Ground state phase diagram of the doped Hubbard model on the four-leg cylinder

Abstract

We study the ground state properties of the Hubbard model on a four-leg cylinder with doped hole concentration per site δ 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 to 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 4k F and 2k F wave vectors that are 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 (nearly) 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 liquid formed from a weakly coupled (BCS like) d-wave superconductor on the ladder where the interactions have only the effect of stabilizing a cuprate style magnetic resonance.

Doping Quantum Spin Liquids on the Kagome Lattice

“…The oscillation amplitude A cdw of becomes significantly smaller as increases. Similar with previous studies of Hubbard model on the square lattice, [ 51,52 ] our results demonstrate the importance of second‐neighbor electron hopping which provides a promising pathway to potentially realize superconductivity in doping QSL on the Kagome lattice. However, it is also worth mentioning that even the superconducting correlations can be significantly enhanced by , quasi‐long‐range superconductivity has not yet been realized on the Kagome lattice.…”

“…It has been shown in previous studies [ 51,52 ] that the second‐neighbor electron hopping of the Hubbard model on the square lattice is important to enhance superconductivity and suppress CDW order. In this paper, we will show that this is also true for the lightly doped QSL on the Kagome lattice.…”

Detecting quantum critical points in the t-$$t'$$ Fermi-Hubbard model via complex network theory

“…It would be interesting to conduct a similar analysis for a larger system. The state-of-the-art DMRG allows to study quasi-2d stripes as large 4-by-64 atomic sites [38][39][40][41][42] , and we hope to apply the complex network approach to such systems in the future. Still, already at this point it is instructive to compare our results with what has been found by means of other approaches.…”

“…Still, already at this point it is instructive to compare our results with what has been found by means of other approaches. In the recent paper 39 , a detailed DMRG analysis of the Hubbard model phase diagram with hole doping ≤ 12.5% has been conducted (which would correspond to sectors (7,7), (7,8), (8,8) in our case), and it was shown that for such hole concentration and negative values of t ′ , the model is in the Luther-Emery liquid phase 51 which is very stable upon varying U and t ′ . This is consistent with our observation that the signs of QCP fade away for all values of the next-nearest hopping and Coulomb repulsion when we approach this level of doping.…”

“…This behavior was interpreted in terms of formation of a local plaquette valence bond state. On a larger scale, the ground state of the model has been analyzed by means of density matrix renormalization group (DMRG) [38][39][40] (see also 41 for the related studies of its cousin, t − J-model), and additional arguments in favor of stabilization of superconductivity by the next-to-nearest neighbor hopping were provided (in 40 , the competition between long-range and plaquette d-wave superconducting orders has been demonstrated). In turn, at temperatures above the superconducting phase transition, determinantal Monte Carlo computations 42 demonstrated that the DC resistivity exceeds the Mott-Ioffe-Regel limit and scales linearly with temperature.…”