State-of-the-art techniques for calculating spectral functions in models for correlated materials

The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important step in this method involves the calculation of response functions of a multiorbital impurity problem which is related to the original model. Recently there has been considerable progress in the development of techniques based on the density matrix renormalization group (DMRG) and related matrix product states (MPS) implying a substantial improvement to previous methods. In this article we review some of the standard algorithms and compare them to the newly developed techniques, showing examples for the particular case of the half-filled two-band Hubbard model.Comment: 8 pages, 4 figures, to be published in EPL Perspective

A useful form of the recurrence relation between relativistic atomic matrix elements of radial powers

Recently obtained recurrence formulae for relativistic hydrogenic radial matrix elements are cast in a simpler and perhaps more useful form. This is achieved with the help of a new relation between the $r^a$ and the $\beta r^b$ terms ($\beta$ is a $4\times 4$ Dirac matrix and $a, b$ are constants) in the atomic matrix elements.Comment: 7 pages, no figure

Lagrangian Description of the Variational Equations

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system

Dataset for holiday rentals’ daily rate pricing in a cultural tourism destination

This data article describes a holiday rental dataset from a medium-size cultural city destination. Daily rate and variables related to location, size, amenities, rating, and seasonality are highlighted as the main features. The data was extracted from Booking.com, legal registration of the accommodation (RTA) and Google Maps, among other sources. This dataset contains data from 665 holiday rentals offered as entire flat (rent per room was discarded), with a total of 1623 cases and 28 variables considered. Regarding data extraction, RTA is ordered by registration number, which is taken and, through a Google search with the following structure: "apartment registration no. + Booking + Seville", the holiday rental profile in Booking.com is found. Then, it is verified that both the address of the accommodation and the registration number match in RTA and Booking.com, proceeding with data extraction to a Microsoft Excel's file. Google Maps is used to determine the minutes spent walking from the accommodation to the spot of maximum tourist interest of the city. A price index based on the average price per square meter of real estate per district is also incorporated to the dataset, as well as a visual appeal rating made by the authors of every holiday rental based on its Booking.com photos profile. Only cases with complete data were considered. A statistics summary of all variables of the data collected is presented. This dataset can be used to develop an estimation model of daily prices of stay in holiday rentals through predetermined variables. Econometrics methodologies applied to this dataset can also allow testing which variables included affecting the composition of holiday rentals' daily rates and which not, as well as determining their respective influence on daily rates.info:eu-repo/semantics/publishedVersio

Recurrence relation for relativistic atomic matrix elements

Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.Comment: 10 pages, no figure

Mott-Hubbard quantum criticality in paramagnetic CMR pyrochlores

We present a correlated {\it ab initio} description of the paramagnetic phase of Tl$_2$Mn$_2$O$_7$, employing a combined local density approximation (LDA) with multiorbital dynamical mean field theory (DMFT) treatment. We show that the insulating state observed in this colossal magnetoresistance (CMR) pyrochlore is determined by strong Mn intra- and inter-orbital local electron-electron interactions. Hybridization effects are reinforced by the correlation-induced spectral weight transfer. Our result coincides with optical conductivity measurements, whose low energy features are remarkably accounted for by our theory. Based on this agreement, we study the disorder-driven insulator-metal transition of doped compounds, showing the proximity of Tl$_2$Mn$_2$O$_7$ to quantum phase transitions, in agreement with recent measurements.Comment: 4 pages, 4 figure