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

TL;DR

This paper investigates the pairing wavefunction in a two-leg ladder $t$-$J$ model, revealing that non-BCS wavefunctions better capture the kinetic-energy-driven pairing mechanism in doped Mott insulators.

Contribution

It introduces a non-BCS-like wavefunction that accurately describes pairing in a doped Mott insulator, challenging traditional BCS and RVB approaches.

Findings

Non-BCS wavefunction improves ground state energy predictions.

Conventional BCS/RVB pairing is incompatible with the $t$-$J$ model.

Kinetic-energy-driven pairing is essential in doped Mott systems.

Abstract

Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is \emph{if} any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo (VMC) approach. By comparing with density matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t$-$J$ model, which is kinetic-energy-driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.