Questions tagged [lattice-model]
Lattice is a way of discretizing a quantum field theory for numerical simulations.
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SOLID STATE (FCC LATTICE STRUCTURE) [closed]
How many atoms per mm2 surface area are there in (110) plane for lead which has FCC structure. The radius of atom is 0.74nm.
I'm not able to proceed
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Can the standard Quantum-Mechanical Path Integral also be evaluated on a lattice?
I have been trying to learn about lattice path integrals. Unfortunately, majority of the literature on this topic is in regard to Lattice Quantum Field Theory and Lattice Quantum Chromodynamics. That ...
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Difference between Bravais lattice, point lattice and space lattice
I am good at crystallographic terminologies. Can somebody explain to me what is the difference between Bravais lattice, point lattice, and space lattice, if any?
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At temperature $T>0K$, are all normal vibrational modes present simultaneously in a one-dimensional solid?
I am studying Debye theory of Specific heat.
hyperphysics has this picture and there it says
"Considering a solid to be a periodic array of mass points, there are constraints on both the minimum ...
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How to calculate volume fraction from the fugacity?
1:1 electrolytes is in a lattice whose each volume is $a^{3}$. The number of positive and negative particle is $N_{\pm} = N/2$.
From the grand canonical partition function, we can calculate $N_{\pm} = ...
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Lattice symmetry operations in strongly spin-orbit coupled systems
I think this is a FAQ when we are studying the rotation operations of lattice spin systems, but I can't find much references.
Background
Considering a Hamiltonian defined on a triangular lattice:
\...
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Lattice $SU(2)$ Higgs model in unitary gauge
I'm currently reading the book Quantum Fields on a Lattice by I. Montvay and G.Münster, and in section 6.1 they describe lattice actions for various higgs models. And I got confused at the moment ...
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What's the matrix representation of Slave-Boson operators?
$\newcommand{\ket}[1]{\left|#1\right>}$
I think I'm not understanding the construction of the slave-particle operators.
In the Bose-Hubbard model, the slave-boson approach attempts to alter the ...
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Is there Difference Between 1D and 2D in Spin model?
The Motivation is That:In the Tensor Network method, they say 'time evolution MPS(Matrix Product State) work quite well in 1 Dimension'.
but as I think any 2D could be expressed by 1D
for example in ...
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Current Operators on Lattice
Peierls substitution method by taking the functional derivative of Hamiltonian can be used to determine the form of current-operator in continuum model (See Bruus-Flensberg) as well as lattice model. ...
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How do we construct an action on a superspace lattice?
I am interested in the formulation of supersymmetric theories on a discrete spacetime, such as a lattice. I know that there are some difficulties in preserving supersymmetry on a lattice, such as the ...
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About 3D Ising model
In the 2D Ising model, Onsager provided an exact solution for the lattice model in 1944. However, despite numerous efforts, exact solutions for higher-dimensional Ising models have yet to be derived.
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References to lattice supermanifolds
Do you have any references (textbooks and/or internet links) to lattice supermanifolds or, more generally, discrete superspaces?
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Question on the elementary cell of a rectangular/square lattice in magnetic firld?
In all references on the rectangular/square lattice in the presence of a magnetic field, they mention that you get a periodic structure of the model if and only if the flux per plaquette is a rational ...
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How to calculate a momentum space of a semi-finite lattice?
If we have a 2D square lattice of lattice constant a whose $x$ axis has only $N_x$ cells each with one atom and no with spin degeneracy, and periodic boundary conditions on $y$ with $N_y$ cells along ...
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Entanglement entropy in states with particle content
I am studying entanglement and its measurements in the context of a lattice model of the Dirac theory. The idea is that one has two bands, symmetric with respect to $E=0$, and the groundstate is ...
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Sampling a 2D Ising Model [closed]
I am fairly new to statistical mechanics and I am coming from a computing background. I am trying to calculate the mutual information of a lattice representing the 2D ferromagnetic Ising Model using ...
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Quantum Information Theory: How do I perform entanglement quantification calculations using the Quantum Heisenberg model?
I have been reading Quantum Computation and Quantum Information (10th edition) by Nielsen and Chuang and I am interested in calculating the level of entanglement (with entropy or some other measure I ...
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Exact ground state degeneracy for quantum spin system with non commuting terms and its quantum phase transition?
Let's say I have a 2D quantum spin model of N spin-1/2 particles, with two terms:
$$
H = -J \sum_N \prod_{i \in G} \sigma^x_i - h \sum_N \prod_{i \in G'} \sigma^z_i
$$
The first is a collection of ...
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Dirac delta in Fourier space for finite volume
In some class notes about cosmology I have found the following claim. The author starts by stating that the Dirac delta is given by:
$$\delta^{(D)}(\vec{x}+\vec{x}')=\int\dfrac{d^3q}{(2\pi)^3}e^{i(\...
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Sublattice symmetry and the Fermi level
I am a math student who is learning topological phases from this website.
Let's assume the fermi level is zero. For the graphene, the sublattice symmetry $\sigma_z H \sigma_z = -H$ makes the ...
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Are field theories where free energy density depends on 2nd-order derivative non-local?
It is accepted that infinite order of derivatives in field theory lead to non-local effects while finite number of them local.
reference within physics stack exchange
Let’s take a lattice with next-...
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Simulating Dirichlet Boundary Conditions for Lattice Boltzmann Method
So, I'm going through A.A. Mohammad's book "Lattice Boltzmann Method : Fundamentals and Engineering Applications with Computer Codes." And I'm currently coding the D2Q9 lattice with respect ...
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Dipole operator in a lattice model
If I have a lattice Hamiltonian, say for example the Hubbard model
$$H = \sum_{j,k, \sigma} t_{j,k} \hat{c}^\dagger_{j \sigma}\hat{c}_{k \sigma} + U\sum_{j} \hat{n}_{j \uparrow}\hat{n}_{j \downarrow},$...
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Which dimensions do self-dual even Lorentzian lattice exists?
I am reading page 499 of Peter West's Introduction to Strings and Branes where he stated 'Self-dual even Lorentzian lattices only exist in dimensions $8n+2$, $n=1,2,...$, the simplest such lattice is ...
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Relationship between mode and band
I'm learning solid state physics. I'm very confused about the terms "band" and "mode".
There are acoustic mode and optics mode. There is a gap at the Brillioun zone boundary. They ...
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Recover perturbation theory as appropriate limit of the lattice theory
I remember hearing at some point that pertubation QFT using Feynman diagrams can be thought of as certain limits of lattice QFT. Is there a precise statement of this fact? Or is it just a heuristic ...
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Non-numerical computation of ground state energy and quasiparticle dispersion in lattice models
Recently I have been quite confused in determining a phase transition for anyons in Toric Code model. Here the ground state does not have any particle, and loops (in real and dual lattice, which for $...
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What makes lattice QCD computationally tractable?
I don't know anything about lattice QCD. Therefore, at first glance it seems to me that lattice QCD should be computationally intractable for all practical purposes.
Let's assume that we only care ...
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Why we have $\sum_k= \frac{V}{(2\pi)^3}\int d^3k$ but $\sum_r=\int d^3r$? [closed]
Why we have $\sum_k= \frac{V}{(2\pi)^3}\int d^3k$ but $\sum_r=\int d^3r$? I do not understand why the latter has not the coefficient.
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Diagonalizing a Hamiltonian with translational and reflection symmetries in solid-state physics
I am working on a problem in introductory solid-state physics and have a question. I feel hesitant to ask my professor because I think it might be a simple question. In the problem, an electron can ...
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Are there primitive unit cells which cannot be associated with primitive vectors?
In the theory of Bravais lattices, it is immediate to associate with each set of primitive unit vectors a primitive unit cell (see e.g. here). It is (probably) not hard to show that this map is an ...
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Origin of 3 types of elementary plaquette excitations in Majorana plaquette model
I'm studying Majorana Fermion Surface Code for Universal Quantum Computation by
Sagar Vijay, Timothy H. Hsieh, and Liang Fu. There they consider the Majorana plaquette model on an hexagonal lattice.
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Transition from lattice fluctuations to continuum degrees of freedom
Trying to find the most common and descriptive scheme of continuum limit construction for lattice models I eventually found this lecture on Quantum Condensed Matter Field Theory quite useful. However, ...
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What is the motivation for the Self-Dual Canonical Anticommutation Relation (CAR) algebra?
What exactly is the motivation for the use of the Self-Dual Canonical Anticommutation Relation (CAR) algebra in the context of infinite lattice systems? Why not remain with the CAR algebra, as both ...
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Holley and FKG Lattice Conditions
There's an interesting exercise (page 13, Exercise 11) in Hugo Duminil-Copin's Lectures on the Ising and Potts models on the hypercubic lattice, which states that the following 2 statements are ...
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What is lattice regularization and how is it carried out? [duplicate]
I am new to QFT, and so far I have studied dimensional regularization and Pauli-Villars regularization. These seem to be the only two regularization techniques discussed in most introductory textbooks....
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How to determine the interplanar distance from the Miller Indeces $(h k l)$ of different lattices
I know that for cubic unit cells, there is a simple correspondence between the interplanar distance and the Miller Indeces:
$d=\frac{1}{\sqrt{h^2 + k^2 + l^2}}$
What happens when we have more complex ...
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What is the current status of placing chiral gauge theories in a lattice? Can we place the SM in a lattice?
Schwartz's book on Quantum Field Theory states in Section 25.5:
There are enormous practical difficulties with lattice simulations, and many open theoretical questions (such as how to simulate chiral ...
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Duality relation for the correlation length
In this answer to my previous question, Yvan Velenik mentioned the equality for correlation lengths of dual Ising models on a square lattice
$$
\xi(T) = \xi(T^*)/2.
$$
I have the following questions ...
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How to write a naive Dirac matrix for Lattice QCD?
I'm trying to write down the naive Dirac matrix (with fermion doubling) for a LQCD simulation with one quark, for now. I initialized the $SU(3)$ gauge field and the quark field. The quak field has 4 ...
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Gauging away phases of SSH Hamiltonian
I'm reading 'A short course on Topological Insulators' in which it talks about adding phases to the SSH model that can easily be gauged away
$$
H=
\begin{bmatrix}
0 & v & 0 & 0\\
v &0&...
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Topological classification of (classical, Abelian) vortices on a lattice
Consider the XY model on the square lattice. A field configuration $\theta$ is specified by an element of the Abelian group $\mathbb{R}/2\pi \simeq U(1)$ at each vertex of the lattice. The gradient of ...
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Why doesn't Peierls substitution capture the Lorentz force?
It's well known that the classical Hamiltonian governing the dynamics of a charged particle in a static magnetic field is
$$ S_{cl}[x,\dot{x}] = \int_0^t dt' \frac{1}{2}m\dot{\vec{x}}^2 + e\vec{A}(x)\...
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One-dimensional reciprocal lattice
I've seen that, a possible defining condition for the reciprocal lattice is:
$\vec R_s \cdot \vec G=2 \pi l$, where, $R_s= n_1 \vec a_1+n_2 \vec a_2+n_3 \vec a_3$ is the direct lattice, $\vec G$ is ...
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Ising model rescaling
Consider the 2D classical Ising model. It's understood that there is a critical temperature $T_c$, and that the correlation length $\xi(T)$ defined by:
$$\langle \sigma_i \sigma_j \rangle_\mathrm{...
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How is this term an angle?
This question is regarding the $\Theta_{\mu\nu}$ term given in equation (3.8) of the paper (https://arxiv.org/abs/2206.07725). The term ( I have typed it below )is defined right below in (3.9) and ...
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Gauge degrees of freedom in Schwinger model
Schwinger model is the (1+1)-D QED. The number of gauge degrees of freedom (DOF) after the gauge fixing of the Schwinger model depends on the boundary condition of the model. For example, one can ...
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Current Knowledge of Superlattices [closed]
What is our current understanding of superlattices (such as how they form, their behavior, their physical properties, etc.)? Second, do they fall under the same laws as typical lattices?
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Can phonons experience a photoelectric-like effect? [closed]
In a crystal lattice, could phonons experience some form of the photoelectric effect?