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A Density Functional Theory View of Quantum Phase Transitions.

Á Nagy1,2, M Calixto3, E Romera2,4

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Summary

A one-to-one map exists between ground state wave functions and control parameters in Density Functional Theory (DFT). Monotonous functions and Rényi entropy can also serve as control parameters, offering new avenues for DFT research.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Density Functional Theory

Background:

  • Density Functional Theory (DFT) utilizes electron density to determine system properties.
  • Wu et al. established a link between DFT "density" and the "control parameter" (external potential).

Purpose of the Study:

  • To demonstrate a one-to-one mapping between ground state wave functions and control parameters.
  • To explore alternative methods for manipulating control parameters in DFT.

Main Methods:

  • Proving the existence of a one-to-one correspondence between wave functions and control parameters.
  • Investigating the impact of strictly monotonous functions on density and control parameters.
  • Analyzing the relationship between Rényi entropy and control parameters.

Main Results:

  • A unique ground state wave function corresponds to each control parameter.
  • Strictly monotonous functions can generate new densities and corresponding control parameters.
  • A one-to-one map exists between Rényi entropy and the control parameter.

Conclusions:

  • The control parameter is uniquely determined by the ground state wave function.
  • Rényi entropy can be effectively utilized as a control parameter in DFT.
  • This work provides new insights into the fundamental relationships within Density Functional Theory.