English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We have recently employed periodic Anderson model with electron-phononinteractions to describe Cerium volume collapse ($\gamma \rightarrow \alpha$transition) under pressure. To describe the volume collapse transition inCerium, we have tried to plot the pressure versus volume curves and see when akink structure emerges. One way to obtain the pressure versus volume curve isto calculate the total energy of the system at different temperatures. In orderto solve the periodic Anderson model with electron-phonon interactions, we haveused the continuous time quantum Monte Carlo algorithm by integrating out thephonons to obtain a retarded electron-electron interaction. Monte Carlosimulation results give us the model's electronic Green function and selfenergy, from which we can calculate the system's total energy. A well knownformula for calculating total energy through the knowledge of electron's selfenergy and Green function is derived from the model's Hamiltonian, which is notavailable for our case. Here, we have devised a new method to derive the totalenergy formula purely from a path integral description of the system, withoutresort to its Hamiltonian formulation. Since not all systems can be describedby a Hamiltonian, thus our method has a wider applicability. It is noteworthythat the total energy formula that we derived here takes an identical form withthat obtained from a model's Hamiltonian.

Schwinger-Dyson Equation Method to Calculate Total Energy in Periodic Anderson Model with Electron-Phonon Interactions