Foundation of one-particle reduced density matrix functional theory for excited states

• URL: http://arxiv.org/abs/2106.03918v2
• Date: Thu, 5 May 2022 15:45:10 GMT
• Title: Foundation of one-particle reduced density matrix functional theory for excited states
• Authors: Julia Liebert, Federico Castillo, Jean-Philippe Labb\'e, Christian Schilling
• Abstract summary: A reduced density matrix functional theory (RDMFT) has been proposed for calculating energies of selected eigenstates of interacting many-fermion systems. Here, we develop a solid foundation for this so-called $boldsymbolw$-RDMFT and present the details of various derivations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In [Phys. Rev. Lett. 127, 023001 (2021)] a reduced density matrix functional theory (RDMFT) has been proposed for calculating energies of selected eigenstates of interacting many-fermion systems. Here, we develop a solid foundation for this so-called $\boldsymbol{w}$-RDMFT and present the details of various derivations. First, we explain how a generalization of the Ritz variational principle to ensemble states with fixed weights $\boldsymbol{w}$ in combination with the constrained search would lead to a universal functional of the one-particle reduced density matrix. To turn this into a viable functional theory, however, we also need to implement an exact convex relaxation. This general procedure includes Valone's pioneering work on ground state RDMFT as the special case $\boldsymbol{w}=(1,0,\ldots)$. Then, we work out in a comprehensive manner a methodology for deriving a compact description of the functional's domain. This leads to a hierarchy of generalized exclusion principle constraints which we illustrate in great detail. By anticipating their future pivotal role in functional theories and to keep our work self-contained, several required concepts from convex analysis are introduced and discussed.

Related papers

• Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain [0.0]
  The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) We show that splitting the minimization into the diagonal and off-diagonal part of the 1-RDM can open the way toward the development of functionals of the orbital occupations.
  arXiv  Detail & Related papers  (2024-05-17T07:35:31Z)
• Tempered Calculus for ML: Application to Hyperbolic Model Embedding [70.61101116794549]
  Most mathematical distortions used in ML are fundamentally integral in nature. In this paper, we unveil a grounded theory and tools which can help improve these distortions to better cope with ML requirements. We show how to apply it to a problem that has recently gained traction in ML: hyperbolic embeddings with a "cheap" and accurate encoding along the hyperbolic vsean scale.
  arXiv  Detail & Related papers  (2024-02-06T17:21:06Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Deriving density-matrix functionals for excited states [0.0]
  We first study the symmetric Hubbard dimer, constituting the building block of the Hubbard model, for which we execute the Levy-Lieb constrained search. We demonstrate three conceptually different approaches for deriving the universal functional in a homogeneous Bose gas for arbitrary pair interaction in the Bogoliubov regime. Remarkably, in both systems the gradient of the functional is found to diverge repulsively at the boundary of the functional's domain, extending the recently discovered Bose-Einstein condensation force to excited states.
  arXiv  Detail & Related papers  (2022-09-29T17:03:08Z)
• Reduced Density Matrix Functional Theory for Bosons: Foundations and Applications [0.0]
  This thesis aims to initiate and establish a bosonic RDMFT for both ground state and excited state energy calculations. Motivated by the Onsager and Penrose criterion, we derive the universal functional for a homogeneous Bose-Einstein condensates (BECs) in the Bogoliubov regime. In the second part of the thesis, we propose and work out an ensemble RDMFT targeting excitations in bosonic quantum systems.
  arXiv  Detail & Related papers  (2022-05-05T13:28:18Z)
• Comment on "Self-Consistent-Field Method for Correlated Many-Electron Systems with an Entropic Cumulant Energy" [0.0]
  In [Phys. Rev. Lett. 128, 013001 (2022) a novel ground state method was proposed. It has been suggested that this $i$-DMFT would be a method within one-particle reduced density matrix functional theory. We reassess this work and its suggestions from a conceptual and practical point of view.
  arXiv  Detail & Related papers  (2022-02-11T10:17:55Z)
• Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle [0.0]
  We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems. Various obstacles which historically have doomed such an approach to be unfeasible are overcome.
  arXiv  Detail & Related papers  (2021-06-04T15:49:31Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.