Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr2RuO4

Abstract

Using an imaginary-time matrix-product state (MPS) based quantum impurity solver we perform a realistic dynamical mean-field theory (DMFT) calculation combined with density functional theory (DFT) for Sr2RuO4. We take the full Hubbard-Kanamori interactions and spin-orbit coupling (SOC) into account. The MPS impurity solver works at essentially zero temperature in the presence of SOC, a regime of parameters currently inaccessible to continuous-time quantum Monte Carlo (CTQMC) methods, due to a severe sign problem. We show that earlier results obtained at high temperature, namely that the diagonal self-energies are nearly unaffected by SOC and that interactions lead to an effective enhancement of the SOC, hold even at low temperature. We observe that realism makes the numerical solution of the impurity model with MPS much more demanding in comparison to earlier works on Bethe lattice models, requiring several algorithmic improvements. arXiv:1909.02503v1 [cond-mat.str-el]

Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr$_2$RuO$_4$

“…The low-energy physics of Sr 2 RuO 4 is dictated by the Ru 4d-t 2g orbitals hybridized with the O 2p [62]. Similar to previous work [43,[63][64][65][66][67][68], we construct the minimal one-body tight-binding Hamiltonian H TB using the three maximally-localized t 2g orbitals obtained from the non-SOC DFT Kohn-Sham orbitals [86][87][88]. The full interacting Hamiltonian is then defined as H = H TB + H K by adding the Coulomb term H K (19) with U = 2.3 and J = 0.4 [43,[66][67][68]85].…”

“…1) are closely examined. Following this model study, section V presents the results obtained on a realistic correlated material, Sr 2 RuO 4 , which is among those most studied quantum materials [60,61] and is the subject of many recent theoretical works [43,[62][63][64][65][66][67][68]. We first benchmark our calculations against available results in previous studies, then proceed to present and discuss new results, especially those obtained with SOC, which poses a severely limiting difficulty for QMC solvers and have so far remained completely elusive for real-axis methods.…”

High-pressure synthesis of Ba2RhO4 , a rhodate analog of the layered perovskite Sr-ruthenate

“…The left bottom panel includes a three-dimensional cut, and on the right is shown the first Brillouin zone for the I4/mmm crystal as a reference. The Fermi surface of Sr 2 RuO 4 has been intensively investigated, both experimentally and theoretically [30][31][32][33]. Ab initio calculations based on the local-density approximation qualitatively reproduce the Fermi surface topology, provided that the SOC is taken into account.…”

Quenching the Anderson impurity model at finite temperature: Entanglement and bath dynamics using matrix product states

“…The most popular techniques used so far to study the Anderson model are exact diagonalization (ED), Quantum Monte Carlo [10][11][12]], Wilson's numerical renormalization group (NRG) [13][14][15][16][17][18] and tensor-network-based methods [7,[19][20][21][22][23][24][25], all of them with their own advantages and disadvantages. ED is numerically exact and has equal resolution on all energy scales, but is usually limited in the number of conduction modes that can be treated.…”