Reduced Density Matrix Functional Theory for Bosons

Abstract

Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix $\gamma$ as a natural variable but still recovers quantum correlations in an exact way it is particularly well-suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying $v$-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals for this $N$-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. The respective gradient forces are found to diverge in the regime of Bose-Einstein condensation, ${\nabla }_{\gamma }\mathcal{F}\propto 1/\sqrt{1-N_{\mathrm{BEC}}/N}$, providing a natural explanation for the absence of complete BEC in nature.

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• Weakly interacting Bose gas in a random environment
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• Diverging exchange force and form of the exact density matrix functional
• Landscape of an exact energy functional
• Reduced density-matrix functionals applied to the Hubbard dimer
• One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
• A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder

Cited by in corpus (20)

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• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Towards a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming
• Deriving density-matrix functionals for excited states
• Electron correlation in the Iron(II) Porphyrin by NOF approximations
• 1-matrix functional for long-range interaction energy of two hydrogen atoms
• Functional Theory for Bose-Einstein Condensates
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Orbital-Free Quasi-Density Functional Theory
• Imaging the interface of a qubit and its quantum-many-body environment
• Contactium: A strongly correlated model system
• Natural orbitals and their occupation numbers for free anyons in the magnetic gauge
• Many Electrons and the Photon Field -- The many-body structure of nonrelativistic quantum electrodynamics
• Density-matrix functional theory of the attractive Hubbard model: Statistical analogy of pairing correlations
• Representability for Quantum Theory beyond Particle-Number Conservation
• Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory