| 1. |
- Kaye, Jason, et al.
(författare)
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A fast time domain solver for the equilibrium Dyson equation
- 2023
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Ingår i: Advances in Computational Mathematics. - : Springer. - 1019-7168 .- 1572-9044. ; 49:4
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Tidskriftsartikel (refereegranskat)abstract
- We consider the numerical solution of the real-time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times and is thus well-suited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph and the Sachdev-Ye-Kitaev model.
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| 2. |
- Kaye, Jason, et al.
(författare)
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libdlr : Efficient imaginary time calculations using the discrete Lehmann representation
- 2022
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Ingår i: Computer Physics Communications. - : Elsevier. - 0010-4655 .- 1879-2944. ; 280
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Tidskriftsartikel (refereegranskat)abstract
- We introduce libdlr, a library implementing the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. The DLR basis consists of a collection of exponentials chosen by the interpolative decomposition to ensure stable and efficient recovery of Green's functions from imaginary time or Matsubara frequency samples. The library provides subroutines to build the DLR basis and grids, and to carry out various standard operations. The simplicity of the DLR makes it straightforward to incorporate into existing codes as a replacement for less efficient representations of imaginary time Green's functions, and libdlr is intended to facilitate this process. libdlr is written in Fortran, provides a C header interface, and contains a Python module pydlr. We also introduce a stand-alone Julia implementation, Lehmann.jl. Program summary Program Title: libdlr CPC Library link to program files: https://doi .org /10 .17632 /56z594pzsj .1 Developer's repository link: https://github .com /jasonkaye /libdlr Licensing provisions: Apache-2.0 Programming language: Fortran, C, Python, Julia Nature of problem: Discretization and compression of functions (Green's functions and self-energies) with an imaginary time variable. Solution method: Explicit basis functions and discretization points obtained by low rank compression of the analytical continuation kernel.
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| 3. |
- Käser, Stefan, et al.
(författare)
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Interorbital singlet pairing in Sr2RuO4 : A Hund's superconductor
- 2022
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 105:15
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Tidskriftsartikel (refereegranskat)abstract
- We study the superconducting gap function of Sr2RuO4. By solving the linearized Eliashberg equation with a correlated pairing vertex extracted from a dynamical mean-field calculation we identify the dominant pairing channels. An analysis of the candidate gap functions in orbital and quasiparticle band basis reveals that an interorbital singlet pairing of even parity is in agreement with experimental observations. It reconciles in particular the occurrence of a two-component order parameter with the presence of line nodes of quasiparticles along the c axis in the superconducting phase. The strong angular dependence of the gap along the Fermi surface is in stark contrast to its quasilocality when expressed in the orbital basis. We identify local interorbital spin correlations as the driving force for the pairing and thus reveal the continuation of Hund's physics into the superconducting phase.
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| 4. |
- Suzuki, H., et al.
(författare)
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Distinct spin and orbital dynamics in Sr2RuO4
- 2023
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Ingår i: Nature Communications. - : Springer Nature. - 2041-1723. ; 14:1
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Tidskriftsartikel (refereegranskat)abstract
- The unconventional superconductor Sr2RuO4 has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru L3-edge resonant inelastic x-ray scattering to obtain comprehensive maps of the electronic excitations of Sr2RuO4 over the entire Brillouin zone. We observe multiple branches of dispersive spin and orbital excitations associated with distinctly different energy scales. The spin and orbital dynamical response functions calculated within the dynamical mean-field theory are in excellent agreement with the experimental data. Our results highlight the Hund metal nature of Sr2RuO4 and provide key information for the understanding of its unconventional superconductivity.
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| 5. |
- Van Loon, Erik G.C.P., et al.
(författare)
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Dual Bethe-Salpeter equation for the multiorbital lattice susceptibility within dynamical mean-field theory
- 2024
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 109:15
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Tidskriftsartikel (refereegranskat)abstract
- Dynamical mean -field theory describes the impact of strong local correlation effects in many -electron systems. While the single -particle spectral function is directly obtained within the formalism, two -particle susceptibilities can also be obtained by solving the Bethe-Salpeter equation. The solution requires handling infinite matrices in Matsubara frequency space. This is commonly treated using a finite frequency cutoff, resulting in slow linear convergence. A decomposition of the two -particle response in local and nonlocal contributions enables a reformulation of the Bethe-Salpeter equation inspired by the dual boson formalism. The reformulation has a drastically improved cubic convergence with respect to the frequency cutoff, considerably facilitating the calculation of susceptibilities in multi -orbital systems. This improved convergence arises from the fact that local contributions can be measured in the impurity solver. The dual Bethe-Salpeter equation uses the fully reducible vertex which is free from vertex divergences. We benchmark the approach on several systems including the spin susceptibility of strontium ruthenate Sr 2 RuO 4 , a strongly correlated Hund's metal with three active orbitals.
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| 6. |
- van Loon, Erik, et al.
(författare)
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Larmor precession in strongly correlated itinerant electron systems
- 2023
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Ingår i: Communications Physics. - : Springer Nature. - 2399-3650. ; 6:1
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Tidskriftsartikel (refereegranskat)abstract
- Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials.
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