The Technology

Exact Self-Consistent Effective Hamiltonian Theory

Xindong Wang, Xiao Chen, Liqin Ke, Hai-Ping Cheng, and Bruce Harmon

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.

Many-Body Fermions and Riemann Hypothesis

Xindong Wang and Alex Shulman

We study the algebraic structure of the eigenvalues of a Hamiltonian that corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in fermion creation and/or annihilation operators, the system is exactly integrable and the complete single fermion excitation energy spectrum is constructed using the non-interacting fermions that are eigenstates of the quadratic matrix related to the system Hamiltonian. Connection to the Riemann Hypothesis is discussed.

Low Frequency Electrical Resonance in Water

Xindong Wang and Qiang Fu

We report the observation of sharp electrical resonance of water with width ~2 neV in the low radio frequency range at room temperature. The neV level of the resonant width under room temperature (~25 meV) is consistent with the theory in Wang et al (2020) that predicts a macroscopic long-range coherent quantum mechanical excited states, Majorana fermions, resulting from quantum entanglement of proton hopping at hydrogen bonds.

Mathematical Theory of Locally Coherent Quantum Many-Body Fermionic System

Xindong Wang

We provide a mathematical foundation to the formulation of the SCEHT (“Self-Consistent Effective Hamiltonian Theory”) that enables further study of excited states of the system in a more systematic and theoretical manner. Gauge fields are introduced and correct total energy functional in relations to the coupling gauge field is given. We also provides a Monte-Carlo numerical scheme for the search of the ground state that goes beyond the SCEHT.

Self-Consistent Effective Hamiltonian Theory for Fermionic Many Body Systems

Xindong Wang and Hai-Ping Cheng

Accepted and forthcoming in International Journal of Modern Physics B 

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2-d, a highly unconventional quadruple-fermion non-Cooper-pair order parameter is discovered.