Superconducting and SDW condensation energies in the 2D Hubbard model and the meaning to the stripe phase

Abstract

The variational Monte Carlo calculations give a finite bulk-limit value of superconducting (SC) condensation energy E cond in the 2D Hubbard model with next-nearest-site transfer energy t′ when electron density ρ≥0.84 with −0.25≤ t′≤−0.10; our energy unit is the transfer energy between the nearest-neighbor (n.n.) sites. However, the SDW E cond computed by the same method is larger than the SC one in such a region. This suggests that the SC region is very restricted, if it exists. When we improved the trial wave function taking into account the n.n.-site correlation, the SC E cond increased moderately while the SDW E cond decreased considerably. With this modified variational Monte Carlo method we have found a set of parameter values for which the bulk-limit SC E cond is finite whereas that for the SDW vanishes. The SC E cond obtained in both ways around the optimal doping is in fair agreement with the experimental value ∼0.26 meV/site for YBCO estimated from the specific heat and the critical magnetic field, in contrast to the case of the t– J model which gives a value larger by almost two orders of magnitude. In the low-doping region the SDW E cond is overwhelmingly larger than the SC E cond. Further, the striped SDW state seems more stable here. This is considered to be the energetic origin of the stripe features and presumably of the consequent pseudogap in the underdoped region.