24 research outputs found
Magneto-electric spectroscopy of Andreev bound states in Josephson quantum dots
We theoretically investigate the behavior of Andreev levels in a
single-orbital interacting quantum dot in contact to superconducting leads,
focusing on the effect of electrostatic gating and applied magnetic field, as
relevant for recent experimental spectroscopic studies. In order to account
reliably for spin-polarization effects in presence of correlations, we extend
here two simple and complementary approaches that are tailored to capture
effective Andreev levels: the static functional renormalization group (fRG) and
the self-consistent Andreev bound states (SCABS) theory. We provide benchmarks
against the exact large-gap solution as well as NRG calculations and find good
quantitative agreement in the range of validity. The large flexibility of the
implemented approaches then allows us to analyze a sizeable parameter space,
allowing to get a deeper physical understanding into the Zeeman field,
electrostatic gate, and flux dependence of Andreev levels in interacting
nanostructures.Comment: 17 pages, 12 figure
Functional renormalization group beyond the perturbative regime
This thesis aims at developing new schemes for the treatment of correlation effects in condensed matter systems using quantum field theoretical approaches. In particular, our goal is to extend the description of correlation physics at the two-particle level. This is necessary for an unbiased treatment of condensed matter systems that exhibit electronic correlations and competing ordering tendencies. In this respect, the functional renormalization group (fRG) approaches have surely contributed substantially over the last
years, as they account for all scattering channels and their mutual feedback effects in an unbiased way. In spite of its flexibility, the application of the fRG is limited by its inherent perturbative nature. To go beyond the conventional weak-coupling implementations, we discuss the general idea to extend fRG based computational schemes by using an exactly
solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this solution accounts for a non-perturbative inclusion of correlations at both, the one-particle (self-energy) and two-particle (vertex functions) level. The full treatment of the two-particle vertex functions, however, poses a huge limitation to the numerical performance, not only in the fRG, but in several forefront many-body algorithms.
In this perspective, we provide a detailed diagrammatic analysis of the frequency and momentum structures of the vertex functions, together with their physical interpretation.
This constitutes the basis for sophisticated parametrization schemes. We then explain the technical details necessary for cutting-edge numerical implementations, and further benchmark our ideas using refined implementations of both, the fRG and the parquet approximation (PA).Diese Doktorarbeit beschäftigt sich mit der Entwicklung neuer Ansätze für die Behandlung von Korrelationseffekten in Materialien. Mit Hilfe quantenfeldtheoretischer Methoden steht dabei besonders die korrekte Berücksichtigung von zwei-Teilchen Streuprozessen im Vordergrund, die für die Beschreibung konkurrierender Instabilitäten essenziell ist. Zu deren Verständnis hat die funktionale Renormierungsgruppe (fRG), die die verschiedenen Streukanäle sowie deren Wechselspiel gleichermaßen beinhaltet, in den letzten Jahren wesentlich beigetragen. Trotz der hohen Flexibilität in der Anwendung weist die fRG als perturbative Methode aber Einschränkungen auf. Wir stellen hier einen allgemeinen Ansatz für eine Erweiterung über das Regime schwacher Kopplung hinaus vor, in dem ein exakt lösbares Referenzsystems als Startpunkt für den Renormierungsgruppenfluss verwendet wird. Die systematische Entwicklung um diese Lösung ermöglicht es Korrelationseffekte sowohl auf dem ein-Teilchen (Selbstenergie) als auch auf dem zwei-Teilchen Niveau (Vertex-Funktionen) nicht-perturbativ einzubeziehen. Die numerische Handhabung von zwei-Teilchen Vertex-Funktionen stellt jedoch für die fRG wie auch für zahlreiche andere moderne Vielteilchenmethoden eine große Herausforderung dar. In dieser Arbeit präsentieren wir eine umfassende diagrammatische Analyse der Frequenz- und Impulsstrukturen der Vertex-Funktionen sowie deren physikalische Interpretation.
Die daraus gewonnen neuen Einsichten bilden die Grundlage für die Entwicklung effizienterer Parametrisierungen. Wir diskutieren die technischen Details der numerischen Implementierung und testen diese am Beispiel der fRG und der parquet Näherung (PA)
TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data
We present the TRIQS/Nevanlinna analytic continuation package, an efficient
implementation of the methods proposed by J. Fei et al in [Phys. Rev. Lett.
126, 056402 (2021)] and [Phys. Rev. B 104, 165111 (2021)]. TRIQS/Nevanlinna
strives to provide a high quality open source (distributed under the GNU
General Public License version 3) alternative to the more widely adopted
Maximum Entropy based analytic continuation programs. With the additional Hardy
functions optimization procedure, it allows for an accurate resolution of wide
band and sharp features in the spectral function. Those problems can be
formulated in terms of imaginary time or Matsubara frequency response
functions. The application is based on the TRIQS C++/Python framework, which
allows for easy interoperability with other TRIQS-based applications,
electronic band structure codes and visualization tools. Similar to other TRIQS
packages, it comes with a convenient Python interface.Comment: 15 pages, 5 figure
Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin- fermions
`Strange metals' with resistivity depending linearly on temperature down
to low- have been a long-standing puzzle in condensed matter physics. Here,
we consider a model of itinerant spin- fermions interacting via on-site
Hubbard interaction and random infinite-ranged spin-spin interaction. We show
that the quantum critical point associated with the melting of the spin-glass
phase by charge fluctuations displays non-Fermi liquid behaviour, with local
spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This
extends the quantum spin liquid dynamics previously established in the
large- limit of symmetric models, to models with physical
spin- electrons. Remarkably, the quantum critical regime also features a
Planckian linear- resistivity associated with a -linear scattering rate
and a frequency dependence of the electronic self-energy consistent with the
Marginal Fermi Liquid phenomenology
Correlated starting points for the functional renormalization group
We present a general frame to extend functional renormalization group (fRG)
based computational schemes by using an exactly solvable interacting reference
problem as starting point for the RG flow. The systematic expansion around this
solution accounts for a non-perturbative inclusion of correlations. Introducing
auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation,
we derive the flow equations for the auxiliary fields and determine the
relation to the conventional weak-coupling truncation of the hierarchy of flow
equations. As a specific example we consider the dynamical mean-field theory
(DMFT) solution as reference system, and discuss the relation to the recently
introduced DMFRG and the dual-fermion formalism.Comment: 14 pages, 6 figure
MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language
The Matsubara Green's function formalism stands as a powerful technique for
computing the thermodynamic characteristics of interacting quantum
many-particle systems at finite temperatures. In this manuscript, our focus
centers on introducing MatsubaraFunctions.jl, a Julia library that implements
data structures for generalized n-point Green's functions on Matsubara
frequency grids. The package's architecture prioritizes user-friendliness
without compromising the development of efficient solvers for quantum field
theories in equilibrium. Following a comprehensive introduction of the
fundamental types, we delve into a thorough examination of key facets of the
interface. This encompasses avenues for accessing Green's functions, techniques
for extrapolation and interpolation, as well as the incorporation of symmetries
and a variety of parallelization strategies. Examples of increasing complexity
serve to demonstrate the practical utility of the library, supplemented by
discussions on strategies for sidestepping impediments to optimal performance.Comment: 37 pages, 10 figure
Low rank Green's function representations applied to dynamical mean-field theory
Several recent works have introduced highly compact representations of
single-particle Green's functions in the imaginary time and Matsubara frequency
domains, as well as efficient interpolation grids used to recover the
representations. In particular, the intermediate representation with sparse
sampling and the discrete Lehmann representation (DLR) make use of low-rank
compression techniques to obtain optimal approximations with controllable
accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT)
calculations, and in particular, show that the standard full Matsubara
frequency grid can be replaced by the compact grid of DLR Matsubara frequency
nodes. We test the performance of the method for a DMFT calculation of
SrRuO at temperature K using a continuous-time quantum Monte Carlo
impurity solver, and demonstrate that Matsubara frequency quantities can be
represented on a grid of only nodes with no reduction in accuracy, or
increase in the number of self-consistent iterations, despite the presence of
significant Monte Carlo noise.Comment: 5 pages, 4 figure