The biggest enemy of quantum computing technology is “noise,” perturbation at the atomic level that can disrupt the resilience of the materials that form the basis of quantum computing applications. New research from Professor Ian Affleck’s team at the Stewart Blusson Quantum Matter Institute (SBQMI) has found new clues as to the physics behind a class of materials that are robust enough to withstand such noise. The findings, published recently in the journal *Physical Review Letters*, offer clarity on the ideal atomic structure for quantum computing materials.

The celebrated Kitaev (K) model describes a peculiar way in which spin 1/2 electrons in a honeycomb lattice material may interact. Electrons are the negatively charged particles of an atom and the term "spin" refers to their intrinsic angular momentum, as they can be loosely viewed as microscopic spinning rigid bodies.

In this model, proposed by physicist Alexei Kitaev, the spins interact with bond-directional dependent Ising interactions (a mathematical model regulating the ferromagnetic and/or antiferromagnetic relative alignment of the spins) with a strength K while all other parameters are zero. Kitaev was able to show that this model realizes a phase of matter—a spin liquid—that can be very useful for quantum computing applications.

"The material we are looking at is a 2D material wherein a layer of atoms is organized into a honeycomb lattice structure; this material is interesting for us because it has the potential to realize the Kitaev model," explained Research Associate Alberto Nocera, who worked with Postdoctoral Fellow Wang Yang and PhD student Tarun Tummuru, colleagues in the Affleck lab, as well as with Professor Hae-Young Kee at the University of Toronto.

The movement of electrons in any material at low temperature is affected by the presence of defects and atomic vibrations, and how electrons respond to these perturbations affects the stability of the material as a whole.

The main question the team is asking now is, what if we add an interaction or perturbation that is common in nature? To answer this, they took a one-dimensional version of the Kitaev model (pictured above) and added an off-diagonal “Gamma” interaction term to see how Kitaev physics reacted to this additional perturbation.

"The model is theoretical but realistic," said Nocera, who believes the model is useful in that it may show researchers what they might be looking for in two dimensions.

What they found is that the system wants to be ordered antiferromagnetically, in a very specific way. Due to large quantum fluctuations, "true" order is never achieved, and the spins are in a highly correlated state. At long distances, the highly correlated motions of the spinning electrons generate a hierarchy of collective "dancing" patterns that can be classified by an infinite dimensional symmetry, which is an extension of the spatial rotational symmetry.

These "dancing" patterns in this one dimensional "cut" of the honeycomb lattice are interesting in that they reveal an organization principle based on infinite dimensional symmetry, but it may also be useful in giving clues to the correlated dynamics of electrons in two dimensional layers.

One material the researchers are interested in exploring in this context is made from ruthenium chloride (RuCl_{3}). At SBQMI, Nocera and colleagues are using the Laboratory for Interdisciplinary Science Application (LISA) computational resources to determine the phase diagram of the model, isolating a row of atoms in order to imagine that the material only had a single dimension.

"These materials are made of several layers in 3D, but the layers are only weakly coupled between each other; this is the first approximation," Nocera explains. "We are doing another approximation; we imagine that a single layer can be studied as a collection of one-dimensional substructures which, coupled together, form a two-dimensional honeycomb lattice. We focus our attention on only one of these one-dimensional substructures."

Further work, using LISA and a the newer and potentially more powerful LISA-2 cluster, will explore new quantum phases stabilized by the addition of a Heisenberg interaction term in order to study the new phases of matter which this more generic model might sustain. These studies will provide theoretical predictions for future neutron and x-ray scattering experiments on Kitaev-1D model materials.