1
vote
1answer
69 views

A puzzle of thermalization in simulating the 3D XY-model

I am learning the classical Monte Carlo simulation. When I simulate the 3D XY-model $$ \beta H = -\beta J \sum_{<i,j>} cos(\theta_i-\theta_j) $$ where $\beta$ is the inverse of the temperature ...
0
votes
0answers
46 views

Monte carlo simulation for continuous spin model (e.g. XY or Heisenberg model)

Unlike the Ising model, the XY model and the Heisenberg model have a continuous spectrum. So one need discretize them for a numerical simulation. But how to make sure the discretization procedure ...
1
vote
1answer
66 views

Ground state Phase Diagram of Bose-Hubbard Model

The Hamiltonian of Bose-Hubbard model reads as $$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1)-\mu\sum\limits_in_i~~~~~~~~~(1)$$ For this we plot phase ...
5
votes
1answer
236 views

Numerical analytic continuation for Green's function

Recently, I happened to hear about the possibility of doing analytic continuation numerically. That sounds attractive for the ubiquitous $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ procedure, ...
3
votes
0answers
485 views

Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
3
votes
1answer
170 views

confusion in discrete transform to solve kronig penney matrix equation in fourier space

I have a periodic potential $$V(x) =\sum_{K}e^{iKx}V_{K} =\sum_{n}e^{\iota2\pi nx/a}V_{n} $$ where $K =\frac{2\pi n}a$ is the reciprocal lattice vector and $a$ is the lattice constant and $n =\pm ...
1
vote
0answers
182 views

How to solve Boltzmann equation using monte carlo methods? [closed]

I'm trying to solve for electron and hole distribution function using Boltzmann equation with various scattering mechanisms. Since I land up with an integro-differential equation, analytical soln. is ...
3
votes
1answer
204 views

What states are satisfying an entropic area law and why do they satisfy it? More specificly why do matrix product states satisfy it?

I am currently reading some papers concerning the question why the density matrix renormalization group (DMRG) method is working well for simulating one dimensional systems and bad for higher ...
4
votes
2answers
247 views

Difference between Monte Carlo and Quantum Monte Carlo methods?

What are the differences between Classical Monte Carlo methods and Quantum Monte Carlo methods in condensed matter physics? If one want to study strongly correlated systems with Quantum Monte Carlo ...
1
vote
2answers
263 views

Where does Computer Science background students fit in Theoretical Physics [closed]

I am basically an Electronics student - background in computer science (that's where I want to work). I applied for an internship in USA in a research institute where the group is focused in ...
3
votes
2answers
555 views

Can I use imaginary time propagation for many-body problems?

There are various ways to numerically find the ground state energy and wavefunction of a many-body Hamiltonian. You can diagonalize the Hamiltonian and pick out the lowest eigenstate, or you use ...
5
votes
2answers
328 views

In condensed matter simulations, how is particle number density computed in practice?

I have been reading a recent paper. In it, the authors performed molecular dynamics (MD) simulations of parallel-plate supercapacitors, in which liquid resides between the parallel-plate electrodes. ...
6
votes
4answers
3k views

Why is the canonical ($NVT$) ensemble often used for (classical) molecular dynamics (MD) simulations?

Molecular dynamics (MD) simulation is a common approach to the (classical) many-body problem. It relies on integration of Newton's equations of motion to simulate the trajectories of many (e.g., ...
10
votes
1answer
126 views

Consideration of static atomic displacements in electronic structure calculations

I am hoping to discuss some details of electronic structure calculations. I am not an expert on this topic, so please forgive any abuse of terminology. It is my understanding that first principles ...
3
votes
1answer
122 views

Looking for a good introductory-level review of pseudopotential methods

I'm looking for a good introductory-level review of pseudopotential methods. In particular, I'd like to understand how the self-consistent pseudopotential methods work.