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"Strong-coupling" continuous-time impurity solver

Speaker: Philipp Werner, Columbia
Date & Time: September 26, 2006 - 1:30pm
Location: Serin 385E


"Strong-coupling" continuous-time impurity solver
Physics and Astronomy


Philipp Werner, Columbia
1:30pm Serin 385E

One of the fundamental challenges of theoretical condensed matter physics is the accurate solution of quantum impurity models. They are important both in their own right and as a crucial ingredient in the dynamical mean field method of approximating the properties of interacting fermions on a lattice.

For two decades, the Hirsch-Fye algorithm and exact diagonalization have been the methods of choice. Hirsch-Fye type methods require a fine grid spacing to capture the short time behavior of the Green function, which makes simulations at low temperature and strong interactions prohibitive, while exact diagonalization represents the continuous density of states of the reservoir by a small number of levels.

Recently, a new class of impurity solvers has been developed, based on the stochastic evaluation of a diagrammatic expansion of the partition function and the resummation of diagrams into determinants. Two complimentary approaches are possible: a weak-coupling expansion in powers of the coupling constants or a "strong-coupling" expansion in powers of the impurity-bath mixing. These algorithms require neither auxiliary fields nor a time
discretization.

I will discuss the strong-coupling approach in a representation which is suitable for density-density interactions as well as a generalization to models with exchange and pair hopping terms. The important feature is that the perturbation order which is needed decreases as the interaction strength is increased. I will demonstrate that the new algorithm allows unprecedented access to the low-temperature physics for interaction strengths of the order of the critical value for the Mott transition.

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