Week 3
Aug. 1
11:00- (A615, 6th floor of the main building)

Y. Motome (Department of Applied Physics, University of Tokyo)
Exact diagonalization study of Mott transition in the Hubbard model on an anisotropic triangular lattice

We present our recent results on the effect of geometrical frustration on the Mott transition. Recently it has been suggested in both experiments and theories that the frustration can open a way to have an insulating phase without any conventional symmetry breaking such as an antiferromagnetic order. To examine this possibility further, we theoretically study the metal-insulator transition in the Hubbard model on an anisotropic triangular lattice by the Lanczos exact diagonalization method. We carefully analyzed finite-size effects by imposing the twisted boundary conditions to extract intrinsic properties of phase transitions. The phase diagram is obtained by the systematic analyses of the Drude weight, double occupancy and magnetic correlations, and is discussed in comparison with other theoretical results.
This work has been done in collaboration with T. Koretsune and A. Furusaki.
14:00- (A615, 6th floor of the main building)

J. Corney (Department of Physics, The University of Queensland)
Gaussian Quantum Monte Carlo Methods

Gaussian Quantum Monte Carlo Methods are a class of simulation methods based on phase-space representations of quantum states. By use of an appropriate over-complete basis set, one can represent arbitrary quantum density operators as positive distributions over a generalised phase-space. Such a representation allows quantum evolution, either in real time or inverse temperature, to be viewed as a continuous stochastic evolution of phase-space variables.

Phase-space methods based on coherent-state expansions have long been used to simulate bosonic systems, with great success. The original positive-P representation, based on a coherent-state expansion, was successful in simulating light propagation in nonlinear media and calculating the resultant quantum correlations. It was also used to simulate the short-time dynamics of Bose-Einstein condensate formation. The extension to general Gaussian bases means that fermionic systems, such as the Hubbard model, can also be simulated.

In this talk, I will give an overview of phase-space methods in general and Gaussian QMC in particular. I discuss the limitations of coherent-state based methods and the advantages of using a Gaussian basis. Using the example of the Hubbard model, I will show how the Gaussian method can be applied to nontrivial problems, discussing its advantages and challenges. I will also cover issues to do with numerical implementation, and ways to extend the applicability of Gaussian QMC beyond the current implementations.