# Condensed Matter Seminar Series

## A Monte Carlo Study of Spatially Anisotropic Spin-1/2 Heisenberg Models

### Fu-Jiun Jiang

#### MIT

##### Tuesday March 23,  3:30pm,  Room 298,  Physics Building

Heisenberg models have been studied in great detail, because of their phenomenological as well as theoretical importance. For instance, the discovery of high temperature (high $T_c$) superconductivity in the cuprate materials has triggered vigorous research investigation on spin-1/2 Heisenberg-type models, which are argued and believed to be the correct models for the undoped precursors of high $T_c$ cuprates. On the other hand, despite being well-studied, several recent Monte Carlo investigations of spatially anisotropic Heisenberg models have led to unexpected results. For example, numerical evidence shows that the anisotropic spin-1/2 Heisenberg model with a staggered arrangement of the antiferromagnetic couplings may belong to a new universality class, in contradiction to the theoretical $O(3)$ universality prediction. Further, Monte Carlo data indicates an unconventional behavior for the transition of the spin-1/2 Heisenberg model with different antiferromagnetic couplings in the 1- and 2-spatial directions to its 1-D limit, namely decoupled Heisenberg chains. Because of these surprising results, we use first principles Monte Carlo simulations to investigate these two spatially anisotropic spin-1/2 Heisenberg models. In particular, by employing the idea of fixing the ratio of spatial winding number squareds in the simulations, we show a clear O(3) universality class signal for the first model. We provide a convincing evidence for an unconventional transition of the second model to its 1-D limit as well. Specifically the critical exponent $\nu$ obtained from the simulations is given by $\nu = 0.92(3)$ which is not known in the literature.

Host: Shailesh Chandrasekharan