Minimal loop currents in doped Mott insulators

TL;DR

This paper investigates doped Mott insulators using the $t$-$J$ model, revealing minimal loop currents, a new pairing mechanism, and the breakdown of quasiparticle Landau theory, with results supported by variational Monte Carlo and DMRG.

Contribution

It introduces a novel understanding of loop currents and pairing in doped Mott insulators, highlighting a minimal superconducting building block and challenging traditional quasiparticle concepts.

Findings

Incoherent loop currents form a $4\times4$ pattern on the lattice.

Two holes fuse into a tightly bound incoherent $d_{xy}$ pair.

The $d_{xy}$ pairing resonates with $d_{x^2-y^2}$ channel, forming a minimal superconducting unit.

Abstract

For the $t$-$J$ model, variational wave functions can generally be constructed based on an accurate description of antiferromagnetism (AFM) at half-filling and an exact phase-string sign structure under doping. The single-hole-doped and two-hole-doped states, as determined by variational Monte Carlo (VMC) simulations, display sharply contrasting behaviors. The single-hole state constitutes a ``cat state'' that resonates strongly between a quasiparticle component and a local loop-current component, with approximately equal weights. In the ground state, the quasiparticle spectral weight $Z_{\mathbf{k}}$ peaks at momenta $\mathbf{k}_0 \equiv (\pm\frac{\pi}{2},\pm\frac{\pi}{2})$. The total-energy dispersion versus $\mathbf{k}$ agrees remarkably well with the Green function Monte Carlo results. However, Landau's one-to-one correspondence hypothesis for quasiparticles breaks down here with the incoherent component exhibiting intrinsic magnetization originating from a minimal $2\times2$ loop current that forms a $4\times4$ pattern on the square lattice--a finding in excellent agreement with density matrix renormalization group (DMRG) calculations. In the two-hole ground state, a new pairing mechanism is revealed: the two holes are automatically fused into a tightly bound object consisting of an incoherent $d_{xy}$ pairing along the diagonal direction by compensating the local loop currents. This hole pair is again a ``cat state'' that resonates strongly between the incoherent $d_{xy}$ and a coherent $d_{x^2-y^2}$ Cooper channel to gain substantial hopping energy. Its size extends over an area of about $4\times 4$ lattice spacings, much smaller than the divergent AFM correlation length, implying that it should survive as a minimal superconducting building block even in the dilute doping regime. Experimental implications and the generalization to the finite-doping case are briefly addressed.