scholarly journals On Strongly Correlated Eelectrons in Metals

2021 ◽  
Author(s):  
Jacob Szeftel
Keyword(s):  
Spatial Dimension ◽  
Strongly Correlated ◽  
Electron Band ◽  
One Dimensional ◽  
Hubbard Hamiltonian ◽  
Correlated Electron ◽  
Normal Metals ◽  
Interacting Electrons ◽  
The One ◽  
Groundstate Energy

A procedure, dedicated to superconductivity, is extended to study the properties of interacting electrons in normal metals in the thermodynamic limit. Each independent-electron band is shown to split into two correlated-electron bands. Excellent agreement is achieved with Bethe's wave-function for the one-dimensional Hubbard model. The groundstate energy, reckoned for the two-dimensional Hubbard Hamiltonian, is found to be lower than values, obtained thanks to the numerical methods. This analysis applies for any spatial dimension and temperature.

scholarly journals Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
S. Bera ◽  
B. Chakrabarti ◽  
A. Gammal ◽  
M. C. Tsatsos ◽  
M. L. Lekala ◽  
...  
Keyword(s):  
Interaction Strength ◽  
Dipolar Interaction ◽  
Spatial Dimension ◽  
Strongly Correlated ◽  
Body Density ◽  
One Dimensional ◽  
Confinement Potential ◽  
Strongly Interacting ◽  
The One ◽  
Infinite Repulsion

AbstractFermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases – due to their repulsion – the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For N interacting bosons, a splitting into an N-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that this splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

UNIFIED THEORY ON ANGLE-RESOLVED PHOTOEMISSION AND LIGHT ABSORPTION SPECTRA OF STRONGLY CORRELATED ELECTRON SYSTEMS

2002 ◽  
Vol 09 (02) ◽  
pp. 1017-1021
Author(s):  
NORIKAZU TOMITA ◽  
KEIICHIRO NASU
Keyword(s):  
Light Absorption ◽  
Quantum Monte Carlo ◽  
Electron System ◽  
Photoemission Spectrum ◽  
Apparent Difference ◽  
Strongly Correlated ◽  
Strongly Correlated Electron ◽  
One Dimensional ◽  
Correlated Electron ◽  
The One

Very recently, the angle-resolved photoemission spectrum (ARPES) of [ Ni(chxn) 2 Br]Br 2 (chxn=1R, 2R-cyclohexanediamine), which is a typical one-dimensional Mott insulator, has been experimentally observed. The experiment has strongly suggested that a one-body gap, which is defined as double the ARPES gap, is much smaller than an optical gap given by the light absorption spectrum (LAS). The apparent difference between these two gaps indicates the breakdown of a mean field description of this strongly correlated electron system. In this paper, we show, by using a quantum Monte Carlo method, that the ARPES and LAS of [Ni(chxn) 2 Br]Br 2 are consistently explained within the framework of the one-dimensional extended Hubbard model. It is suggested that the large difference between the one-body and optical gaps is caused by the dynamical Zeeman field induced by the quantum fluctuations.

scholarly journals Probing non-thermal density fluctuations in the one-dimensional Bose gas

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Jacopo De Nardis ◽  
Milosz Panfil ◽  
Andrea Gambassi ◽  
Leticia Cugliandolo ◽  
Robert Konik ◽  
...  
Keyword(s):  
Spatial Dimension ◽  
Bose Gas ◽  
Density Fluctuations ◽  
Dynamical Structure ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Fluctuation Dissipation ◽  
Quantum Integrable Models ◽  
The One

Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained for the Bose gas in one spatial dimension by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations.

The general Lie group and similarity solutions for the one-dimensional Vlasov–Maxwell equations

1985 ◽  
Vol 33 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Dana Roberts
Keyword(s):  
Lie Group ◽  
Maxwell Equations ◽  
Transformation Group ◽  
Spatial Dimension ◽  
Similarity Solutions ◽  
One Dimensional ◽  
Special Cases ◽  
General Similarity ◽  
The One ◽  
The Individual

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

scholarly journals Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian

2009 ◽  
Vol 80 (4) ◽  
Author(s):  
M. I. Makin ◽  
Jared H. Cole ◽  
Charles D. Hill ◽  
Andrew D. Greentree ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Time Evolution ◽  
One Dimensional ◽  
Hubbard Hamiltonian ◽  
The One

scholarly journals Flat-band dark polaritons in two-dimensional chiral-waveguide quantum electrodynamics

2021 ◽  
Vol 2015 (1) ◽  
pp. 012088
Author(s):  
Y. Marques ◽  
I. A. Shelykh ◽  
I. V. Iorsh
Keyword(s):  
Quantum Dots ◽  
Quantum Electrodynamics ◽  
Semiconductor Quantum Dots ◽  
Flat Band ◽  
Combined Effects ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
One Dimensional ◽  
Flat Bands ◽  
The One

Abstract We consider a two-dimensional extension of the one-dimensional waveguide quantum electrodynamics and investigate the nature of linear excitations in two-dimensional arrays of qubits (particularly, semiconductor quantum dots) coupled to networks of chiral waveguides. We show that the combined effects of chirality and long-range photon mediated qubit-qubit interactions lead to the emergence of the two-dimensional flat bands in the polaritonic spectrum, corresponding to slow strongly correlated light.

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