## Michael J. Lawler

### Associate Professor

### Background

Michael Lawler's primary interests lie in the field of strongly correlated condensed matter physics. In this field, they seek to gain an understanding of the behavior of many strongly interacting particles. This is a far from well understood subject. However, they are fortunately aided in their exploration of it by an intimate connection between experiment and theory. Below are some of the topics related to this phenomenon that form his particular interest.

**Frustrated Quantum Mechanical Systems**

Suppose for the moment that we could turn off Heisenberg’s uncertainty principle so that we could know the exact position and momentum of our particles or that we could know the precise direction a particle’s spin is pointing. Now suppose these classical particles are placed in a configuration in which Newton’s law cannot tell us what they will do next because there are many options available, all equally likely. We say that these particles are frustrated.

This can happen, for example, when interacting classical spins are placed on certain lattices such that there are many spin configurations, each of which minimize the total energy. A central question in the field is what happens when we turn on Heisenberg’s uncertainty principle? The spins can no longer point in a specific direction and it turns out that the laws of quantum mechanics then help the spins decide what they want to do. Should this happen, then the spin system is actually governed by the laws of quantum mechanics at a macroscopic scale.

Recently, experimentalists have fabricated a number of materials (Herbertsmithite, NIO, κ-BETD, diamond lattice spinels, ...) that may shed much light on the above central question. For some time now, we have had theories of quantum spin liquids based on the emergence of either fermions or bosons interacting via gluons, photons or “visons” as the new particles describing this exotic phase. With these new materials, we can finally compare theory with experiment and so it is an exciting time for the field.

**Quantum Liquid Crystals**

It stands to reason that increasing the strength of interactions between particles in a gas phase will cause them to want to crystallize, to form a solid phase. If the particles are electrons, Wigner discovered in 1931 that this indeed happens. However, a transition to a Wigner crystal phase need not happen directly, but could in principle happen through a series of intermediate phases each progressively more crystalline. Examples of such intermediate phases include the electron “nematic” phase, which spontaneously breaks rotational symmetry, and an electron “smectic” or stripe phase, which involves the formation of an array of one-dimensional electronic “rivers”.

While symmetry provides a guiding principle in the theory of quantum liquid crystals, it alone cannot characterize a quantum world. As such, the general theory is fundamentally incomplete. It is very exciting, therefore, to study quantum liquid crystals found in nature, such as the nematic states found in Sr3Ru2O7 and quantum Hall systems and the stripe phases in cuprate superconductors. An interesting question, for example, is what happens at a continuous phase transition between two quantum liquid crystals? Or, can the stripes in a stripe phase slide freely next to each other? Can electrons in quantum liquid crystals pair easily to form a superconductor? At the heart of these questions is the quantum nature of these new phases, and their answers rely on the deep connection between experiment and theory achievable in condensed matter physics.

### Education

- PhD, University of Illinois at Urbana-Champaign

### Research Interests

- Condensed matter physics

### More Info

**Selected Publications:**

"Gapless spin liquids on the three dimensional hyper-kagome lattice of Na4IR3O8", MJL, Arun Paramekanti, Yong Baek Kim and Leon Balents, arXiv:0806.4395

"Quantum order by disorder in frustrated diamond lattice antiferromagnets", Jean-Sebastien Bernier, MJL and Yong Baek Kim, arXiv:0801.0598 (to be published in Phys. Rev. Lett.)

"Fluctuating stripes in strongly correlated electron systems and the nematic-smectic quantum phase transition", Kai Sun, Benjamin Fregoso, MJL and Eduardo Fradkin, arXiv: 0805.3526 (to be published in Phys. Rev. B)

"Theory of the nodal nematic quantum phase transition in superconductors" Eun-Ah Kim, MJL, Paul Oreto, Eduardo Fradkin and Steven A. Kivelson, Phys. Rev. B 77, 184514 (2008)