Momentum Distribution Critical Exponents for 1D Hubbard model in a Magnetic Field

2015 ◽  
Vol 11 (3) ◽  
pp. 3091-3098
Author(s):  
Nelson Nenuwe ◽  
John O. A. Idiodi
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Distribution Function ◽  
Hubbard Model ◽  
Momentum Distribution ◽  
Critical Exponents ◽  
Smooth Curve ◽  
One Dimensional ◽  
Conformal Field ◽  
Momentum Distribution Function

Critical exponents at  and   for the momentum distribution function are studied for one-dimensional Hubbard model in the presence of magnetic field, using conformal field theory (CFT) approach. Exponents at  and  are reproduced. Results at  is in contrast to earlier numerical prediction of 1, while at , the exponent is 49/8. The singularities at  and  appears to be weak and gradually degenerating into a smooth curve.

scholarly journals Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Oleksandr Gamayun ◽  
Oleg Lychkovskiy ◽  
Mikhail Zvonarev
Keyword(s):  
Distribution Function ◽  
Momentum Distribution ◽  
Fredholm Determinant ◽  
Solvable Model ◽  
Fourth Power ◽  
Large Momentum ◽  
Zero Temperature ◽  
One Dimensional ◽  
Polaron State ◽  
Momentum Distribution Function

We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas \deltaδ-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons.

scholarly journals CRITICAL EXPONENTS IN THE ONE-DIMENSIONAL HUBBARD MODEL

1994 ◽  
Vol 08 (04) ◽  
pp. 403-415 ◽  
Author(s):  
Holger Frahm ◽  
V. E. Korepin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behaviour ◽  
Hubbard Model ◽  
Critical Exponents ◽  
Correlation Functions ◽  
Exact Results ◽  
Quantum Field ◽  
One Dimensional ◽  
The One

Exact Bethe Ansatz results on the spectrum of large but finite Hubbard chains in conjunction with methods from conformal quantum field theory can be used to obtain exact results for the asymptotic behaviour of correlation functions. We review this method and discuss some interesting consequences of the results.

Negative elektrische Leitfähigkeiten

1960 ◽  
Vol 15 (5-6) ◽  
pp. 484-489 ◽  
Author(s):  
Jürgen Schneider
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Transport Equation ◽  
Momentum Distribution ◽  
Collision Frequency ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Free Carriers ◽  
Momentum Distribution Function ◽  
Hf Conductivity

The complex electric HF-conductivity σ of a plasma in a magnetic field has been calculated on the basis of the BOLTZMANN transport equation. Negative values of the real part of σ can occur, if the system is in a state of overpopulation, i. e. if ∂f0/dp > 0. where f0 is the momentum distribution function of the free carriers. Furthermore, the collision frequency or the mass of the carriers must be dependent on the momentum p.

The probe particle scattering cross-section off the many-fermion systems in the impulse approximation

2021 ◽  
Author(s):  
Yahya Younesizadeh ◽  
Fayzollah Younesizadeh
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Spectral Function ◽  
Cross Section ◽  
Response Function ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
System Response ◽  
Probe Particle ◽  
Momentum Distribution Function

In this work, we study the differential scattering cross-section (DSCS) in the first-order Born approximation. It is not difficult to show that the DSCS can be simplified in terms of the system response function. Also, the system response function has this property to be written in terms of the spectral function and the momentum distribution function in the impulse approximation (IA) scheme. Therefore, the DSCS in the IA scheme can be formulated in terms of the spectral function and the momentum distribution function. On the other hand, the DSCS for an electron off the [Formula: see text] and [Formula: see text] nuclei is calculated in the harmonic oscillator shell model. The obtained results are compared with the experimental data, too. The most important result derived from this study is that the calculated DSCS in terms of the spectral function has a high agreement with the experimental data at the low-energy transfer, while the obtained DSCS in terms of the momentum distribution function does not. Therefore, we conclude that the response of a many-fermion system to a probe particle in IA must be written in terms of the spectral function for getting accurate theoretical results in the field of collision. This is another important result of our study.

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