Exact Self-Consistent Effective Hamiltonian Theory

Abstract

We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in quadratic form which can then be exactly solved. The theory can be constructed within 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 system and an symmetric and asymmetric Hubbard dimer and corresponding lattice models and the the single fermion excitation spectra show a persistent gap due to the fermionic entanglement induced pairing condensate. For disordered system, density of state at the edge of the gap diverges in the thermodynamic limit, suggesting a topologically ordered phase and 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 quantum phase transition between the AFM and SC is a continuous phase transition.

Low Frequency Electrical Resonance in Water

“…The sharpest resonance has a half width less than 0.5 MHz, i.e., ~2 neV, suggesting that the lifetime of the resonant excitation to be in the order of higher than milliseconds. This long lifetime of the observed resonance has not been documented before and is consistent with the theory in Wang et al (2020) that predicts a macroscopic long-range coherent quantum mechanical excited state resulting from proton hoping at hydrogen bonds..…”

“…The sharp changes in the amplitude and the phase point to a change in the permittivity of water caused by a resonant response of water around the resonant frequency. Resonant response of water in this low frequency range has not been documented before, and is consistent with the prediction in Wang et al (2020)..…”

Solving Anderson Impurity Model by the Effective Hamiltonian Theory

“…A new approach was recently proposed in the form of a Self-Consistent Effective Hamiltonian Theory (SCEHT), , in which a general variational Fermionic many-body wave function is used to generate an effective Hamiltonian in a quadratic form. This theory promised to treat the finite number of local degrees of freedom exactly, while providing a mean field treatment of the interactions between the local system and its environment through a self-consistency condition.…”

Majorana Fermions in Self-Consistent Effective Hamiltonian Theory

“…Majorana fermion solution is obtained from the self-consistent effective Hamiltonian theory [1]. The ground state is conjectured to be a non-empty vacuum with 2 fermions, one for each type.…”

“…al. [1] apply the Bogolyubov transformation to the 4 local many-body basis states and conjectured that for ground state, due to Pauli exclusion principle, only 3-local basis is needed and further derived a tight-binding version of the quadratic Hamiltonian. In this letter, we formulate a similar variational Ansatz in the continuum limit and solves the two chiral-symmetry broken modes for fermionic excitations.…”