scholarly journals Majorana Fermions in Self-Consistent Effective Hamiltonian Theory

2021 ◽  
Author(s):  
Xindong Wang
Keyword(s):  
Ground State ◽  
The Self ◽  
Majorana Fermion ◽  
Majorana Fermions ◽  
Effective Hamiltonian ◽  
Charged Fermion ◽  
Hamiltonian Theory ◽  
Self Consistent

Majorana fermion solution is obtained from the self-consistent effective Hamiltonian theory. The ground state is conjectured to be a non-empty vacuum with 2 fermions, one for each type. The first type is the original charged fermion and the second type the chiral charge-less Majorana fermion. The Marjorana fermion is like a shadow of the first fermion cast by the non-empty vacuum.

scholarly journals Self-consistent effective Hamiltonian theory for fermionic many-body systems

2020 ◽  
pp. 2150019
Author(s):  
Xindong Wang ◽  
Hai-Ping Cheng
Keyword(s):  
Hubbard Model ◽  
Order Parameter ◽  
Cooper Pair ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Body System ◽  
Many Body ◽  
Hamiltonian Theory ◽  
Self Consistent ◽  
Many Body Systems

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 (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

scholarly journals Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD

2020 ◽  
Vol 8 (5) ◽  
Author(s):  
Aleksey Cherman ◽  
Theo Jacobson ◽  
Yuya Tanizaki ◽  
Mithat Ünsal
Keyword(s):  
Gauge Theory ◽  
Ground State ◽  
Chiral Symmetry Breaking ◽  
Index Theorem ◽  
Majorana Fermion ◽  
Ground State Structure ◽  
Majorana Fermions ◽  
State Structure ◽  
Symmetry Protected

We show that 22d adjoint QCD, an SU(N)SU(N) gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 22 index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of NN, are matched by spontaneous chiral symmetry breaking. We find that massless 22d adjoint QCD confines for N >2N>2, except for test charges of NN-ality N/2N/2, which are deconfined. In other words, \mathbb Z_NℤN center symmetry is unbroken for odd NN and spontaneously broken to \mathbb Z_{N/2}ℤN/2 for even NN. All of these results are confirmed by explicit calculations on small \mathbb{R}\times S^1ℝ×S1. We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when NN is even. Furthermore, for most values of NN, 22d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 88. As a result, it fits into the classification of (1+1)(1+1)d SPT phases of interacting Majorana fermions in an interesting way.

Phonon Anharmonicity and Thermodynamic Properties of Strongly Correlated Iron Monosilicide

2016 ◽  
Vol 257 ◽  
pp. 203-210 ◽  
Author(s):  
Aleksandr A. Povzner ◽  
Anton N. Filanovich ◽  
Tatyana A. Nogovitsyna
Keyword(s):  
Experimental Data ◽  
Thermodynamic Properties ◽  
Thermodynamic Model ◽  
Ground State ◽  
The Self ◽  
Strongly Correlated ◽  
Optical Phonons ◽  
Computational Approaches ◽  
Self Consistent ◽  
Iron Monosilicide

Two computational approaches – a thermodynamic model based on results of ab initio calculations of the ground state and the self-consistent thermodynamic model have been applied to study thermal and elastic properties of iron monosilicide. It is shown that conventional DFT fails to reproduce experimental data for this strongly correlated compound. In addition, we have performed comparative analysis of anharmonicity of the acoustic and optical phonons in FeSi and their impact on the temperature dependencies of thermodynamic properties of FeSi.

The self-consistent field with exchange for some 10 and 12 electron systems

1957 ◽  
Vol 53 (1) ◽  
pp. 206-213 ◽  
Author(s):  
Charlotte Froese
Keyword(s):  
Ground State ◽  
The Self ◽  
Electron Systems ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

ABSTRACTThe results of self-consistent field calculations with exchange for the ground-state configurations of F−, Fe+16, +14, Al+3, +1 are presented.

Bilayered Spin-S Heisenberg Model in Fractional Dimensions

1998 ◽  
Vol 12 (18) ◽  
pp. 1809-1812 ◽  
Author(s):  
K. K. Ng
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Ground State ◽  
Heisenberg Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
The Self ◽  
Self Consistent ◽  
Ferromagnetic Heisenberg Model ◽  
Fractional Dimensions

The ground state and the phase transitions of the bilayered spin-S anti-ferromagnetic Heisenberg model were studied by Ng et al.1 by using the Schwinger boson mean field theory. In this paper, an analytic continuation of the self-consistent equations is carried out in order to study the extension of the model to fractional dimensions from 1 to 2. Decreasing the dimensionality from 2 has an effect similar to that of decreasing the spin S. The corresponding phase diagram and phase transition will also be discussed.

scholarly journals Mathematical Theory of Locally Coherent Quantum Many-Body Fermionic System

2020 ◽  
Author(s):  
Xindong Wang
Keyword(s):  
Excited States ◽  
Energy Functional ◽  
Gauge Fields ◽  
Effective Hamiltonian ◽  
Many Body ◽  
Fermionic System ◽  
Hamiltonian Theory ◽  
System P ◽  
Fermionic Systems ◽  
Self Consistent

Recently Wang and Cheng proposed a self-consistent effective Hamiltonian theory (SCEHT) for many-body fermionic systems (Wang & Cheng, 2019). This paper attempts to provide a mathematical foundation to the formulation of the SCEHT 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.

Sign in / Sign up

Export Citation Format

Share Document