Two-Hole Ground State: Dichotomy in Pairing Symmetry

TL;DR

This paper investigates the two-hole ground state in the t-J model using variational Monte Carlo, revealing a novel pairing state with a dichotomy in pairing symmetry and a pairing mechanism driven by quantum phase-strings.

Contribution

It uncovers a new pairing state with mixed d-wave and s-wave symmetries and identifies quantum phase-strings as the pairing mechanism, advancing understanding of doped Mott insulators.

Findings

Two holes form a pairing state with a quantum number matching exact methods.

The pairing exhibits a dichotomy: d-wave in electrons, s-wave in quasiparticles.

The pairing mechanism is driven by quantum phase-strings, not magnetic order.

Abstract

A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method. Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics. In this work, we further investigate the ground state of two holes by VMC. It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations. A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d-wave in terms of the electron c operators and an s-wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function. A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result. We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic order nor the resonating-valence-bound pairing in the spin background but is the consequence of the quantum phase-strings created by the hopping of holes. The resulting spin-current pattern mediating the pairing force is explicitly illustrated in the VMC calculation. Physical implications to superconductivity at finite doping are also discussed.