Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr${}_2$RuO${}_4$

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 Sr${}_2$RuO${}_4$. 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 comment9 pages, 7 figures

References in corpus (51)

• Maximally-localized generalized Wannier functions for composite energy bands
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Maximally-localized Wannier functions for entangled energy bands
• Efficient simulation of one-dimensional quantum many-body systems
• Continuous-time Monte Carlo methods for quantum impurity models
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• A continuous-time solver for quantum impurity models
• Strong electronic correlations from Hund's coupling
• Unifying time evolution and optimization with matrix product states
• Time-evolution methods for matrix-product states
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Dynamical density-matrix renormalization-group method
• Strong Peak in $T_c$ of Sr${}_2$RuO${}_4$ Under Uniaxial Pressure
• TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
• The coherence-incoherence crossover and the mass-renormalization puzzles in Sr2RuO4
• Strong spin-orbit coupling effects on the Fermi surface of Sr2RuO4 and Sr2RhO4
• TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials
• Spectral functions in one-dimensional quantum systems at T>0
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• High-resolution photoemission on Sr2RuO4 reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies
• Chebyshev matrix product state approach for spectral functions
• The role of spin-orbit coupling for the superconducting state in Sr_2RuO_4
• Dynamical Mean Field Theory with the Density Matrix Renormalization Group
• Coulomb-Enhanced Spin-Orbit Splitting: The Missing Piece in the Sr2RhO4 Puzzle
• Pairing symmetry and dominant band in Sr2RuO4
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Spin-Orbit Coupling and Electronic Correlations in Sr2RuO4
• Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver
• The Fermi surface of Sr2RuO4: spin-orbit and anisotropic Coulomb interaction effects
• Chebyshev expansion for Impurity Models using Matrix Product States
• Efficient DMFT impurity solver using real-time dynamics with Matrix Product States
• Strongly correlated materials from a numerical renormalization group perspective: How the Fermi-liquid state of Sr${}_2$RuO${}_4$ emerges
• Optical Response of Sr${}_2$RuO${}_4$ Reveals Universal Fermi-liquid Scaling and Quasiparticles Beyond Landau Theory
• Transport properties of Metallic Ruthenates: a DFT+DMFT investigation
• Imaginary-time matrix product state impurity solver for dynamical mean-field theory
• Spectral functions and time evolution from the Chebyshev recursion
• Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain
• Electron spectra close to a metal-to-insulator transition
• Identifying spin-triplet pairing in spin-orbit coupled multi-band superconductors
• Magnetic response of Sr${}_2$RuO${}_4$: quasi-local spin fluctuations due to Hund's coupling
• Single-Particle Dynamics in the Vicinity of the Mott-Hubbard Metal-to-Insulator Transition
• Electronic theory for the normal state spin dynamics in Sr${}_2$RuO${}_4$: anisotropy due to spin-orbit coupling
• Multi-orbital physics in Fermi liquids prone to magnetic order
• Hall coefficient signals orbital differentiation in the Hund's metal Sr${}_2$RuO${}_4$
• Dynamical Mean-Field Theory on the Real-Frequency Axis: p-d Hybridizations and Atomic Physics in SrMnO${}_3$
• Spin-orbit coupling and correlations in three-orbital systems

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