Hubbard ladders at small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math> revisited
Yuval Gannot, Yi‐Fan Jiang, Steven A. Kivelson
Abstract
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 $U\ensuremath{\gtrsim}{U}^{★}$, there is a single emergent correlation length $ln[\ensuremath{\xi}]\ensuremath{\sim}1/U$, characterizing the gapped modes of the system, but for $U\ensuremath{\lesssim}{U}^{★}$, 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.