Quantum Monte Carlo study of the multi-orbital Anderson model including the SU(2) invariant Hund's coupling

昌久 古賀, Akihisa Koga

Tetsuro Saso

Anna Kauch, Krzysztof Byczuk

志朗 酒井, Ryotaro Arita, Karsten Held +1 more

We propose to combine the Trotter decomposition and a series expansion of the partition function for Hund's exchange coupling in a quantum Monte Carlo (QMC) algorithm for multiorbital systems that preserves spin and orbital rotational symmetries. This enables us to treat the Hund's (spin-flip and pair-hopping) terms, which is difficult in the conventional QMC method. To demonstrate this, we first apply the algorithm to study ferromagnetism in the two-orbital Hubbard model within the dynamical mean-field theory (DMFT). The result reveals that the preservation of the SU(2) symmetry in Hund's exchange is important, where the Curie temperature is grossly overestimated when the symmetry is degraded, as is often done, to Ising $({\mathrm{Z}}_{2})$. We then calculate the ${t}_{2g}$ spectral functions of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ by a three-band DMFT calculation with tight-binding parameters taken from the local density approximation with proper rotational symmetry.

Nicolaus Parragh, A. Toschi, Karsten Held +1 more

In the context of realistic calculations for strongly correlated materials with $d$ or $f$ electrons the efficient computation of multi-orbital models is of paramount importance. Here we introduce a set of invariants for the $SU(2)$-symmetric Kanamori Hamiltonian, which allows us to massively speed up the calculation of the fermionic trace in hybridization-expansion continuous-time quantum Monte Carlo algorithms. We show that by exploiting this set of good quantum numbers the study of the orbital-selective Mott transition in systems with up to seven correlated orbitals becomes feasible.

Seema Priyadarshini, Rajiv Mishra, Ruchi Kumari +3 more

We have studied numerically exact auxiliary field quantum Monte Carlo scheme for the spin and orbital rotational invariant Hamiltonian by combining series expansion and Trotter decomposition. We have used algorithm to solve the dynamical field theory equations. We have employed Boltzmann operator with respect to the total interaction. The method significantly relaxes the sign problem and allows in principle for more than two orbitals. The computational effort increases with the perturbation orders appearing in the Mote Carlo samples. The order become very large in multiorbital systems. To remove this difficulty we have used the Hirsch-Fye quantum Monte Carlo and parturbation series expansion quantum Monte Carlo methods. This algorithm enabled us not only to handle three or more orbitals but also to reach much stronger coupling than in Hirsch-Fye quantum Monte Carlo calculations, even for the two orbital Hubbard model.