Minimal generating sets of non-modular invariant rings of finite groups

It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case. Apart from very few explicit computations of Groebner bases, the algorithm only involves very basic operations, and is thus rather fast. As a test bed for comparative benchmarks, we use transitive permutation groups on 7 and 8 variables. In most examples, our algorithm implemented in Singular works much faster than the one used in Magma, namely by factors between 50 and 1000. We also compute some further examples on more than 8 variables, including a minimal generating set for the natural action of the cyclic group of order 11 in characteristic 0 and of order 15 in characteristic 2. We also apply our algorithm to the computation of irreducible secondary invariants.Comment: 14 pages v3: Timings updated. One example adde

Lightcone renormalization and quantum quenches in one-dimensional Hubbard models

The Lieb-Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolution of prepared initial states in the thermodynamic limit in one-dimensional quantum systems. The algorithm does not require translational invariance and allows for an easy implementation of local conservation laws. We use the algorithm to investigate the relaxation dynamics of double occupancies in fermionic Hubbard models as well as a possible thermalization. For the integrable Hubbard model we find a pure power-law decay of the number of doubly occupied sites towards the value in the long-time limit while the decay becomes exponential when adding a nearest neighbor interaction. In accordance with the eigenstate thermalization hypothesis, the long-time limit is reasonably well described by a thermal average. We point out though that such a description naturally requires the use of negative temperatures. Finally, we study a doublon impurity in a N\'eel background and find that the excess charge and spin spread at different velocities, providing an example of spin-charge separation in a highly excited state.Comment: published versio

Identifying a forward scattering superconductor through pump-probe spectroscopy

Electron-boson scattering that is peaked in the forward direction has been suggested as an essential ingredient for enhanced superconductivity observed in FeSe monolayers. Here, we study the superconducting state of a system dominated by forward scattering in the time-domain and contrast its behavior against the standard isotropic BCS case for both s- and d-wave symmetries. An analysis of the electron's dynamics in the pump-driven non-equilibrium state reveals that the superconducting order in the forward-focused case is robust and persistent against the pump-induced perturbations. The superconducting order parameter also exhibits a non-uniform melting in momentum space. We show that this behavior is in sharp contrast to the isotropic interaction case and propose that time-resolved approaches are a potentially powerful tool to differentiate the nature of the dominant coupling in correlated materials.Comment: Updated the introduction and the methods section, 6 Pages, 5 figure

Theory of light-enhanced phonon-mediated superconductivity

We investigate the dynamics of a phonon-mediated superconductor driven out of equilibrium. The electronic hopping amplitude is ramped down in time, resulting in an increased electronic density of states. The dynamics of the coupled electron-phonon model is investigated by solving Migdal-Eliashberg equations for the double-time Keldysh Green's functions. The increase of the density of states near the Fermi level leads to an enhancement of superconductivity when the system thermalizes to the new state at the same temperature. We provide a time- and momentum-resolved view on this thermalization process, and show that it involves fast processes associated with single-particle scattering and much slower dynamics associated with the superconducting order parameter. The importance of electron-phonon coupling for the rapid enhancement and the efficient thermalization of superconductivity is demonstrated, and the results are compared to a BCS time-dependent mean-field approximation.Comment: 12 pages, 8 figure

General principles for the non-equilibrium relaxation of populations in quantum materials

We examine the problem of how excited populations of electrons relax after they have been excited by a pump. We include three of the most important relaxation processes: (i) impurity scattering; (ii) Coulomb scattering; and (iii) electron-phonon scattering. The relaxation of an excited population of electrons is one of the most fundamental processes measured in pump/probe experiments, but its interpretation remains under debate. We show how several common assumptions about non-equilibrium relaxation that are pervasive in the field may not hold under quite general conditions. The analysis shows that non-equilibrium relaxation is more complex than previously thought, but it yields to recently developed theoretical methods in non-equilibrium theory. In this work, we show how one can use many-body theory to properly interpret and analyze these complex systems. We focus much of the discussion on implications of these results for experiment.Comment: 13 pages, 10 figure

Determining the forsterite abundance of the dust around Asymptotic Giant Branch stars

Aims. We present a diagnostic tool to determine the abundance of the crystalline silicate forsterite in AGB stars surrounded by a thick shell of silicate dust. Using six infrared spectra of high mass-loss oxygen rich AGB stars we obtain the forsterite abundance of their dust shells. Methods. We use a monte carlo radiative transfer code to calculate infrared spectra of dust enshrouded AGB stars. We vary the dust composition, mass-loss rate and outer radius. We focus on the strength of the 11.3 and the 33.6 \mu m forsterite bands, that probe the most recent (11.3 \mu m) and older (33.6 \mu m) mass-loss history of the star. Simple diagnostic diagrams are derived, allowing direct comparison to observed band strengths. Results. Our analysis shows that the 11.3 \mu m forsterite band is a robust indicator for the forsterite abundance of the current mass-loss period for AGB stars with an optically thick dust shell. The 33.6 \mu m band of forsterite is sensitive to changes in the density and the geometry of the emitting dust shell, and so a less robust indicator. Applying our method to six high mass-loss rate AGB stars shows that AGB stars can have forsterite abundances of 12% by mass and higher, which is more than the previously found maximum abundance of 5%.Comment: Accepted for publication in A&