Competing orders in the honeycomb lattice $t$-$J$ model

TL;DR

This study investigates the competing orders in the honeycomb lattice $t$-$J$ model using fermionic tensor networks, revealing stripe and uniform states with different doping levels and pairing symmetries, enhancing understanding of doped Mott insulators.

Contribution

It introduces a fermionic tensor network approach to analyze the honeycomb lattice $t$-$J$ model, identifying various stripe and uniform states and their doping-dependent properties.

Findings

At low doping, uniform $d$-wave superconductivity coexists with antiferromagnetism.

At higher doping, stripe-ordered states dominate with decreasing stripe period.

Stripe states with lowest energy exhibit $d_{x^2-y^2}$ pairing symmetry.

Abstract

We study the honeycomb lattice $t$-$J$ model using the fermionic tensor network approach. By examining the ansatz with various unit cells, we discover several different stripe states with different periods that compete strongly with uniform states. At very small doping $\delta < 0.05$, we find almost degenerate uniform $d$-wave superconducting ground states coexisting with antiferromagnetic order. While at larger doping $\delta > 0.05$, the ground state is an approximately half-filled stripe-ordered state, where the stripe period decreases with increasing hole doping $\delta$. Furthermore, the stripe states with the lowest variational energy always display $d_{x^2-y^2}$-wave pairing symmetry. The similarity between our results and those on the square lattice contributes to a more comprehensive understanding of doped Mott insulators.