Exact Self-Consistent Effective Hamiltonian Theory

TL;DR

This paper introduces an exact self-consistent effective Hamiltonian approach for fermionic many-body systems, enabling precise solutions and revealing novel insights into disordered and correlated lattice models, including topological phases and quantum phase transitions.

Contribution

It presents a new variational wavefunction framework that generates exactly solvable effective Hamiltonians within density functional theory, applicable to complex disordered and strongly correlated systems.

Findings

Persistent energy gap due to fermionic entanglement

Diverging density of states at the gap edge indicating topological order

Continuous quantum phase transition between antiferromagnetic and superconducting phases

Abstract

We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework, and a self-consistent scheme is proposed for solving the exact density functional theory. We apply the theory to structurally-disordered systems, symmetric and asymmetric Hubbard dimers, and the corresponding lattice models. The single fermion excitation spectra show a persistent gap due to the fermionic-entanglement-induced pairing condensate. For disordered systems, the density of states at the edge of the gap diverges in the thermodynamic limit, suggesting a topologically ordered phase. A sharp resonance is predicted as the gap is not dependent on the temperature of the system. For the symmetric Hubbard model, the gap for both half-filling and doped case suggests that the quantum phase transition between the antiferromagnetic and superconducting phases is continuous.