Questions tagged [model-hamiltonians]
Questions examining the various types of Hamiltonian models that are used in materials modeling.
40
questions
6
votes
1answer
77 views
How to formulate the second quantization of Dzyaloshinskii-Moriya interaction?
The Dzyaloshinskii-Moriya interaction (DMI) existing in the interface of the ferromagnetic insulator and the metal with strong spin-orbit coupling (SOC) is shown below.
Mathematically, it can be ...
4
votes
1answer
61 views
Hubbard model SU(2) symmetry: manifest invariance
Could someone explain, is it possible to make Hubbard Hamiltonian manifestly SU(2) invariant? I know about the interaction term, but how would kinetic (hopping effect) term have to look like?
Here I'm ...
17
votes
3answers
1k views
Why is uncertainty not a big problem in computational chemistry?
The molecular Hamiltonian (or, for simplicity, the Fock operator) contains coulomb potentials as well as momentum operators. To evaluate the coulomb potential, we need to know where the electrons are. ...
6
votes
1answer
77 views
Help with definitions in k-space twisted bilayer graphene model
I am trying to numerically do calculations using Eq. 8 of MacDonald's simple model for twisted Bilayer graphene. I only want to calculate the Berry phase. However, I don't think I have my definitions ...
6
votes
0answers
32 views
Example of 2D k-space models allowing interband transitions after a closed-loop trajectory?
I have been mainly exposed to 2D momentum-space condensed matter models in the context of Berry-related topology. I now want to study models where, if I take a closed loop in momentum space, I will ...
9
votes
0answers
54 views
What is special about valley-focused Hamiltonians that make them give quantized/rational (valley) Chern numbers?
I have been thinking about so-called valley Chern numbers $C_v$ and associated topological phenomena. To my knowledge, they are usually applicable when inter-valley scattering is suppressed, leaving ...
5
votes
1answer
55 views
Help with definitions of SOC and ferromagnetic exchange terms in MoS2 Hamiltonian
I am trying to write eq. 2 in this PDF into matrix form (reproduced below) for numerical purposes. There are some definitions that I am not too familiar with, and don't seem to be given in the paper.
$...
11
votes
1answer
172 views
How to use wavefunctions/density to determine which orbitals lead to edge states?
I have a large matrix for a 1D zigzag edge model of an otherwise $3\times 3$ tight-binding Hamiltonian (3 basis functions, each corresponding to an atomic orbital), involving the variable $k_x$. The ...
9
votes
1answer
213 views
Help with translating Hamiltonian into matrix
Eq. 19 in this paper gives the following Hamiltonian:
$\sigma_a, \tau_a, \eta_a$ are respectively the spin, sublattice pseudospin and valley pseudospin respectively.
Normally, I would have chosen a ...
10
votes
0answers
76 views
Wavefunction magnitudes being degenerate everywhere on parameter space even though energy degeneracies occur at isolated points?
Cross-posted here.
Consider the usual simple 2-level gapless graphene Hamiltonian in momentum-space where the energy dispersion is degenerate/gapless at a Dirac point:
\begin{equation}\tag{1}
{\small
...
9
votes
1answer
308 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 ...
8
votes
1answer
66 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 ...
10
votes
1answer
130 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 ...
8
votes
0answers
92 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
60 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 ...
9
votes
0answers
119 views
How to interpret WannierTools Python code that generates tight-binding model in the wannier90_hr.dat format? [closed]
I am getting myself acquainted with Wannier Tools. Wannier Tools requires two inputs, a wt.in file, and a .dat file. This ...
12
votes
1answer
599 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
359 views
How to use hp.x in Quantum ESPRESSO to calculate Hubbard parameter [closed]
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 ...
14
votes
1answer
120 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 ...
18
votes
3answers
793 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
164 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
262 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
55 views
For which materials is the Bethe lattice a good model to compute the density of states of the conduction band? [closed]
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....
9
votes
2answers
92 views
What packages exist for building quantum Monte Carlo simulations of spin or Hubbard Hamiltonians?
What packages exist that can help someone, especially a new masters/PhD student get started with QMC on spin or Hubbard systems?
As an example, for writing a stochastic series expansion QMC program ...
12
votes
1answer
179 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 ...
11
votes
0answers
102 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{...
7
votes
1answer
102 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 ...
6
votes
1answer
142 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
278 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 ...
17
votes
1answer
172 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^\...
13
votes
1answer
353 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
80 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
148 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
259 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
223 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 ...
21
votes
2answers
278 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 ...
28
votes
0answers
306 views
Where/when did the fields of Operations Research and Spin Physics or Molecular Dynamics begin to cross-pollinate?
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
379 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 ...
