Abstract
We study the ground state properties of the Hubbard model on a 4-leg cylinder with doped hole concentration per site $\delta\leq 12.5\%$ using density-matrix renormalization group. By keeping a large number of states for long system sizes, we find that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor hopping $t'$. Without $t'$ the ground state of the system corresponds with the insulating filled stripe phase with long-range charge-density-wave (CDW) order and short-range incommensurate spin correlations appears. However, for a small negative $t'$ a phase characterized by coexisting algebraic d-wave superconducting (SC)- and algebraic CDW correlations. In addition, it shows short range spin- and fermion correlations consistent with a canonical Luther-Emery (LE) liquid, except that the charge- and spin periodicities are consistent with half-filled stripes instead of the $4 k_F$ and $2 k_F$ wavevectors generic for one dimensional chains. For a small positive $t'$ yet another phase takes over showing similar SC and CDW correlations. However, the fermions are now characterized by a (near) infinite correlation length while the gapped spin system is characterized by simple staggered antiferromagnetic correlations. We will show that this is consistent with a LE formed from a weakly coupled (BCS like) d-wave superconductor on the ladder where the interactions have only the effect to stabilize a cuprate style magnetic resonance.
Highlights
The Hubbard model is the simplest model that captures essential features of strongly interacting electrons realized in solids containing transition-metal and/or rare-earth elements, characterized by a compromise between kinetic energy and strong local repulsion
Resting on the fact that it has become possible recently to compute reliably the ground states of four-leg ladder Hubbard systems by density-matrix renormalization group (DMRG), we have systematically investigated the ground state properties in the low doping regime
Given that these ladder systems renormalize into one-dimensional systems at large distances, one can use the well understood universal properties of 1D physics to diagnose the physics
Summary
The Hubbard model is the simplest model that captures essential features of strongly interacting electrons realized in solids containing transition-metal and/or rare-earth elements, characterized by a compromise between kinetic energy and strong local repulsion. We will report on how the ground states of the Hubbard model look in a much larger regime of physically relevant parameters [27,28] Another aspect is that already the very first four-leg cylinder results showed a strong appetite to form “intertwined order,” of the spin-stripe variety [20,21,22,23,29]. The outcomes of various methods characterized by qualitatively different systematic errors were compared and such insulating filled stripes ground states were established This includes the DMRG results on the four-leg cylinders at t = 0 and U = 8t [17,18,19,20]. In the conclusions we will further discuss potential relations between these findings and the situation in these experimental systems
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