Principe variationnel en physique quantique

Résumé

L'énergie de l'état fondamental d'un système quantique E_0 est une borne inférieure à la valeur moyenne de l'énergie calculée par toute fonction d'onde approchée normée \Phi \langle\Phi\vert\hat H\vert\Phi\rangle \ge E_0 Le principe variationnel est utilisé pour optimiser les fonctions d'onde approchées. Il permet en outre d'établir les deux théorèmes de Hohenberg et Kohn. Catégorie:Physique quantique Variationnel en physique quantique

Source officielle

https://fr.wikipedia.org/wiki/Principe_variationnel_en_physique_quantique

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Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems

Alexandra Nagy, Vincenzo Savona

The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom (d.o.f.) is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge posed by this task lies in the complexity of the density matrix increasing exponentially with the system size. Here, we develop a variational method to efficiently simulate the nonequilibrium steady state of Markovian open quantum systems based on variational Monte Carlo methods and on a neural network representation of the density matrix. Thanks to the stochastic reconfiguration scheme, the application of the variational principle is translated into the actual integration of the quantum master equation. We test the effectiveness of the method by modeling the two-dimensional dissipative XYZ spin model on a lattice.

AMER PHYSICAL SOC2019

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Stripes in the two-dimensional t-J model with infinite projected entangled-pair states

We simulate the t-J model in two dimensions by means of infinite projected entangled-pair states (iPEPS) generalized to arbitrary unit cells, finding results similar to those previously obtained by the density-matrix renormalization group (DMRG) for wide ladders. In particular, we show that states exhibiting stripes, that is, a unidirectional modulation of hole-density and antiferromagnetic order with a p-phase shift between adjacent stripes, have a lower variational energy than uniform phases predicted by variational and fixed-node Monte Carlo simulations. For a fixed unit-cell size the energy per hole is minimized for a hole density rho(l) similar to 0.5 per unit length of a stripe. The superconducting order parameter is maximal around rho(l) similar to 0.75-0.8.

2011

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The Kohn-Sham formulation of density functional theory (DFT) has posed itself as one of the most popular and versatile methods for condensed phase studies owing to its reasonable accuracy and affordable computational cost. DFT, in principle, yields exact ground state energy, including dispersion forces that are of primordial importance in chemical and biological systems. Yet with many exchange-correlation functionals in practical use such as the local density approximation or generalized gradient approximations, DFT either provides sporadic results or fails completely to account for these forces. In consequence, various methods offering remedy for this shortcoming have been proposed in this active field of research. In particular, dispersion-corrected atom-centered potentials (DCACPs) serve as a robust and efficient way to include these weak forces in a fully self-consistent manner within current DFT frameworks. The aim of this thesis is twofold: first, to improve the predictive power and the understanding of the DCACP concept; second, applying DCACPs to systems of increasing complexity starting with dimers, continuing through larger clusters and ending with the condensed phase. The success of the second aim not only justifies the use of DCACPs but more importantly, provides insights to the role dispersion forces play in the systems investigated. We first draw on the atoms-in-molecules theory and a multi-center density expansion to justify the form and universality of DCACPs. A library of DCACPs calibrated with an improved penalty functional against high-level ab initio references is presented. With the library in hand, we extend our studies to systems of biological significance, mainly constituents of proteins and DNA; polycyclic aromatic molecules intercalated in between segments of DNA are the center of focus. The application of DCACPs is then furthered to the condensed phase and the importance of van der Waals interactions in liquid water is investigated.

EPFL2008

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EPFL2008