limit, both analytically and using density-matrix renormalization group (DMRG). We find a ubiquitous Luther-Emery phase, but with a crossover in behavior at a characteristic interaction strength, $U^{★}$; for $U\gtrsim U^{★}$, there is a single emergent correlation length $ln\left[\xi \right]\sim 1/U$, characterizing the gapped modes of the system, but for $U\lesssim U^{★}$, there is a hierarchy of length scales, differing parametrically in powers of $U$, reflecting a two-step renormalization group flow to the ultimate fixed point. Finally, to illustrate the versatility of the approach developed here, we sketch its implications for a half-filled triangular lattice Hubbard model on a cylinder and find results in conflict with inferences concerning the small $U$ phase from recent DMRG studies of the same problem.

中文翻译：

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小型哈伯梯子

我们重新检查小腿中两腿哈伯德梯子的零温度相图 $ü$分析和使用密度矩阵重归一化组（DMRG）的最大限制。我们发现了一个普遍存在的路德·埃默里（Luther-Emery）阶段，但是在具有特定相互作用强度的情况下行为发生了交叉，${ü}^{★}$; 对于$ü\gtrsim {ü}^{★}$，只有一个紧急相关长度 $ln\left[\xi \right]〜\mathrm{1个}/ü$，表征系统的空白模式，但对于 $ü\lesssim {ü}^{★}$，存在一个长度刻度的层次结构，其参量在参数上有所不同 $ü$，反映了到最终固定点的两步重归一化组流。最后，为了说明此处开发的方法的多功能性，我们绘制了其对圆柱体上半填充三角晶格哈伯德模型的含义，并发现与小模型推论相冲突的结果$ü$ DMRG最近对相同问题的研究得出的第一阶段。