Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [lattice-model]

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

-1
votes
0answers
14 views

Periodicity condition for electron gas [closed]

How does the wave function of a free electron gas satisfy the periodicity condition
3
votes
0answers
37 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
16 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
26 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
26 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 ...
1
vote
1answer
12 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 ...
0
votes
0answers
24 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_bTln(\frac{c}{(1-c)q}) $ , where c is the concentration of particles on the lattice, T is the temperature, and $k_b $ is the ...
0
votes
0answers
50 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
23 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 ...
0
votes
0answers
38 views

Does the polarized Kagome antiferromagnet contain Dirac or Weyl points?

I've been reading about frustrated quantum magnets lately and a prominent topic is the study of antiferromagnets on the Kagome lattice. A calculation of the spectrum for the sort of model I have in ...
0
votes
1answer
37 views

Two Dimensional Self-Reciprocal BravaisLattice

I've been reading Quantum States of Atoms Molecules and Solids by Morrison et al. for a condensed matter course. They make the claim that all 2D Bravais lattices are self-reciprocal, but I'm having ...
2
votes
1answer
69 views

Can we numerically find ground-state of a 1D tight binding Hamiltonain with odd sites at half filling?

We can numerically find ground state energy and wavefunction of a 1D Hamiltonian at half-filling ($L = \#$ of sites and $N = \# $ of particles) using exact diagonalization. i.e at $L = 10$ and $N = 5$,...
0
votes
0answers
23 views

Why is this Pilot-wave model on a discrete spacetime is stochastic? [duplicate]

In Gluza & Kosek (2015) (DOI 10.1007/s10701-016-0026-7; paper available at Springer (NB: PDF)) It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is ...
1
vote
0answers
54 views

How do irrational numbers give incommensurate potential (in lattice models)?

I am trying to understand Aubry-Andre model. It has the following form $$H = \sum_n c_n^\dagger c_{n+1}+H.C.+V\sum_n \cos{(2\pi\beta n)}c_n^\dagger c_n$$ This reference (at 3rd page) says that if $\...
1
vote
1answer
79 views

Einstein solid: one or three dimensional quantum harmonic oscillator?

The Einstein model for solids assumes all atoms vibrate with the same frequency $\omega$, each atom being modeled as a quantum harmonic oscillator. The thing is: solids are three-dimensional objects, ...
0
votes
0answers
22 views

Strain field and periodic boundary conditions

Let's say I have a lattice, and I impose periodic boundary conditions. I want to construct a tight-binding model on a strained lattice, and I can determine the change in the hopping parameter based on ...
1
vote
0answers
108 views

In Hamiltonian lattice QFT, does low energy imply low momentum?

In relativistic quantum field theory (QFT), the spectrum of the total energy and total momentum operators is supposed to be restricted to the forward light-cone (the relativistic spectrum condition), ...
-1
votes
1answer
59 views

What is the meaning of the notation $\langle a_1, \ldots, a_n \mid X_i(u) \mid a_1', \ldots, a_n' \rangle$? [closed]

I am from the math department and reading Belavin & Gebner's On the Algebraic Approach to Solvable Lattice Models. I am trying to understand the left-hand side of Equation (2.2) on page 4. What ...
0
votes
0answers
10 views

Formula for Boltzmann weight

I am reading the paper. I am trying to understand the formula (2.1): \begin{align} \lim_{u \to i \infty} g(u) \omega \left( \begin{matrix} a & b \\ c & d \end{matrix} \mid u \right) = C_{c,d} ...
0
votes
1answer
36 views

Wigner Seitz cell

While searching the difference between primitive cell and unit cell I have seen that "Primitive unit cells contain only one lattice point, which is made up from the lattice points at each of the ...
1
vote
1answer
62 views

Discretization of Hamiltonian with first derivative

In a particular 1D system, the Hamiltonian can be writen as $$H=\mathrm{i}\left(f(r)\frac{\partial}{\partial r}+\frac{1}{2}f'(r)\right)\; ,$$ wher $\mathrm{i}$ is the imaginary unit, and $f(r)$ is a ...
2
votes
0answers
34 views

Why can the spin operator be written as a product of fermions?

I was studying the Hubbard model, where we define the spin operator $\vec{S} = \frac{1}{2} c^\dagger \vec{\sigma} c$, where the creation and annihilation operators are both vectors of the form $c^\...
1
vote
1answer
65 views

A computation problem on reciprocal lattice

I am reading David Tong’s lecture notes on Application of Quantum Mechanics. My confusion is about the following paragraph: Consider a function $f(\vec{x}) $, suppose $f(\vec{x})=f(\vec{x}+\vec{r})$...
0
votes
1answer
152 views

Drawing reciprocal lattice structures

I am currently trying to understand why and how reciprocal lattice relates to the diffraction plane, so I did some research on Wiki about reciprocal lattice, but I seem to be stuck as I would like to ...
0
votes
0answers
66 views

How does one construct the $n$th Brillouin Zone in a rectangular lattice geometrically?

What are the general rules of constructing the Brillouin Zone in a rectangular lattice geometrically? While the construction of the 1st and 2nd Brillouin zone is rather simple, starting to construct ...
1
vote
0answers
73 views

How to find groundstate energy of a simple Hamiltonian at $N/L$-filling using Jordan-Wigner (JW) transformation?

$\underline{\textbf{Model:}}$ Let we have the $t-V$ model for spinless fermions on a 1D lattice, which is defined in second quantization operators as follows: $$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
0
votes
0answers
14 views

Collimated Beam through Palladium Powder to identify the lattice structure

I came across the following Problem: A collimated beam with a wavelength of $0.162 \ [nm]$ is incident upon a powdered sample of simple cubic metal palladium. Now, five angles are given, which ...
0
votes
1answer
28 views

Different ways to write t-V model Hamiltonian

The $t-V$ model is usually written as: $$H = -t\sum_{i}^{L}c_i^\dagger c_{i+1} + c_{i+1}^\dagger c_i + V\sum_i n_i n_{i+1}$$ where $c_i^\dagger(c_i)$ are creation (annahilation) operators and $n_i$ is ...
0
votes
0answers
87 views

What's wrong with lattice quantum gravity?

Assume one can write the metric field on a lattice, so on each lattice point one has a value of $g^{\mu\nu}$. Similar to the way lattice QCD is formulated. Then later taking the distance between ...
3
votes
0answers
62 views

Lattice model realization of $SU(2)$ WZW model at level $k$?

Is there any lattice model realization of the following model: $c=1$ boson at the self-dual radius, or the $SU(2)$ WZW model at $k=1$. This is a question inspired by: Orbifolds of the $c =1$ ...
5
votes
1answer
129 views

Temperature-dependence of quark potential in Abelian lattice gauge theory

I am working with Kapusta's "Finite-Temperature Field Theory" textbook, and am working through the first part of chapter 10. When building the correlator of the two quarks a distance $R$ apart in the ...
2
votes
0answers
85 views

Questions on how Wilson loops relate to field & charge conservation, and lattice QFT

The path-ordered exponential from which the Wilson loop is traced is, crudely, $$ \prod (I+ A_\alpha dx^\alpha) = \mathcal{P}\,\mathrm{exp}(i \oint A_\alpha dx^\alpha )$$ which returns a matrix $\...
3
votes
0answers
106 views

Why does Bell's field theory model need to be stochastic on a space-time lattice?

In "Beables for quantum field theory", John Bell has presented a realistic interpretation of any fermionic quantum field theory, along the pilot-wave ideas. This model is formulated on a spatial lattice ...
2
votes
1answer
121 views

Negative Miller indices and parallel planes

The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. https://en.m.wikipedia.org/wiki/Miller_index Does this mean, that parallel planes are generally ...
0
votes
0answers
54 views

Possible ground state wavefunctions of anti-ferromagnetic Heisenberg spin chains

What are the ground state wavefunctions of the anti-ferromagnetic (AFM) Heisenberg spin chains? Is that which of the following? $$| ↑↓↑↓ · · · ↑↓>$$ or $$| ↓↑↓↑ . . . ↓↑>$$ or $$| ↑↓↑↓ · · · ↑↓...
0
votes
0answers
8 views

Fractal discrete networks approximations and Poincaré invariance?

In the link below one may find interesting paper by Sabine Hossenfelder, about finite networks symmetry due to Poincaré group. According to this thesis locally finite networks cannot be Poincaré ...
3
votes
2answers
145 views

What is the meaning of propagator in the context of lattice theory?

Say in $1+1D$ free fermion theory, it is easy to calculate the propagator in the (effective) field theory to be $$\langle \psi^\dagger(z)\psi(z')\rangle = \frac{1}{2\pi}\frac{1}{z-z'}$$ (in the ...
3
votes
1answer
129 views

Perturbative vs Wilsonian renormalization in 2D

In 2D a scalar field is dimensionless so terms in the Lagrangian $\phi^n$ of arbitrary power are renormalizable (indeed we can even have two derivatives). This has two consequences that seem to be in ...
0
votes
1answer
38 views

One dimensional paramagnet

I have a lattice model consisting of $N$ spins $s_{j}$ which can take the values $s_{j}=\pm1$. The spins are considered to be non interacting. The probability for a spin spin to be 1 is p and the ...
2
votes
0answers
69 views

Non-vanishing matrix elements in QFT after discretization

In QFT, introducing the lattice size $L$ implies that the momentum of plane wave solutions is discretized as $$\vec{p}_\vec{n} = \dfrac{2\pi}{L}\vec{n}\quad,\qquad \vec{n}\in\mathbb{Z}^D$$ I would ...
1
vote
1answer
36 views

Constructing PEPS representation of an arbitrary quantum state

Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS ...
4
votes
0answers
94 views

Quantum phase transitions in a finite lattice

Sachdev begins his book on Quantum Phase Transitions by asserting that, for a system on a finite lattice, the ground state energy of a Hamiltonian H(g) (where g is some coupling) is a smooth, analytic ...
8
votes
0answers
109 views

Lattice QFT of the Jones Polynomial

Start with a gauge theory with Chern-Simons action $$ S[A] = \frac{k}{4 \pi} \text{Tr} \intop_{M} \left( A \wedge dA + \frac{2}{3} A \wedge A \wedge A \right) $$ and a Wilson loop observable in the ...
0
votes
0answers
26 views

What is an intuitive explanation of wave ordering vector $Q$? (Pierls Instability)

How does the wave ordering vector $Q$ order a CDW? I saw this vector while studying the following system. We have a system with $N$ sites and $N/2$ spinless fermions and system is in the fully ...
4
votes
2answers
299 views

Comparing momentum cutoff and lattice regularization in Quantum Field Theory

Usually, it is heuristic to say that we can understand a QFT with a momentum cutoff $|k|<\Lambda$ by imagining that the system is living on a lattice. I would like to ask: (1) Is there any ...
3
votes
1answer
148 views

What is the effect of including additional representations in the action of a lattice gauge theory?

I'm reading Introduction to Quantum Fields on a Lattice by Jan Smit. When introducing the lattice gauge-field action as a sum over plaquettes, Smit says that in general the action should include a sum ...
0
votes
0answers
42 views

How does the Dirac equation follow from the algebra of order and disorder operators in the Ising model?

In his book "Statistical Field Theory", Mussardo derives the Dirac equation for the Majorana fermions in the scaling limit of the Ising model. He does this by defining order operators (the Pauli ...
2
votes
0answers
87 views

Defining the renormalized coupling constant in a lattice phi fourth simulation

I'm currently studying a scalar quantum field theory with a $\lambda\phi^4$ interaction (commonly referred to as $\phi^4$ theory. To study this theory non perturbatively I've written a program in ...
8
votes
1answer
154 views

Determining bound state masses from a lattice $\phi^4$ simulation

I've recently written a program in python that simulates the $\phi$ to the fourth scalar quantum field theory in a 4 dimensional euclidean spacetime. The lagrangian for this theory is that of a free ...
0
votes
0answers
84 views

Is simulating quantum field theoretical equations in the continuous limit the same as simulating really quantum continuous processes?

At the end of this article: https://hal.archives-ouvertes.fr/hal-00542373/document it is said that: "For example, several works simulate quantum field theoretical equations in the continuous limit of ...