Variational Monte Carlo Study of the Doped $t$-$J$ Model on Honeycomb Lattice

TL;DR

This study uses variational Monte Carlo to analyze the doped $t$-$J$ model on a honeycomb lattice, revealing unique ground state properties, emergent chiral currents, and a novel pairing mechanism with potential implications for superconductivity.

Contribution

It constructs and studies variational ground states for the doped $t$-$J$ model on honeycomb lattice, highlighting emergent chiral currents and a dichotomous pairing mechanism.

Findings

Degenerate single-hole ground states with spin-1/2 and orbital angular momentum $L_z=\pm 2$.

Emergence of chiral spin/hole currents surrounding the hole.

Two-hole pairing with $d+id$ symmetry and tightly bound $s$-wave pairs.

Abstract

The ground state of the bipartite $t$-$J$ model must satisfy a specific sign structure, based on which the single-hole and two-hole ground state $Ans\ddot{a}tze$ on honeycomb lattice are constructed and studied by a variational Monte Carlo (VMC) method. The VMC results are in good agreement with the exact diagonalization (ED) calculation. For the single-hole case, the degenerate ground states are characterized by quantum numbers of a spin-1/2 and an orbital angular momentum $L_z=\pm 2$. The latter is associated with the emergent chiral spin/hole currents mutually surrounding the hole/spin-1/2 as a composite object or ``twisted hole''. A vanishing quasiparticle spectral weight is shown in the large-sample limit. In the two-hole ground state, the holes form a spin-singlet pairing with $d$+$id$ symmetry in the Cooper channel, but are of $s$-wave symmetry as a tightly bound pair of the ``twisted holes''. Such a pairing mechanism of dichotomy can be attributed to eliminating the local spin currents which has nothing to do with the long-range antiferromagnetic correlation. Superconducting ground state at finite doping is briefly discussed in terms of the tightly bound hole pairs as the building blocks.