# Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid

## TL;DR

This study uses large-scale DMRG to show that light doping in a Kagome quantum spin liquid leads to a holon Wigner crystal, challenging expectations of superconductivity or exotic metals.

## Contribution

It provides the first large-scale numerical evidence that light doping of a Kagome spin liquid results in a holon Wigner crystal, not a superconductor or topological metal.

## Key findings

- Doped holes form an insulating charge-density wave with one hole per unit cell.
- Spin correlations remain short-ranged, indicating a holon crystal rather than a hole crystal.
- Results suggest relevance to doped Herbertsmithite materials.

## Abstract

We address the problem of a lightly doped spin-liquid through a large-scale density-matrix renormalization group (DMRG) study of the $t$-$J$ model on a Kagome lattice with a small but non-zero concentration, $\delta$, of doped holes. It is now widely accepted that the undoped ($\delta=0$) spin 1/2 Heisenberg antiferromagnet has a spin-liquid groundstate. Theoretical arguments have been presented that light doping of such a spin-liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal (FL$^\ast$). Instead, we infer that the doped holes form an insulating charge-density wave state with one doped-hole per unit cell - i.e. a Wigner crystal (WC). Spin correlations remain short-ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons (WC$^\ast$), rather than of holes. Our results may be relevant to Kagome lattice Herbertsmithite $\rm ZnCu_3(OH)_6Cl_2$ upon doping.