Fock-Space Embedding Theory: Application to Strongly Correlated Topological Phases.

Ryan Requist,E K U Gross

doi:10.1103/physrevlett.127.116401

Abstract

A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated.

Highlights

First-principles calculations of topological invariants usually rely on the Kohn-Sham band structure
This is problematic for correlated materials: the topological phase inferred from a mean-field band structure need not coincide with the actual topological phase determined from the correlated many-body wave function
Since topological invariants depend on the global k dependence of the state, either through the twisting of Bloch functions in the Brillouin zone [14] or the behavior of the many-body wave function under twisted boundary conditions [15,16,17], it is natural to ask whether alternative embedding theories might be better suited to capturing momentum-dependent correlations

Summary

Introduction

First-principles calculations of topological invariants usually rely on the Kohn-Sham band structure. This Letter proposes a novel embedding theory rooted in the exact factorization (EF) methodology [18,19,20], a scheme for splitting the many-body wave function into marginal and conditional probability amplitudes describing different degrees of freedom.

Results

Conclusion