Spin Liquids from Mott insulators
In the band theory of solids, a half-filled band predicts an ordinary metal. The presence of strong electron-electron interactions, however, can instead induce a “Mott insulator.” In the simplest of cases, a Mott insulator will be an antiferromagnet but, in more complex cases, a variety of spin-liquids can emerge.
In the first part of the talk, we will discuss the effect of geometric frustration on a Mott insulator—the Hubbard model on the triangular lattice. Since there is no obvious ordered state for antiferromagnetically interacting spins, it was thought that the Mott insulator might be a spin-liquid, and Anderson introduced the resonating valence bond (RVB) state as a potential ground state wave-function. In fact, the ground state is ordered, but, at weaker interactions between the metal and ordered phase, there is a non-magnetic insulating (NMI) phase whose classification has proved elusive. I’ll discuss our group’s recent numerical evidence that the NMI is actually the nu=1/2 spin analog of the fractional quantum hall state. We additionally develop a mean-field argument as to why chiral symmetry is spontaneously broken. Due to its relevance to several materials, this result may point to the measurement and manipulation of novel anyons.
In the second part of the talk we will discuss the effect of spin-orbit coupling on a Mott insulator to obtain the Kiteav materials. We will discuss the Kitaev model—an exactly solvable model with special excitations—and its material implementation. Although experimental data is plentiful, being able to calculate exact results only for the Kitaev model makes the interpretation of the data challenging. I’ll discuss our recent work on one way of extending the exact results to facilitate fitting of the data and detection of a Kitaev spin-liquid.
Tessa Cookmeyer is a fifth-year PhD candidate in the Moore group. Her research is focused on quantum materials, such as quantum spin-liquids and heavy-fermion materials, and quantum phase transitions, and she collaborates closely with experimentalists in the Analytis group. She received her BS in Physics and Math from Haverford college in 2017. She is a former Berkeley Connect Fellow and current NSF Graduate Research Fellow. Outside of research, she enjoys rock-climbing, ultimate frisbee, and playing the guitar.