Mardi 21 août 2012 à 11h15
Salle 234, Ecole de Physique

Exactly solvable 1D lattice model for the Laughlin states on torus geometries

Masaaki Nakamura, Tokyo Institute of Technology, Japan

We introduce a one-dimensional lattice model with an exact ground state describing the fractional quantum Hall (FQH) states in Laughlin series (filling factors $ u=1/q$) on torus geometry. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using matrix product method, density functions and correlation functions are calculated analytically. The exactly solvable Hamiltonian has the same degrees of freedoms as those of the Trugman-Kivelson type pseudo potential, and it naturally derives the general properties of the Laughlin wave function such as the $Z_2$ classification of the FQH states and the fermion-boson relation. References: [1] M. Nakamura, Z.-Y. Wang and E. J. Bergholtz, Phys. Rev. Lett. 109, 016401 (2012) [2] Z.-Y. Wang, M. Nakamura, arXiv:1206.3071