Spin Liquid state of the S=1/2 Heisenberg model on the anisotropic triangular lattice

Journal Club talk by Dariush Heidarian on July 8, 2010
(click here for slides in pdf format)

Summary by Vijay Shankar Venkataraman

References:

Theoretical Papers:
1) D. Heidarian, S. Sorella, and F. Becca, Phys. Rev. B 80, 012404 (2009)
2) T. Pardini and R. R. P. Singh, Phys. Rev. B 77, 214433 (2008)
3) O. A. Starykh and L. Balents, Phys. Rev. Lett. 98, 077205 (2007)
4) S. Yunoki and S. Sorella, Phys. Rev. B 74, 014408 (2006)
5) Zheng Weihong, R. H. McKenzie, and R. P. Singh, Phys. Rev. B 59, 14367 (1999)
6) M. Bocquet, F. H. L. Essler, A. M. Tsvelik, and A. O. Gogolin, Phys. Rev. B 64, 094425 (2001).

Experimental Papers:
1) R. Coldea, D. A. Tennant, A. M. Tsvelik, and Z. Tylczynski, Phys. Rev. Lett. 86, 1335 (2001)
2) Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, and G. Saito, Phys. Rev. Lett. 91, 107001 (2003).

The existence of spin-liquids is still mired in controversy although there are various promising candidates. Prominent among these is a quasi-two-dimensional class of organic compounds comprised of dimers of an organic molecule. A single electron is localized on each dimer and the compound forms layers of triangular lattices.

Dariush began with a quick review of the experimental results of Shimizu et al where these materials show no sign of long range order down to very low temperatures. He then introduced the anisotropic Heisenberg model on the triangular lattice with nearest-neighbour interactions but with exchange anisotropy. This led to a vigorous discussion on the possible types (Ferromagnetic/Antiferromagnetic) and strengths of coupling constants that would cause frustration. After the audience reached a consensus, Dariush gave a brief survey of previous theoretical work on the model.

Dariush moved on to discussing his own work studying the Hamiltonian by using a variational wavefunction approach. After discussing different methods of doing a variational calculation, he showed us the different variational wavefunctions that he used in his work. Dariush then presented his results for the ground state energy and compared it with previous work.

Discussing results for the spin-spin correlation function as a function of anisotropy for different lattice sizes, he showed how the structure factor scales as a function of lattice size for different anisotropies. Dariush then showed us the phase diagram as a function of anisotropy which told us that the variational calculation points towards the existence of a stable spin-liquid state in the anisotropic triangular lattice.

Time had run out by this point and an excursion into the technicalities of the variational Monte Carlo calculation was reserved for another journal club meeting.