Hubbard Definition and 32 Threads

I'm reading "Lecture Notes on Electron Correlation and Magnetism" by P. Fazekas, and I came across a question regarding the form of the Heisenberg term in the t-J model. In Chapter 5.1.4, the t-J model is written where there is an additional density-density term in the exchange interaction...

Hello, I am interested in the following model: $$ H = \sum_{<i,j>} -t (c_i c_j^{\dagger} + \text{H.C.}) + U (n_i n_j) + \sum_{<<i,j>>} -t' (c_i c_j^{\dagger} + \text{H.C.}) + U' (n_i n_j) $$ where \( <i,j> \) indicates nearest neighbors, and \( <<i,j>> \) indicates next-nearest neighbors...

I’ve been working on solving gap equations related to superconductivity using Python, in the context of RMFT using the t-J model of the Hubbard Hamiltonian. My goal is to calculate and plot the variables (\Delta_x), (\Delta_y), (\xi_x), and (\xi_y) against the doping concentration (x). However...

In the youtube lecture “electron interaction and the Hubbard model” at the time 2:23:00, we have the following self-consistent equation with energy appearing at both sides: $$(\hat P \hat H_0 \hat P+\hat P \hat H_1 \hat Q (E-\hat Q \hat H_0 \hat Q)^{-1} \hat Q \hat H_1 \hat P) |\phi...

L. Ron Hubbard was a con man, abuser, liar, cheat, megalomaniac, pathetic excuse for a human being. Everyone, myself included, knows that. But that was the man. When it comes to his art, I'll bet at least 1% of his work can be called decent, to say the least. What do you guys say? Yay or nay?

PhysRevLett.106,236805 (2011) seems to state that Graphene has U=9.3eV and PRB 55-R11973 (1997) states that nanotube has U=u/N. However, it's not unusual for them to be hubbard U systems

Please see this page and give me an advice. https://physics.stackexchange.com/questions/499269/simultanious-eigenstate-of-hubbard-hamiltonian-and-spin-operator-in-two-site-mod Known fact 1. If two operators ##A## and ##B## commute, ##[A,B]=0##, they have simultaneous eigenstates. That means...

Above

I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Section 1.7: Derivatives in Several Variables as Linear Transformations ... I need some help in order to understand some...

Hi guys! I am starting to study Hubbard model with application in DFT and I have some doubts how to solve the Hubbard Hamiltonian. I have the DFT modeled to Hubbard, where the homogeneous Hamiltonian is $$ H = -t\sum_{\langle i,j \rangle}\sigma (\hat{c}_{i\sigma}^{\dagger}\hat{c}_{j\sigma} +...

I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Section 3.1: Manifolds ... I need some help in order to understand Example 3.1.3 ... ... Example 3.1.3 reads as follows:In...

I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Chapter 6: Forms and Vector Calculus ... I need some help in order to understand some notes by H&H following Figure 6.1.6 ...

Sir currently I am trying to solve a system which has 8 sites and each site can have 3 possible states(0 or 1 or 2).So the dimension of matrix is 6561*6561.The lapack works good till 3000*3000.But for larger system it fails.I have studied the dsdrv1.f example from arpack where they have solved...

I am trying to diagonalize hubbard model in real and K-space for spinless fermions. Hubbard model in real space is given as: H=-t\sum_{<i,j>}(c_i^\dagger c_j+h.c.)+U\sum (n_i n_j) I solved this Hamiltonian using MATLAB. It was quite simple. t and U are hopping and interaction potentials. c...

Hi, I read a chapter about the Heisenberg-model, and then something about the Hubbard-Model. The Heisenberg-model just shows, that neighbouring spins allign antiparallel if J<0. The Hubbard-Model says, that there is a hopping probability t and an Coulomb replsion, so that a material becomes...

Hi, I'm trying to calculate the partition function for a certain system and I arrived at an expression for the partition function $Z$, and have been stuck here for two weeks at the least. This is not a homework problem. If this is the wrong place to post a question like this, could you please...

I've taken the single and multivariate calculus classes at my school, (college class offered in my high school for accelerated students). I'm currently a junior, but in the summer of my senior year, I plan to read a book on proofs, brush up on math glossed over by the american education system...

I'm using the general Hubbard model (H = U \sum n_{i,\uparrow} n_{i,\downarrow} - t \sum (c^{\dagger}_{i,\sigma} c_{i+1,\sigma} + c^{\dagger}_{i+1,\sigma} c_{i,\sigma})) to solve for eigenstates of simple quantum dot configurations. For the case of a double dot with two electrons in singlet...

I am currently in 11th grade and will, by the end of the year, complete calculus I II and III, as well as linear algebra. The rigor of these programs at my school is, from my point of view, hardly satisfying, though I haven't had issues with it yet. (we use the stewart book, and anton for linear...

Hello everyone, How far can the book take me before I have to read another book on the subject? Thanks :)

Homework Statement I am trying to solve the model analitically just for 2 sites to have a comparison between computational results. The problem is my professor keeps saying that the result should be a singlet ground state and a triplet of excited states, but when I compute it explicitally I...

Introducing the Hubbard Stratonovich transformation my book uses an expression for completeness that I don't understand (the one indicated on the picture). Can anyone explain why this is indeed unity?

I do not know multivariable calculus. I have studied out of Apostol Vol.1. I do not want to learn the material from Apostol Vol. II. Therefore I want to know If it would be worthwhile to go through Hubbard and Hubbard's 'Vector Calculus, Linear Algebra, and Differential Forms' after going...

What is the difference between Hubbard and tJ model? Does anyone knows?

This is a question from Altland and Simons book "Condensed Matter Field Theory". In the second exercise on page 64, the book claims that if we define \hat P_s, \hat P_d to be the operators that project onto the singly and doubly occupied subspaces respectively, then at half-filling the...

Too familiar with Bose Hubbard model, but suddenly got stuck by a simple question: Why is the kinetic term (to be precise should be single body part) negative?

Author: John Hubbard, Barbara Hubbard Title: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach Amazon Link: https://www.amazon.com/dp/0971576653/?tag=pfamazon01-20

Homework Statement L.S., I'm breaking my head over this problem! To anyone who can help me out: thanks a lot! Consider a two-point grid (point a en point b) and two electrons occupying those points, (they can both occupy one point at the same time), both wit spin-up or spin-down. Now, they...

Does anyone know of a COMPLETE derivation of the Hubbard Model and then the Heisenberg model from it. What I mean by complete is pedagogical including all (or at least most) steps. Books like Assa Auerbach's and Altland and Simons are worthless for these kind of things (in fact IMHO those...

Hi, Suppose we have a 2 site Hubbard model, with the hopping Hamiltonian given by H_t and the Coulomb interaction Hamiltonian given by \hat{H}_U. In the strong coupling limit (U/t >> 1), we define a canonical transformation of \hat{H} = \hat{H}_U + \hat{H}_t, as H' =...

After considering the thread https://www.physicsforums.com/showthread.php?t=474384 I began to think about the bonding in graphene. As long as we can neglect electron electron interaction, the ground state can be obtained almost trivially in a tight binding approximation. On the other hand...

Hello everyone, I want to know the presently existing works on the topic of ground state properties of Hubbard model (spin-1/2-, or extended- ). I am nonexpert and have not googled for useful information. Please tell me some articles or monographs on this if you know. Thanks!