Wavefunction-Based Methods

Peter Fulde

The electronic-structure theory of solids is presently dominated by density-functional methods which avoid calculations of the many-body wavefunction, and instead compute directly properties of the ground state. We argue that methods which determine the many-electron wavefunctions should receive particular attention in the future. A survey is given of our present knowledge of how to calculate these wavefunctions for a solid. The accuracy we envisage compares with the one obtainable for small molecules when applying quantum-chemical methods.

Kohei Motegi

We present a method to analyze the wavefunctions of six-vertex models by extending the Izergin–Korepin analysis originally developed for domain wall boundary partition functions. First, we apply the method to the case of the basic wavefunctions of the XXZ-type six-vertex model. By giving the Izergin–Korepin characterization of the wavefunctions, we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed Grothendieck polynomials. As a second example, we show that the Izergin–Korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions. As a third example, we apply the method to the elliptic Felderhof model which is a face-type version and an elliptic extension of the trigonometric Felderhof model. We show that the wavefunctions can be expressed as one-parameter deformations of an elliptic analog of the Vandermonde determinant and elliptic symmetric functions.

Jincheng Zhang

This paper introduces Hyperdimensional Wavefunction Collapse (HWC), a novel method for generating highly complex and diverse wavefunctions. We propose a dynamically collapsing algorithm that generates wavefunctions at multiple scales, combining them to produce intricate patterns. The core of HWC lies in its multi-scale, adaptive approach, which significantly enhances sampling efficiency and versatility compared to existing methods. We detail the algorithm's design, the resulting wave function generation process, and the resulting impact on wave function diversity. This work demonstrates the potential of HWC to produce complex wavefunctions with improved efficiency and adaptability.

Volker Schmidt