The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems, ranging from molecules to solids, giving rise to a plethora of physical phenomena experimentally accessible using time‐resolved techniques. Green's function methods offer an invaluable interpretation tool since scattering mechanisms of growing complexity can be selectively incorporated in the theory. Cheers is a general‐purpose nonequilibrium Green's function code that implements virtually all known many‐body approximations and is designed for first‐principles studies of ultrafast processes in molecular and model solid‐state systems. The aims of generality, extensibility, efficiency, and user friendliness of the code are achieved through the underlying theory development and the use of modern software design practices. Herein, the necessity for the creation of such a code is motivated and its design and capabilities are overviewed.The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems, ranging from molecules to solids, giving rise to a plethora of physical phenomena experimentally accessible using time‐resolved techniques. Green's function methods offer an invaluable interpretation tool since scattering mechanisms of growing complexity can be selectively incorporated in the theory. Cheers is a general‐purpose nonequilibrium Green's function code that implements virtually all known many‐body approximations and is designed for first‐principles studies of ultrafast processes in molecular and model solid‐state systems. The aims of generality, extensibility, efficiency, and user friendliness of the code are achieved through the underlying theory development and the use of modern software design practices. Herein, the necessity for the creation of such a code is motivated and its design and capabilities are overviewed.

arXiv:2312.00468physica status solidi (b)Dec 29, 202318 citations

Phonon renormalization and Pomeranchuk instability in the Holstein model

Niklas Cichutek, Max Hansen, Peter Kopietz

The Holstein model with dispersionless Einstein phonons is one of the simplest models describing electron-phonon interactions in condensed matter. A naive extrapolation of perturbation theory in powers of the relevant dimensionless electron-phonon coupling ${\ensuremath{\lambda}}_{0}$ suggests that at zero temperature the model exhibits a Pomeranchuk instability characterized by a divergent uniform compressibility at a critical value of ${\ensuremath{\lambda}}_{0}$ of order unity. In this work, we re-examine this problem using modern functional renormalization group (RG) methods. For dimensions $d>3$ we find that the RG flow of the Holstein model indeed exhibits a tricritical fixed point associated with a Pomeranchuk instability. This non-Gaussian fixed point is ultraviolet stable and is closely related to the well-known ultraviolet stable fixed point of ${\ensuremath{\phi}}^{3}$-theory above six dimensions. To realize the Pomeranchuk critical point in the Holstein model at fixed density both the electron-phonon coupling ${\ensuremath{\lambda}}_{0}$ and the adiabatic ratio ${\ensuremath{\omega}}_{0}/{\ensuremath{\epsilon}}_{F}$ have to be fine-tuned to assume critical values of order unity, where ${\ensuremath{\omega}}_{0}$ is the phonon frequency and ${\ensuremath{\epsilon}}_{F}$ is the Fermi energy. However, for dimensions $d\ensuremath{\le}3$ we find that the RG flow of the Holstein model does not have any critical fixed points. This rules out a quantum critical point associated with a Pomeranchuk instability in $d\ensuremath{\le}3$.The Holstein model with dispersionless Einstein phonons is one of the simplest models describing electron-phonon interactions in condensed matter. A naive extrapolation of perturbation theory in powers of the relevant dimensionless electron-phonon coupling ${\ensuremath{\lambda}}_{0}$ suggests that at zero temperature the model exhibits a Pomeranchuk instability characterized by a divergent uniform compressibility at a critical value of ${\ensuremath{\lambda}}_{0}$ of order unity. In this work, we re-examine this problem using modern functional renormalization group (RG) methods. For dimensions $d>3$ we find that the RG flow of the Holstein model indeed exhibits a tricritical fixed point associated with a Pomeranchuk instability. This non-Gaussian fixed point is ultraviolet stable and is closely related to the well-known ultraviolet stable fixed point of ${\ensuremath{\phi}}^{3}$-theory above six dimensions. To realize the Pomeranchuk critical point in the Holstein model at fixed density both the electron-phonon coupling ${\ensuremath{\lambda}}_{0}$ and the adiabatic ratio ${\ensuremath{\omega}}_{0}/{\ensuremath{\epsilon}}_{F}$ have to be fine-tuned to assume critical values of order unity, where ${\ensuremath{\omega}}_{0}$ is the phonon frequency and ${\ensuremath{\epsilon}}_{F}$ is the Fermi energy. However, for dimensions $d\ensuremath{\le}3$ we find that the RG flow of the Holstein model does not have any critical fixed points. This rules out a quantum critical point associated with a Pomeranchuk instability in $d\ensuremath{\le}3$.

arXiv:2203.08641Physical review. B./Physical review. BMay 31, 20225 citations

Coding theory for robust computing: Models, tools, and applications

Lara Dolecek

Computing under uncertainty has become increasingly important in modern information processing systems. In this work, we first review exciting recent results on the multi-faceted role coding approaches can play in this important discipline, including fundamental performance limits of noisy iterative algorithms and decoders, implications on system design, and coding-theoretic methods for approximate computing. We also explore connections between coding theory and other disciplines in modern computing, and we present several new and promising research directions in coding for modern computing and noisy iterative information processing.Computing under uncertainty has become increasingly important in modern information processing systems. In this work, we first review exciting recent results on the multi-faceted role coding approaches can play in this important discipline, including fundamental performance limits of noisy iterative algorithms and decoders, implications on system design, and coding-theoretic methods for approximate computing. We also explore connections between coding theory and other disciplines in modern computing, and we present several new and promising research directions in coding for modern computing and noisy iterative information processing.

International Symposium on Turbo Codes and Iterative Information ProcessingSep 1, 20160 citations

Phonons from a many-body viewpoint

R. D. Mattuck

Annals of PhysicsFeb 1, 19640 citations

d>3

we find that the RG flow of the Holstein model indeed exhibits a tricritical fixed point associated with a Pomeranchuk instability. This non-Gaussian fixed point is ultraviolet stable and is closely related to the well-known ultraviolet stable fixed point of ${\ensuremath{\phi}}^{3}$-theory above six dimensions. To realize the Pomeranchuk critical point in the Holstein model at fixed density both the electron-phonon coupling ${\ensuremath{\lambda}}_{0}$ and the adiabatic ratio ${\ensuremath{\omega}}_{0}/{\ensuremath{\epsilon}}_{F}$ have to be fine-tuned to assume critical values of order unity, where ${\ensuremath{\omega}}_{0}$ is the phonon frequency and ${\ensuremath{\epsilon}}_{F}$ is the Fermi energy. However, for dimensions $d\ensuremath{\le}3$ we find that the RG flow of the Holstein model does not have any critical fixed points. This rules out a quantum critical point associated with a Pomeranchuk instability in $d\ensuremath{\le}3$.