# Questions tagged [model-hamiltonians]

Questions examining the various types of Hamiltonian models that are used in materials modeling.

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### Where is the extended Hückel method (EHM) still used today?

The extended Hückel method (EHM) proved to be very useful through time, but there are better and affordable models today. One interesting thing about the model is the independence of the Hamiltonian ...
217 views

### What are examples of materials that closely correspond to the Heisenberg model?

I use the antiferromagnetic Heisenberg model all the time: $H = J \sum \limits_{\langle i,j \rangle} \vec S_i \cdot \vec S_j$ What are some examples of materials that are well-described by this ...
218 views

### Where/when did the fields of Operations Research and Materials Modeling begin to cross-pollinate? [closed]

Operations Research is a field of mathematics in which optimal or near-optimal solutions are sought for complicated problems. In the modeling of materials, we often optimize Ising models, in which the ...
203 views

### Is there a list of all universality classes for phase transitions with examples of each?

I've often had this problem: I have a model that has a phase transition in it, but I don't know what universality class it falls into or what the universality class is called. Is there anywhere on ...
140 views

### What class of materials are closest to realizing the tunable coupling Hamiltonian?

From a physics point of view, there is an effective (approximation to second-order coupling Jaynes-Cummings) Hamiltonian of the form [1] H=\sum_j\omega_j(t)\sigma_j^z+\sum_{\langle i,...
624 views

### Ising model: How can I spot the critical point?

Consider a zero-field Ising model with $N$ spins and periodic boundary conditions, with the Hamiltonian given by: $$H = -K \sum _{(ij)} s_i s_j\tag{1}$$ in 1D and 2D, where $K = \frac{J}{k_BT}$, where ...
68 views

### Is there a list of models that do and do not have the QMC sign problem?

The sign problem is a huge limitation of QMC, but it's not easy to tell by looking at a Hamiltonian if it has the sign problem. Often there will be some clever transformation that allows you to avoid ...
144 views

### How to construct a Tight-Binding Hamiltonian from first-principles computations?

Effective Hamiltonian approaches such as the Tight-Binding method played a central role in the reconciliation between chemistry and in physics in the solid state. A classical and complete treatment of ...
115 views

### How to find the projected Hamiltonian for lowest flat-band in general?

In [1], starting with the bosonic Hamiltonian (Eqn. 1) for the dice lattice model with half flux density (with Ahronov-Bohm phases incorporated), H=-t\sum_{\langle j,\mu\rangle}(a^\...
172 views

### Autocorrelation function problem in Monte Carlo simulation of 2D Ising model

Currently, I did a Monte Carlo simulation with the local update and Wolff cluster updated in 2D classical Ising model. I use the autocorrelation function to compare 2 different algorithm in critical ...
528 views

### When do we abandon ab initio methods?

This question is related to (and was originally asked in) another post about "quantum protectorates" I made here. Ab initio methods are nice because they directly solve a sort of "...
282 views

### Is Heisenberg model or in its simplier form Ising model a good approximation to study magnetic systems?

Heisenberg model $$\hat{H}=-\sum_{\langle i j\rangle}J\hat{S}_i\hat{S}_j$$ And in its simplified version, the Ising model $$\hat{H}=-\sum_{\langle ij\rangle}J\hat{S}_i^z\hat{S}_j^z$$ are widely ...
186 views

### How to derive the effective Hamiltonian of two-dimensional TMDCs monolayers?

TMDs are transition metal dichalcogenides and have the chemical formula MX$_2$ where M is the transition metal and X is the chalcogen. An example of a TMD is MoSe$_2$. I would like to demonstrate that ...
122 views

### Ising models with many-body interactions

I find it surprisingly difficult to find researches/papers on systematic "many-body interaction" extensions of the Ising model. Can somebody tell me a good review/article etc on this matter ...
97 views

### What are the physical consequences of adding a constant to the diagonal of the effective Hamiltonian of monolayer materials?

Effective Hamiltonians modeling many-layered materials are often tuned using some sort of bias voltage. For instance, in a $4\times 4$ Hamiltonian matrix to describe biased bilayer graphene using some ...
296 views

### Proper handling of change of units in numerical calculations

Let's say I want to calculate the energy spectrum of Heisenberg model: $H = J \sum \limits_{\langle i,j \rangle} \vec S_i \cdot \vec S_j -g ~\mu_B \sum \limits_{i} \vec S_i \cdot \vec B$ but value of ...
83 views

### How can I calculate the J value in an antiferromagnetic material?

I am new to DFT, especially in doing DFT for magnetic materials. I recently came across this paper which indicated the calculation of the J value in the case of antiferromagentic materials as per the ...
66 views

### How to choose the values of J and spin parameters in a heterogeneous spin system?

In this work, graphene-based systems that are described by mixed spin-3/2 and spin-5/2 are studied using the ising-model. A diagram of the structure is shown bellow: The Hamiltonian used is: \begin{...
66 views

### Formulate the Model Quantum Spin Hamiltonian for low dimensional (1D or 2D) magnetic materials [closed]

Recently I have started studying the properties of low dimensional magnetic materials by solving the MODEL QUANTUM SPIN HAMILTONIAN. I am finding difficulties in formulating the model quantum spin ...
51 views

### For which materials is the Bethe lattice a good model to compute the density of states of the conduction band?

The Bethe lattice is exactly solvable in the limit where each lattice site has an infinite number of nearest-neighbors. In this limit it yields a semi-circular density of states in the conduction band....
48 views

### What's the most efficient way to obtain the ground state of spin models exactly?

(Note: an earlier version of this question had been asked on Phys.SE before) It is known that finding the ground state of classical spin glasses is NP-hard: it will take (at least) an exponential ...
89 views

### What measured quantity can be associated to the value of the J parameter in the Heisenberg/Ising hamiltonians?

This question is related to other one here in the MatterModelingSE: Is it possible to calculate/estimate the value of the J parameter to be used in the Heisenberg/Ising hamiltonians? Here J is the ...
55 views

### Example of a standard/archetypal/simple 4-band un-gapped condensed matter model with analytic results?

I am looking to study Berry phase-like phenomena in an un-gapped material model. However, I am having trouble finding a widely-used 4-band model with analytic expressions for wavefunctions and ...
127 views

### Is it possible to calculate/estimate the value of the J parameter to be used in the Heisenberg/Ising Hamiltonians?

Studying magnetic systems, two frequently used approximations are the Heisenberg and Ising models (a discussion about these approximations can be read here): \tag{Heisenberg} \hat{H}...
111 views

### How to calculate the potential in Hubbard-U correction and when to apply it?

I have seen that in certain cases Hubbard-U correction is relevant yet I have seen a number of papers that have not used it. So, I want to know if there is any theoretical basis for finding this ...
70 views

### Example of a standard/archetypal/simple 4-band gapped condensed matter model with analytic results?

I am looking to study Berry phase-like phenomena in a gapped 4-band material model. In particular, I want to numerically and analytically calculate the Abelian Berry curvature integral of each band ...
47 views

### How to interpret WannierTools Python code that generates tight-binding model in the wannier90_hr.dat format?

I am getting myself acquainted with Wannier Tools. Wannier Tools requires two inputs, a wt.in file, and a .dat file. This .dat file should have the structure explained in the manual here. This file ...
57 views

### Wavefunction magnitudes being degenerate everywhere on parameter space even though energy degeneracies occur at isolated points?

Cross-posted here: https://physics.stackexchange.com/questions/635887/wavefunction-magnitudes-being-degenerate-everywhere-on-parameter-space-even-thou Consider the usual simple 2-level gapless ...