Questions tagged [model-hamiltonians]
Questions examining the various types of Hamiltonian models that are used in materials modeling.
27
questions
9
votes
1answer
292 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 ...
7
votes
1answer
44 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 ...
6
votes
0answers
40 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 ...
6
votes
0answers
64 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 ...
6
votes
1answer
53 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 ...
12
votes
1answer
520 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 "...
5
votes
0answers
67 views
How to use hp.x in Quantum ESPRESSO to calculate Hubbard parameter
I want to work with GGA +U on Quantum espresso to calculate the electronic properties of Ni Co co-doped ZnO system, but I can't figure out how to use the hp.x program for my system to calculate the ...
11
votes
1answer
92 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 ...
8
votes
0answers
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 ...
18
votes
3answers
598 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 ...
6
votes
1answer
104 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 ...
11
votes
2answers
178 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 ...
8
votes
0answers
50 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....
11
votes
1answer
112 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 ...
9
votes
0answers
65 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{...
6
votes
1answer
74 views
What measured quantity can be associated to the value of the J parameter in the Heisengerg/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 Heisengerg/Ising hamiltonians?
Here J is the ...
6
votes
1answer
119 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):
\begin{equation}
\tag{Heisenberg}
\hat{H}...
12
votes
2answers
151 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 ...
15
votes
0answers
106 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),
\begin{equation}
H=-t\sum_{\langle j,\mu\rangle}(a^\...
12
votes
1answer
265 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 ...
16
votes
2answers
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 ...
20
votes
1answer
139 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]
\begin{equation}
H=\sum_j\omega_j(t)\sigma_j^z+\sum_{\langle i,...
24
votes
3answers
203 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 ...
16
votes
1answer
128 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 ...
20
votes
2answers
186 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 ...
24
votes
0answers
208 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 ...
26
votes
3answers
286 views
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 ...
