Grand-canonical variational approach for the t-J model

TL;DR

This paper uses a grand-canonical variational Monte Carlo approach to study the 2D t-J model, revealing insights into chemical potential, particle fluctuations, and phase fluctuations, with results aligning with experimental cuprate data.

Contribution

It introduces a grand-canonical variational Monte Carlo method for the t-J model, enabling direct measurement of chemical potential and phase fluctuations, and incorporates a fugacity factor to account for Gutzwiller projection effects.

Findings

Chemical potential behavior matches experimental cuprates for most materials.

Tunneling asymmetry increases with decreasing doping, consistent with STM results.

Phase fluctuations are significantly enhanced in the underdoped regime.

Abstract

Gutzwiller-projected BCS wave function or the resonating-valence-bond (RVB) state in the 2D extended t-J model is investigated by using the variational Monte Carlo technique. We show that the results of ground-state energy and excitation spectra calculated in the grand-canonical scheme allowing particle number to fluctuate are essentially the same as previous results obtained by fixing the number of particle in the canonical scheme if the grand thermodynamic potential is used for minimization. To account for the effect of Gutzwiller projection, a fugacity factor proposed by Laughlin and Anderson few years ago has to be inserted into the coherence factor of the BCS state. Chemical potential, particle number fluctuation, and phase fluctuation of the RVB state, difficult or even impossible to be calculated in the canonical ensemble, have been directly measured in the grand-canonical picture. We find that except for La-214 materials, the doping dependence of chemical potential is consistent with experimental findings on several cuprates. Similar to what has been reported by scanning tunneling spectroscopy experiments, the tunneling asymmetry becomes much stronger as doping decreases. We found a very large enhancement of phase fluctuation in the underdoped regime.