Questions tagged [lattice-model]

Lattice is a way of discretizing a quantum field theory for numerical simulations.

Filter by
Sorted by
Tagged with
0
votes
1answer
65 views

Velocity driven Poiseuille flow using the incompressible lattice Boltzmann method

My goal here is to develop a Poiseuille flow in a channel, using constant pressure and zero velocity as initial conditions. From what I have read, people seem to be mostly using pressure-driven, or ...
1
vote
0answers
30 views

What is the lattice temperature?

I am wondering how the lattice temperature is defined in this context. Is it the temperature on which the energy is big enough to split the crystal in it's components (atoms)?
0
votes
0answers
22 views

Find tools to better understand crystal structure

I am currently studying solid state physics. But I have trouble understanding the crystal structure (or lattice structure), such as the structure in this picture (just to give an example). When I look ...
-1
votes
1answer
29 views

Can someone tell what are primitive translation vectors for BCC lattice?

I referred internet and two very renowned books ( Puri-Babbar and SO PILLAI ). COULDN'T find any primitive translation vector explanation for BCC or FCC. Eventually when I moved on to Reciprocal ...
0
votes
0answers
31 views

What do the points in the reciprocal lattice stand for?

I'm wondering for what the points in the reciprocal lattice physically stand for, I know that they are the k-vectors, that are the fourier-transformed vectors of the lattice in the real space. Do ...
1
vote
0answers
52 views

Ising model operators

Ising model formulated as lattice theory with local degrees of freedom described by $s_i$ $i\in 1, \dots, N$ and energy: $$ E[\sigma_i] = -J\sum_{<ij>} s_i s_j $$ From $s_i$ I can construct a ...
3
votes
0answers
95 views

Phase diagram of ${\rm O}(3)$ lattice model and mean field theory

In David Tong: Lectures on Statistical Field Theory Problem Sheet 1 exist task: I fully understand this problem and I know solution: section 17.2. I am interested in application of mean field theory ...
1
vote
1answer
71 views

Symmetries in the Hubbard model

I would like to understand both in an intuive and in a mathematical way the meaning of the sentence "The Hubbard Hamiltonian has an SU(2) symmetry". What are the symmetry transformations that leave ...
1
vote
0answers
43 views

Partition function of 2D Ising model on a squared lattice in the canonical ensemble in the low temperature limit

I'm currently working through David Tong's script on statistical mechanics (http://www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf) and came across something that I don't quite understand (page 166). ...
1
vote
1answer
23 views

Initial conditions in incompressible lattice Boltzmann method

I have very recently come to LB methods, and, after some reading, have implemented a little 2D code of my own. It uses some of the most basic assumptions : D2Q9 lattice BGK collision operator Zou-He ...
2
votes
2answers
473 views

Spin-orbit coupling Hamiltonian in tight-binding models

Consider spin-orbit coupling (of strength $\lambda_1$) on lattice, with the below Hamiltonian $$H = i \lambda_1 \sum_{<ij>} ~\frac{E_{ij} \times R_{ij}}{|E_{ij} \times R_{ij}|} \cdot \sigma ~...
1
vote
0answers
85 views

Can anyone help me describe the physics of my problem mathematically? [closed]

I was unsure if I should post this here or on the Mathematics page, so I decided to do both. Here's the problem I want to describe: Suppose I have a sphere, discretely represented by a large set of ...
2
votes
0answers
55 views

$T$-duality symmetry of $SU(2)_1$ WZW model

For bosons at self-dual radius, the CFT has T-duality symmetry. My question is can we realize this symmetry on the lattice model? for example antiferromagnetic spin chain.
1
vote
0answers
55 views

Massive Thirring model as continuum limit of Heisenberg model

The massive Thirring model $S = \int d^2 x \left[ \bar{\psi} \gamma^\mu \partial_{\mu} \psi - m \bar{\psi} \psi - \frac{g}{2} \left( \bar{\psi} \gamma_\mu \psi \right) \left(\bar{\psi} \gamma^\mu \...
0
votes
1answer
25 views

How does the distance in reciprocal lattice relate to distance in real lattice?

Suppose a two-slap of silicon is the distance 'a' apart in real space. What is distance between them in reciprocal space.
0
votes
0answers
25 views

Equilibrium in lattice simulations

It will be very kind of you if i am informed if there is any flaw in my understanding, or if there is any advice for my idea. It is said that one has to keep updating until the lattice can produce a ...
0
votes
0answers
12 views

Is it possible to construct a real-space renormalization group for a system with limited self-similarity?

I'm trying to understanding multiscale dynamics in a system which can be loosely mapped to a lattice model embedded in real space, in which the types of entities at the lattice points, and their ...
1
vote
1answer
63 views

What is breathing Kagome lattice?

I know what kagome lattice is. While reading some article I came to know the term breathing kagome lattice. Looked up the web didn't found any definitions of it. My suspicion is that when hopping ...
0
votes
1answer
66 views

Form of the Lagrangian for 1D String Dynamics

I am currently reading part of Franz Gross' Relativistic Quantum Mechanics and Field Theory, and am getting stuck on a particular point in chapter 1 where he attempts to motivate field theory by ...
3
votes
2answers
193 views

How do super-renormalizable theories renormalize?

This question is about a conflict between two facts about scalar field theories in 2D. The same sort of question will apply to any scalar field theory with a polynomial potential, but let's specialize ...
0
votes
0answers
9 views

How can we differentiate different parallel planes with the same Miller indices?

How can we distinguish different parallel planes with the same Miller indices not by graph and just with the numbers?
1
vote
1answer
64 views

Magnetization of the Ising model for an asymptotic vanishing magnetic field

I am considering the following ferromagnetic Hamiltonian for the 2-d Ising Model, say with periodic boundary condition in the torus $\Lambda_n=\mathbb{T}^2_n := (\mathbb{Z}/ \mathbb{Z}_n)^2$: $$ H_n(\...
3
votes
1answer
103 views

Do all the classical critical lattice models have emergent conformal invariance?

I understand that any quantum lattice model at the critical point which can be described by a massless relativistic quantum field theory has emergent conformal invariance. My question is what about ...
0
votes
1answer
66 views

Are all lengths multiples of the Planck length? [duplicate]

If the Planck length is the smallest unit of length that has any physical meaning then is it true to think that all the lengths are multiple of the Planck length?
0
votes
1answer
30 views

Geometrical proof of number of lattice points in 3D lattice

It is well known that number of lattice points in three-dimensional (3D) objects of simple cubic lattice, body-centered cubic lattice, and face-centered cubic lattice are 1, 2, and 4, respectively (...
2
votes
1answer
103 views

Physical Hilbert space of dimension $N$ factorial?

In many-body physics, Hilbert spaces are usually equipped with a tensor structure (ie: $\mathcal{H}=\mathcal{V}^{\otimes N}$). If the dimension of local degrees of freedom is set to be $dim(\mathcal{...
1
vote
0answers
27 views

Low energy continuous model to lattice model(tight binding) in solid physics state

It is widely employed to link the low-energy continuous model to lattice tight-binding model using this strategy as shown in Section IIA Page.1063 of RMP 83, 1057 : Just replace $k_i$ by using $\frac{...
4
votes
0answers
91 views

The frame of truncated momentum basis on a 1D lattice

$\def\ket#1{\left|#1\right\rangle } \def\bra#1{\left\langle #1\right|}$ (This is part of a research problem) The Setup: Consider a single particle on a finite 1D lattice with the Hilbert space ...
0
votes
0answers
50 views

Is QCD computable?

Are arbitrarily good approximations of the time evolution of any QCD system, given initial and boundary conditions, Turing computable? Can lattice QCD simulations be used to do so in theory? How ...
0
votes
0answers
56 views

Finding eigenvalue and eigenvector of non-Hermitian matrix product operator

Suppose we have a matrix product operator (MPO) $X$ with a periodic boundary, which is not necessarily Hermitian. That is, $$X^{s_1\cdots s_n}_{s^{\prime}_1\cdots s^{\prime}_n}:=\mathrm{Tr}(G_1[s_1,...
1
vote
1answer
47 views

Getting the Bose-Hubbard Hamiltonian from cold atoms

In the famous paper by Dieter Jaksch, it is shown that the usual Hamiltonian for cold bosonic atoms interacting by s-wave scattering (Equation (1) in the paper): $$ \hat{H}=\int d^3 x\hat{\psi}^\...
1
vote
0answers
34 views

Is is cheating to use alpha strong (instead of V_QCD) to argue that there is asymptotic freedom of QCD?

For asymptotic freedom of QCD, people give the argument that alpha_strong decreases at high energy (thus there is freedom at low distance). But if we make the reasoning on the QCD potential, for ...
1
vote
2answers
136 views

Is the QCD potential really monotonic ? How does it prevent two quarks from meson to annihilate?

The QCD potential is made of two terms -(4/3) * alpha_s / r that describes the short distance and the term +k*r that describes the long distance Of course, alpha is a function of energy, so it is ...
0
votes
0answers
44 views

Quantum Monte Carlo Loop Algorithm for quantum spin: why is the freezing graph present in ferromagnetic Ising model?

I study the loop algorithm (Evertz et al). I cannot understand, why the freezing graph type where we have to flip all 4 spins together is not present for the quantum-XY model and the anti-/...
9
votes
2answers
401 views

Correlation length anisotropy in the 2D Ising model

In the Ising model, the two-spin correlation function is $$ C(\vec{r}) = \langle \sigma_{\vec{r}_0+\vec{r}}\sigma_{\vec{r}_0}\rangle - \langle \sigma_{\vec{r}_0+\vec{r}}\rangle \langle \sigma_{\vec{r}...
1
vote
1answer
65 views

Spectrum of the momentum operator for free Dirac fermions on a lattice

I am studying lattice field theory and would like to understand the momentum operator for free Dirac fermions on a square lattice. In this case one needs to discretize the momentum operator (which ...
1
vote
2answers
65 views

Emergence of rotational symmetry on 2D square lattice

On page 74 of David Tong's Statistical Field Theory lecture notes, it is said that $(\partial_1\phi)^2 + (\partial_2\phi)^2 $ respects both $D_8$ (that includes discrete four-dimensional rotation ...
1
vote
0answers
22 views

For what choice of the basis atoms origin the Structure Factor is real?

I have a Cuprite Structure: Now, given that I described this structure as a Simple Cubic lattice with a 6 atoms basis, I have to choose the origin for these basis atoms such that the structure ...
1
vote
0answers
28 views

Symmetry properties of Goldstone mode dispersions

I've recently worked on a lattice model relevant to condensed matter physics. The model features an ordered phase with a broken $U(1)$ symmetry, so I anticipated the presence of a Goldstone mode. One ...
0
votes
0answers
39 views

Question about notation of a Jimbo's paper

I am reading Jimbo's Introduction to Yang-Baxter Equations. And I am confused by the notation he used in the definition: Here he uses $u\in C$ without previously mentioning what is $C$. I guess ...
-1
votes
1answer
381 views

How many atoms are in the primitive unit cell for diamond?

The primitive unit cell for diamond is pictured (the parallelepiped inside the cube). How many atoms are in the unit cell? My first guess is 3.5 and i know this must be wrong as the number of atoms in ...
0
votes
0answers
32 views

What is the lattice vector description of diamonds structure for a conventional fcc unit cell?

I understand how diamond has a conventional fcc unit cell with 4 extra atoms in it's basis. I also know that we can construct a primitive lattice cell using the lattice vectors: $\pmatrix{\frac{1}{2} ...
3
votes
0answers
48 views

Lattice construction of 2D topological field theory and Frobenius algebras vs. associative algebras

I have a basic confusion about 2D topological field theories (TFTs). In the lattice construction of 2D TFTs introduced by Fukuma et al (https://arxiv.org/abs/hep-th/9212154) only associative algebras ...
1
vote
1answer
30 views

Am I double counting an interaction in this Heisenberg-like model with next nearest-neighbor interactions?

I'm attempting to model a 1D system that consists of 4 lattice sites. When only considering the nearest-neighbor interactions, the Hamiltonian is simply $$ H_1 = \sum\limits_{i=1}^4 E(i,i+1) $$ where ...
0
votes
2answers
52 views

High temperature phonon heat capacity and equipartition theorem

I have seen the derivation of the high temperature heat capatcity sing integration of the density of states. The heat capacity is $C=3Nk_B$ with $N$ the number of atoms in the lattice. According to my ...
0
votes
0answers
39 views

Using Brillouin zones to write Hamiltonian and find momenta values

This is a homework problem that I have spent a large amount of time on..I will try my best to simplify the questions down to conceptual ones, but I will also write more or less that whole question ...
3
votes
1answer
40 views

What is the physical significance of links between sub lattices in the staggered fermion formulation of lattice gauge theories?

I am currently learning about Lattice Gauge theories and have come across the Lattice formulation in terms of staggered fermions (see e.g. Susskind 1977, Kogut & Susskind 1975). As I understand ...
2
votes
0answers
71 views

How to calculate the chemical potential for a 2D lattice gas with excluded volume?

The chemical potential of a 2D lattice gas is given by $$\mu = k_\mathrm{B}T\ln\left(\frac{c}{(1-c)q}\right),\tag{1}$$ where $c$ is the concentration of particles on the lattice, $T$ is the ...
0
votes
0answers
57 views

“Data structure” for a fermion field

I am understanding the path integral formalism of fermion fields. Most textbooks told me that grassmannian integration is only algebaric notation. It shouldn't be understood in a Lebesgue Integral ...
1
vote
0answers
35 views

How to find propagator for domain wall fermions

I am working on domain wall fermions right now and I am trying to understand how Luescher finds the propagator for the domain wall fermions in this review https://arxiv.org/abs/hep-th/0102028 on pages ...

1
2 3 4 5 6