Investigating spin liquids via projected wavefunctions - Silva, João Augusto Sobral da (2022)
Spin liquids are exquisite states of matter which host fractionalized excitations of spin and show no long-range magnetic order even at zero temperature due to quantum fluctuations. They have been extensively studied using fractionalized representations of the spin degrees of freedom in the so-called parton construction in conjunction with the Gutzwiller projection. Using Mean Field Theories (MFT), this constraint can be imposed on average, and numerical techniques, such as the Variational Monte Carlo (VMC) are required to impose the condition exactly at each site. In this framework, the VMC is a powerful tool to indicate which MFT ansatz is favored energetically to represent the spin liquid state based on the variational principle and the specific spin fractionalized representation. We employed this approach to investigate a putative chiral spin liquid state in the Kagome lattice using the Abrikosov representation which can host spinons: neutral spin-1/2 fermionic quasiparticles. This work was performed in the J1 − Jd − Jχ Kagome Lattice model, and it was inspired by experimental results from the material α − Cu3Zn (OH)6 Cl2 (kapellasite) - a polymorphous structure of ZnCu3(OH)6Cl2 (herbertsmithite) - with no long-range order down to T = 20mK. Our VMC results favor a gapless chiral spin liquid with staggered flux ±π/2 over the triangles and 0 flux on the hexagons in the region with Jd/ |Jχ| > 0 for small |J1| < 0.1. We also investigated the stability of this spin-liquid state to ordered phases known to occur in the model. In addition, new non-coplanar ordered phases were encountered via the gradient descent method in the limit of S » 1 which may be relevant for ordered Kagome materials. By representing the influence of the ordered phases via a fictitious Zeeman field in a spin density wave (SDW) ansatz for the VMC, we have found consistent results with our classical phase diagram, establishing a more realistic region for the spin liquid domain.