For my own understanding, I am trying to computationally solve a simple spinless fermionic Hamiltonian in Quantum Canonical Ensemble formalism . The Hamiltonian is written in the second quantization as
$$H = \sum_{i=1}^L c_{i+1}^\dagger c_i + h.c.$$
In the canonical formalism, the density...
So one can numerically study (I am interested in exact diagonalization) any 1D lattice model with ##L## sites and ##N## number of particles. At half filling, ##L/N = 2##. My question to a professor was that can we study a system of size ##L = 31## at half filling? He replied yes, there is a way...
I want to learn the density matrix renormalization group (DMRG) method in traditional formalism (not MPS). While there are many good introductory level articles available for bosonic (and spin) systems, I have not encountered any introductory level article which deals with fermionic systems i.e...
I want to exactly diagonalize the following Hamiltonian for ##10## number of sites and ##5## number of spinless fermions
$$H = -t\sum_i^{L-1} \big[c_i^\dagger c_{i+1} - c_i c_{i+1}^\dagger\big] + V\sum_i^{L-1} n_i n_{i+1}$$
here ##L## is total number of sites, creation (##c^\dagger##) and...
Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian:
$$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$
where ##c^\dagger (c)## are creation...
I am doing DMRG (in traditional formalism, not MPS) for Hubbard model
H = -t ∑i ∑σci,σ ci+1,σ + U∑ini,σni,σ-
In every iteration we add two sites to the system, but how do we set that how many particles are allowed in the system?
As shown in the figure, the aircraft includes a geomagnetic field convergence layer, which is a superconductor material. The geomagnetic field convergence layer repels the direction of changing the geomagnetic field, so that the geomagnetic field passes between the upper and lower converging...
Hi, for those who don't know, Landau (Lev Davidovitch Landau) had a famous exam called "The theoretical minimum". That exam had to be passed by any future grad-student of his. That test was extremely extensive and difficult, and the student was supposed to be knowledgeable about many fields of...
Hi, I'm an undergrad materials engineering student. I am thinking of studying all the way to a PhD as I'm interested on working in research. Right now I work with Semiconductors and I like the field a lot. However, considering what I'm studying, I want to know if it's a good Idea to look for a...
Hi all, I am having trouble understanding the some ideas presented in some notes I've been reading, help is greatly appreciated!
I've uploaded screenshots of the material I'm referring to below, the last two images are what I'm mainly referencing, and the first few are to provide context...
Greetings!
It is easy to understand that for a free electron, we can easily define the energy state density, and by doing the integration of the State density* Fermi-Dirac distribution we will be able to figure out the chemical potential at zero kelvin, which is the Fermi-Energy. Hence, we can...
Hi all,
It's a few short months before grad school applications are due, and I find myself in a bit of a dilemma. Prior to my junior year, I knew what I wanted to do is physics research for my career, and I'm particularly interested in biological and condensed matter physics. My skills are more...
Hi all,
I've always regarded the coupling Hamiltonian for a bosonic cavity mode coupled to a two-level fermionic gain medium chromophore to be of the form,
$$H_{coupling}=\hbar g(\sigma_{10}+\sigma_{01})(b+b^{\dagger})$$,
where ##b## and ##b^{\dagger}## and annihilation and creation operators...
I'm studying plasmons from "Haken-Quantum Field Theory of Solids", and i need some help in the calculation of the equation of motion of eletrons' density
\begin{equation}
\hat{\rho}_{\overrightarrow{q}} = \frac{1}{\sqrt{V}} \sum_{\overrightarrow{k}}...
hello dear physicists
I will work in my thesis on 1D materials using DFT as a numerical method to find the properietes of these 1D materials
I would be very happy if someone can help me with references (books, links, articles, vedios .....) that could help me to advance in my work
Thank you
Hey,
I read about charge carriers in semiconductors in a magnetic field.
They write that for several revolutions ##\omega_c \tau >>1## holds.
But I think for one revolution it is ##\omega_c \tau = 2 \pi##.
(##\tau## is the scattering time)
Why they do not write ##\omega_c \tau >> 2 \pi##...
Hello!
The time reversal operator, ##\hat{\Theta}## transforms a Bloch state as follows:
##\hat{\Theta} \psi_{nk}=\psi^*_{nk}##.
How does one proceed to prove the condition that ##\psi_{nk}## and ##\psi^*_{nk}## must satisfy in order for our system to be time reversal invariant?
Thanks in advance!
Hello!
I want to know how does a parity transformation affect Bloch states! I always knew that parity takes the position vector to minus itself (in odd number of dimensions), but I have read that it also takes the Bloch wave vector to minus itself but I have not found a satisfactory proof of...
Hi all,
I am trying to learn more about this field. Whether you work or have worked in this area or not, I would like to know where Soft Matter is going in terms of theory and applications.
Thanks,
A.D.
*I apologize in advance if there are already many threads specifically addressing this...
Homework Statement
A triangular lattice of lattice spacing ##a=2 ## angstroms is irradiated with x-rays at time zero of wavelength 20 angstroms at an incident angle of ##\alpha =135##.
1) What is the maximum wavelength of the incident x-rays?
2) What is the scattering angle ##\Omega## for...
I did research on theoretical formulations in general relativity during my MSc studies. I look forward to pursuing PhD and have searched many universities and some research institutes for suitable research themes, but haven't found many research groups undertaking research consistent with my...
Homework Statement
Consider the crystal in the attached image (https://ibb.co/ftMrBH) (a triangular lattice of white atoms with a triangular basis of grey atoms attached to them at angles of 0, 60 and 120. From a previous problem the fractional coordinates of the atoms in the basis are (0,0)...
The Hamiltonian of the Qi, Wu, Zhang model is given by(in momentum space):
## H(\vec{k})=(sink_x) \sigma_{x}+(sink_y) \sigma_{y}+(m+cosk_x+cosk_y)\sigma_{z} ## .
What is the physical meaning of each component of this Hamiltonian?
Note: for the real space Hamiltonian(where maybe the analysis of...
Hi everyone; I have a question, and I hope you could answer it. Well, I have a bachelor degree in physics/computer science and I plan to go to a graduate physics program; however, I don’t know which subfield is good for me. I was looking for computational astrophysics, computational condensed...
What is the value of optical effective electron mass for tin metal (white tin)? What is the value of mean free path for electron of tin metal? At least give me some websites or papers where I can find it?
Hi,
does anybody know of any good sources to learn about the Integer Quantum Hall effect from the perspective of theoretical physics?
Any suggestion will be appreciated, thanks.
Hello!
What are some good sources(preferably textbooks) to learn about Weyl semimetals?
I also want some sources to learn about topological insulators and anything containing the Integer Quantum Hall effect would be great.
As an aside, if you have any good book on theoretical condensed matter...
Greetings all,
I am an undergrad working on my first first-author paper in theoretical / computational condensed matter physics (near the computational materials science end of the spectrum) and I am looking to getting it published. My advisor has published in many journals, from mid to high...