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Title: On the v-representability of ensemble densities of electron systems

Journal Article · · Journal of Physics and Chemistry of Solids
 [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physical and Life Sciences
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Analogously to the case at zero temperature, where the density of the ground state of an interacting many-particle system determines uniquely (within an arbitrary additive constant) the external potential acting on the system, the thermal average of the density over an ensemble defined by the Boltzmann distribution at the minimum of the thermodynamic potential, or the free energy, determines the external potential uniquely (and not just modulo a constant) acting on a system described by this thermodynamic potential or free energy. The study describes a formal procedure that generates the domain of a constrained search over general ensembles (at zero or elevated temperatures) that lead to a given density, including as a special case a density thermally averaged at a given temperature, and in the case of a v-representable density determines the external potential leading to the ensemble density. As an immediate consequence of the general formalism, the concept of v-representability is extended beyond the hitherto discussed case of ground state densities to encompass excited states as well. Specific application to thermally averaged densities solves the v-representability problem in connection with the Mermin functional in a manner analogous to that in which this problem was recently settled with respect to the Hohenberg and Kohn functional. Finally, the main formalism is illustrated with numerical results for ensembles of one-dimensional, non-interacting systems of particles under a harmonic potential.

Research Organization:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1438681
Alternate ID(s):
OSTI ID: 1548883
Report Number(s):
LLNL-JRNL-731185; TRN: US1900484
Journal Information:
Journal of Physics and Chemistry of Solids, Vol. 116; ISSN 0022-3697
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

References (18)

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Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem journal February 2016
On the v-Representabilty Problem in Density Functional Theory: Application to Non-Interacting Systems journal July 2016
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Hohenberg-Kohn theorem and non-V-representable densities journal August 1983
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Lack of Hohenberg-Kohn Theorem for Excited States journal October 2004
Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction journal March 1955
v -Representability and Density Functional Theory journal October 1983
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Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems journal January 2017

Figures / Tables (3)

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Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
density functional theory
v-representability
excited states in DFT
ensemble v-representability
constrained search
constrained search for ensembles