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Superconductivity is usually described in the framework of theBardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes theresonating-valence-bond (RVB) wavefunction proposed for the high-temperaturesuperconductivity in the cuprate. A natural question is \emph{if} anyfundamental physics could be possibly missed by applying such a scheme tostrongly correlated systems. Here we study the pairing wavefunction of twoholes injected into a Mott insulator/antiferromagnet in a two-leg ladder usingvariational Monte Carlo (VMC) approach. By comparing with density matrixrenormalization group (DMRG) calculation, we show that a conventional BCS orRVB pairing of the doped holes makes qualitatively wrong predictions and isincompatible with the fundamental pairing force in the $t$-$J$ model, which iskinetic-energy-driven by nature. By contrast, a non-BCS-like wavefunctionincorporating such novel effect will result in a substantially enhanced pairingstrength and improved ground state energy as compared to the DMRG results. Weargue that the non-BCS form of such a new ground state wavefunction isessential to describe a doped Mott antiferromagnet at finite doping.

Two-hole ground state wavefunction: Non-BCS pairing in a $t$-$J$ two-leg ladder system