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Regensburg 2019 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 2: Correlated Electrons: Electronic Structure Calculations and Other Theoretical Topics

TT 2.10: Vortrag

Montag, 1. April 2019, 12:00–12:15, H7

Lefschetz thimbles approach for the sign problem in Hubbard model away of half-filling — •Maksim Ulybyshev1, Christopher Winterowd2, and Savvas Zafeiropoulos31Institut für Theoretische Physik, Julius-Maximilians-Universität, 97074 Würzburg, Germany — 2University of Kent, School of Physical Sciences, Canterbury CT2 7NH, UK — 3Institute for Theoretical Physics, Universität Heidelberg, Philosophenweg 12, D-69120 Germany

Quantum Monte Carlo simulation of the Hubbard model away of half filling suffer from the sign problem which makes the method almost inapplicable in this case. We applied the Lefschetz thimble approach to the Hubbard model on hexagonal lattice with chemical chemical at van Hove singularity. In this method the integration contour for continuous auxiliary fields is shifted into complex space. There are optimal manifolds ("Lefschetz thimbles"), where fluctuations of the phase of the Monte Carlo weight are substantially suppressed. Thus the sign problem is also suppressed and can be dealt with using conventional reweighting technique. Thimbles are attached to saddle points of the action in complex space. Thus the algorithm includes the search for these saddle points and also the special methods for sampling over curved surfaces in complex space. We made the practical implementation of the above mentioned algorithms, suitable for the Hubbard model, and estimated the complexity of the residual sign problem. We also show that it is possible to manipulate the saddle points of the action using different versions of the Hubbard-Stratonovich transformation, thus also changing the complexity of the sign problem.

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