Fundamental building blocks of strongly correlated wave functions

Abstract

The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body Hilbert space allows an arbitrary many-fermion wave function to be written in terms of a finite number of antisymmetric functions called shapes. Shapes naturally generalize the single-Slater-determinant form for the ground state to more than one dimension. Their number is exactly $N{!}^{d-1}$ in $d$ dimensions. An efficient algorithm is described to generate all fermion shapes in spaces of odd dimension, which improves on a recently published general algorithm. The results are placed in the context of contemporary investigations of strongly correlated electrons.

arXiv commentBased on invited talk at Superstripes 2016 (Ischia), to appear in Journal of Superconductivity and Novel Magnetism

References in corpus (13)

• Conventional superconductivity at 203 K at high pressures
• Crystal Structure of 200 K-Superconducting Phase of Sulfur Hydride System
• Evidence for a Fermi liquid in the pseudogap phase of high-Tc cuprates
• Validity of Kohler's rule in the pseudogap phase of the cuprate superconductors
• Computing total energies in complex materials using charge self-consistent DFT+DMFT
• Supercondutor-Insulator Transition on Annealed Complex Networks
• Origin of the Pseudogap in High-Temperature Cuprate Superconductors
• High temperature superconductivity in sulfur hydride under ultrahigh pressure: A complex superconducting phase beyond conventional BCS
• Natural generalization of the ground-state Slater determinant to more than one dimension
• Fermi arcs and pseudogap emerging from dimensional crossover at the Fermi surface in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Resistance of High-Temperature Cuprate Superconductors
• In-plane oxygens in high-temperature superconducting cuprates
• Fundamental invariants of many-body Hilbert space

Cited by in corpus (3)

• Many-fermion wave functions: structure and examples
• Fundamental invariants of many-body Hilbert space
• Lattice, Charge and Spin phase inhomogeneity in complex striped quantum matter