Multi-level Algorithm for the Anderson Impurity Model

Jaebeom Yoo, Shailesh Chandrasekharan A, Harold U. Baranger

A continuous-time path integral quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low temperatures, the new algorithm has many advantages over conventional algorithms. For example, the model can be easily simulated in the Kondo limit without time discretization errors. Furthermore, many observables including the impurity susceptibility and a variety of fermionic observables can be calculated efficiently. Finally the new approach allows us to explore a general technique, called the multilevel algorithm, to solve the sign problem. We find that the multilevel algorithm is able to generate an exponentially large number of configurations with an effort that grows as a polynomial in inverse temperature such that configurations with a positive sign dominate over those with negative signs. Our algorithm can be easily generalized to other multi-impurity problems.

U. Brandt, Andreas Giesekus

Gerd Bergmann

The multi-electron wave function of an interacting electron system depends on the size of the system, i.e. the number of electrons. Here the question investigated is how the wave function changes for a symmetric Friedel-Anderson impurity when the volume is doubled. It turns out that for sufficiently large volume (when the level spacing is smaller than the resonance width) the change in the wave function can be expressed in terms of a universal single-electron state |q> centered at the Fermi level. This electron state is independent of the number of electrons and independent of the parameters of the Friedel-Anderson impurity. It is even the same universal state for a Kondo impurity and a symmetric Friedel impurity independent of any parameter. The only requirement is that the impurity has a resonance exactly at the Fermi level and that the level spacing is smaller than the resonance width. This result clarifies recent fidelity calculations.

Chuxin Chen, N. E. Bickers

Jaebeom Yoo, Shailesh Chandrasekharan A, Ribhu K. Kaul +2 more

We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further use this insight to analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.

G. Polatsek, K. W. Becker, Vilen Zevin