## Standing

Undergraduate

## Type of Proposal

Oral Research Presentation

## Faculty

Faculty of Science

## Faculty Sponsor

Dr. Jeffrey G. Rau

## Proposal

The physics of many-body systems enables new and novel phases of matter with applications in other areas, including spintronics, quantum computing and information processing. A better understanding of these systems and how to control them offers a world of new technological and computing capabilities. The Kitaev honeycomb model has been of recent interest, exhibiting fascinating properties even at the classical level (Kitaev 2008). Understanding the role of electric and magnetic fields on the classical Kitaev model has been the focus of recent work due to its potential for realizing new phases and states of matter (Rau et al. 2016). Mapping out a phase diagram of the model, which shows its state under electric and magnetic conditions, is the ultimate goal. Using various complementary computer algorithms and methods, electric and magnetic effects on the model are explored. “Iterative minimization” techniques are employed, minimizing the energy of the finite Kitaev model on a step-by-step basis, while also generating the state of the model at this minimum energy. Comparing these results to modified algorithms that minimize the energy in a single, less-restrictive step, help to identify particularly interesting electric and magnetic conditions. Finally, to explore the possibility of states that are not regularly repeating in space, an educated guess in an infinite system is used, allowing for non-periodic states to “fit” in the system. An electric and magnetic phase diagram of the model will be presented, depicting how the magnetic states of this model can be controlled via the electric field.

[1] Kitaev, A. 2008. Anyons in an exactly solvable model and beyond. Annals of Physics.

[2] Rau, J., Lee, E. & Kee, H. 2016. Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems. Annual Review of Condensed Matter Physics.

## Availability

March 30 1:30PM-2:30PM, March 31 2:30PM - 3PM, April 1 12PM-3PM

New & Novel Phases of the Classical Kitaev Honeycomb Model

The physics of many-body systems enables new and novel phases of matter with applications in other areas, including spintronics, quantum computing and information processing. A better understanding of these systems and how to control them offers a world of new technological and computing capabilities. The Kitaev honeycomb model has been of recent interest, exhibiting fascinating properties even at the classical level (Kitaev 2008). Understanding the role of electric and magnetic fields on the classical Kitaev model has been the focus of recent work due to its potential for realizing new phases and states of matter (Rau et al. 2016). Mapping out a phase diagram of the model, which shows its state under electric and magnetic conditions, is the ultimate goal. Using various complementary computer algorithms and methods, electric and magnetic effects on the model are explored. “Iterative minimization” techniques are employed, minimizing the energy of the finite Kitaev model on a step-by-step basis, while also generating the state of the model at this minimum energy. Comparing these results to modified algorithms that minimize the energy in a single, less-restrictive step, help to identify particularly interesting electric and magnetic conditions. Finally, to explore the possibility of states that are not regularly repeating in space, an educated guess in an infinite system is used, allowing for non-periodic states to “fit” in the system. An electric and magnetic phase diagram of the model will be presented, depicting how the magnetic states of this model can be controlled via the electric field.

[1] Kitaev, A. 2008. Anyons in an exactly solvable model and beyond. Annals of Physics.

[2] Rau, J., Lee, E. & Kee, H. 2016. Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems. Annual Review of Condensed Matter Physics.