Ground State Energy Calculations of the Kitaev-Gamma Honeycomb Model Using Neural Quantum States

Abstract

Quantum spin liquids (QSLs) are highly elusive states of matter that are char- acterized by long range quantum entanglement and the lack of long range magnetic ordering. There are a variety of candidate materials with QSLs as well as model Hamiltonians where exact QSL ground states can be proven. The Kitaev honeycomb model is among the few models with an analytically derived QSL ground state. Ad- ditional interactions such as the Gamma and Heisenberg interactions are included to match real behaviours in candidate Kitaev materials to form the larger JKΓΓ′model. Due to the size of the Hilbert spaces associated with many-body systems, numerical techniques centre around the use of more efficient representations of the wavefunc- tion that reduce the need for exponential parameterization. Neural Quantum States (NQS) are one of the latest additions to the toolkit, making use of neural networks to represent the mapping between spin configurations and their corresponding wave- function amplitudes. By using variational monte carlo (VMC) to derive the ground state, the problem of finding the associated NQS representation translates to a Ma- chine Learning task of minimizing a cost function through gradient descent. Group Convolutional Neural Networks (GCNNs) are one of the latest NQS architectures which construct wavefunction ansatzes that are symmetric to a group of symmetries and have yielded state-of-the-art results in benchmark models. In this thesis, ground state calculations were performed using GCNNs for the Kitaev and Gamma honey- comb models and ground state properties were investigated. In the Kitaev model, optimization was affected by a complicated learning landscape, limiting the conver- gence towards the ground state. Performance improved with the Gamma model for smaller systems but still fell short of confirming an identical stripy patterned ground state found with iDMRG and iPEPS.