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.

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 ROTATING FERMIONS IN TWO DIMENSIONS: A THOMAS–FERMI APPROACH

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2799-2810
Author(s):  
SANKALPA GHOSH ◽  
M. V. N. MURTHY ◽  
SUBHASIS SINHA
Keyword(s):  
Ground State ◽  
Analytical Approach ◽  
State Energy ◽  
Critical Size ◽  
Energy Functional ◽  
Two Dimensions ◽  
Fermionic System ◽  
Thomas Fermi ◽  
Fermionic Systems ◽  
Analytical Expressions

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy functional for a finite fermionic system within the Thomas–Fermi approximation in two dimensions. We show that for specific interactions the problem may be exactly solved. We derive analytical expressions for the density, the critical size as well as the ground state energy of such systems in a given angular momentum sector.

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 Chebyshev Matrix Product States with Canonical Orthogonalization for Spectral Functions of Many-Body Systems

2021 ◽  
Author(s):  
Tong Jiang ◽  
Jiajun Ren ◽  
Zhigang Shuai
Keyword(s):  
Ab Initio ◽  
Excited States ◽  
Time Dependent ◽  
Matrix Product ◽  
Effective Hamiltonian ◽  
Many Body ◽  
Spectral Functions ◽  
Matrix Product States ◽  
Many Body Systems ◽  
First Time

We propose a method to calculate the spectral functions of many-body systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. For the first time we demonstrate that Chebyshev MPS can be used to deal with ab initio electronic Hamiltonian effectively. We emphasize the strength of coCheMPS to calculate the low excited states of systems with sparse discrete spectrum. We also caution the application for electron-phonon systems with dense density of states.

Many-body Green functions in nuclear physics

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740025 ◽  
Author(s):  
J. Speth ◽  
N. Lyutorovich
Keyword(s):  
Nuclear Physics ◽  
Green Functions ◽  
Many Body ◽  
General Applicability ◽  
Pair Correlations ◽  
Self Consistent ◽  
The Many ◽  
The One ◽  
General Relations ◽  
Three Body

Many-body Green functions are a very efficient formulation of the many-body problem. We review the application of this method to nuclear physics problems. The formulas which can be derived are of general applicability, e.g., in self-consistent as well as in nonself-consistent calculations. With the help of the Landau renormalization, one obtains relations without any approximations. This allows to apply conservation laws which lead to important general relations. We investigate the one-body and two-body Green functions as well as the three-body Green function and discuss their connection to nuclear observables. The generalization to systems with pair correlations are also presented. Numerical examples are compared with experimental data.

scholarly journals Erratum: Diabatic-ramping spectroscopy of many-body excited states [Phys. Rev. A 90 , 062334 (2014)]

2017 ◽  
Vol 96 (3) ◽  
Author(s):  
Bryce Yoshimura ◽  
W. C. Campbell ◽  
J. K. Freericks
Keyword(s):  
Excited States ◽  
Many Body

scholarly journals Exciton-polaron Rydberg states in monolayer MoSe2 and WSe2

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Erfu Liu ◽  
Jeremiah van Baren ◽  
Zhengguang Lu ◽  
Takashi Taniguchi ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Boron Nitride ◽  
Excited States ◽  
Ground State ◽  
Transition Metal Dichalcogenides ◽  
Rydberg States ◽  
Energy Shift ◽  
Many Body ◽  
Electron Hole ◽  
Metal Dichalcogenides ◽  
Excitonic States

AbstractExciton polaron is a hypothetical many-body quasiparticle that involves an exciton dressed with a polarized electron-hole cloud in the Fermi sea. It has been evoked to explain the excitonic spectra of charged monolayer transition metal dichalcogenides, but the studies were limited to the ground state. Here we measure the reflection and photoluminescence of monolayer MoSe2 and WSe2 gating devices encapsulated by boron nitride. We observe gate-tunable exciton polarons associated with the 1 s–3 s exciton Rydberg states. The ground and excited exciton polarons exhibit comparable energy redshift (15~30 meV) from their respective bare excitons. The robust excited states contradict the trion picture because the trions are expected to dissociate in the excited states. When the Fermi sea expands, we observe increasingly severe suppression and steep energy shift from low to high exciton-polaron Rydberg states. Their gate-dependent energy shifts go beyond the trion description but match our exciton-polaron theory. Our experiment and theory demonstrate the exciton-polaron nature of both the ground and excited excitonic states in charged monolayer MoSe2 and WSe2.

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