Fermionic and Continuous Time Quantum Monte Carlo

Emanuel Gull

U.‐J. Wiese

Mauro Iazzi, Matthias Troyer

Efficient continuous-time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state of the art for most discrete quantum models. They have not been widely used yet for fermionic quantum lattice models, such as the Hubbard model, nor other fermionic lattice systems due to a suboptimal scaling of $O({\ensuremath{\beta}}^{3})$ with inverse temperature $\ensuremath{\beta}$, compared to the linear scaling of discrete-time algorithms. Here we present a CT-QMC algorithm for fermionic lattice systems that matches the scaling of discrete-time methods but is more efficient and free of time discretization errors. This provides an efficient simulation scheme that is free from the systematic errors opening an avenue to more precise studies of large systems at low and zero temperature.

Karlis Mikelsons, Alexandru Macridin, Mark Jarrell

Two weak-coupling continuous time quantum Monte Carlo (CTQMC) methods are shown to be equivalent for Hubbard-type interactions. A relation between these CTQMC methods and the Hirsch-Fye quantum Monte Carlo (HFQMC) method is established, identifying the latter as an approximation within CTQMC and providing a diagrammatic interpretation. Both HFQMC and CTQMC are shown to be equivalent when the number of time slices in HFQMC becomes infinite, implying the same degree of fermion sign problem in this limit.

I. Morgenstern

Lei Wang, Mauro Iazzi, Philippe Corboz +1 more

While efficient algorithms exist for the simulation of bosons simulations of fermions are more challenging because of the infamous fermion sign problem. In this paper the authors take a step toward solution and develop continuous-time quantum Monte Carlo algorithm for lattice fermions that scales linearly with projection time and interaction strength. This method is benchmarked on the problem of the fermionic quantum critical point of spinless fermions on a honeycomb lattice.