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Questions tagged [lattice-model]

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

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Help in plotting the band structure of a maple leaf lattice

I was trying to plot the band structure of a maple leaf lattice. The Hamiltonian is given by: $H = t_1 \sum_{ij} (c^\dagger_i c_j + c^\dagger_j c_i e^{\phi_{ij}}) + \sum_{ij} \sum^{4}_{n=2} t_n (c^\...
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Symmertry of $R$-tensor of Stark Effect in diamond structure

Currently, I am studying the effects of electric fields on color centers in diamonds. However, I have encountered a problem: when addressing the Stark effect caused by the electric field, I use the R ...
Annihilation's user avatar
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Restoring Poincaré symmetries in Hamiltonian lattice field theories

I can imagine how the continuum limit of a non-relativistic quantum field theory discretized on a spatial lattice restores the Galilean symmetries of the original theory. But how does this work for ...
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Ising model in a magnetic field (phase transition?)

I have some questions regarding the Ising model in the presence of a magnetic field which is non-uniform. Let us define the Ising Hamiltonian on a $d-$dimensional lattice, $$ H = -\frac{1}{2} \sum_{i,...
math-int's user avatar
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How can I construct a trivial product state in the continuum?

When working on the lattice it is easy to define a trivial product state. A state $|\psi\rangle$ is a trivial product state if it admits the following tensor decomposition, \begin{equation} |\psi\...
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Why is Wigner-Seitz cell considered primitive?

During the lecture I listened, as well as in the internet, in Wikipedia for example, unit cell was defined as the parallelepiped spanned by the translation vectors. Primitive cell was defined as the ...
Максим Неважно's user avatar
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Zou He boundary condition for Lattice Boltzmann

I am utilizing this paper "https://arxiv.org/pdf/0811.4593.pdf" to implement the Zou-He boundary condition, aiming to enforce a velocity of 1 at the inlet of the complex geometry. The ...
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Total momentum operator of the Klein-Gordon field (before limit to the continuum)

I'm following K. Huang's QFT: From Operators to Path Integrals book. In the second chapter, he introduces the Klein-Gordon equation (KGE), and its scalar field $\phi(x)$, which satisfies this equation....
SweetTomato's user avatar
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Non-adiabatic evolution and time-dependent adiabatic parameter

I am dealing with the dynamics of a two-bands lattice system. The idea is that you have a lattice model of free fermions, with some hopping amplitudes and on-site energies.The lattice have two fermion ...
TopoLynch's user avatar
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How to understand this Dirac delta function?

I am reading this paper about quantization of the electromagnetic field, and there is a point where the author imposes the fundamental commutation relation between the vector potential and its ...
Claudio Saspinski's user avatar
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The 2d Ising transfer matrix and the effect of anisotropy on more general transfer matrices

The 2d Ising model has a row-to-row transfer matrix that can be written suggestively as $$T = e^{\tau \sum_i \sigma^z_i \sigma^z_{i+1}} e^{ \lambda \tau \sum_i \sigma^x_i}$$ where $\tau$ and $\lambda$ ...
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Periodic Zone Scheme - Bloch Theorem in Lattices

I am quite confused about the different representations of the dispersion relation in a lattice. This image makes a lot of sense to me, since it only represents one dispersion curve and transforms it ...
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On discretization in QFT and second quantization

Some time ago i saw in a QFT lecture series by the IFT UNESP that in QFT we need to discretize space by dividing it into tiny boxes of an arbitrary Volume $ \Delta V $ and then define canonical ...
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Intuition for ground state degeneracy of Majorana checkerboard model

I'm now trying to learn about Fracton. In the very early paper studying Majorana checkerboard model, it is claimed that the ground state degeneracy ${D_0}$ on ${L \times L \times L}$ 3-torus is ${...
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Approximating the $U(1)$ Schwinger model with a $\mathbb{Z}_2$ symmetry

The Schwinger model or $(\text{QED})_2$ essentially is quantum electrodynamics defined in $1 + 1$ spacetime dimensions. In https://arxiv.org/abs/2305.02361 they use the Hamiltonian formulation to ...
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Breaking a classical ground state degeneracy by a quantum term and order-by-disorder

Let’s assume we have a Hamiltonian for spin-1/2 particles with two terms, a classical interaction term and a “quantum” (non-diagonal) term. For simplicity, let’s assume that the quantum term is a ...
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Why each normal mode is treated as a harmonic oscillator in Debye's calculation of specific heat?

So in Einstein's calculation of specific heat each oscillator is assumed to be vibrating with same frequency and its average energy is given by hv(n+1/2) where n is bose factor. Debye said that ...
Mr. Wayne's user avatar
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Symmetry of Crystalline Lattice

In the book Solid State Physics by Kittel, it is written in Bravais Lattice's definition that "the arrangement of atoms in the crystal looks the same when viewed from the point r as when viewed ...
Lusypher's user avatar
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Phase transition in Ising Model with local $\mathbb{Z}_2$ symmetry

I am studying the Ising model with a local $\mathbb{Z}_2$ gauge symmetry \begin{equation} \mathcal{H} = -\sum_{\text{plaquettes}} \sigma^z(\vec{x}, \vec{\mu})\sigma^z(\vec{x}+\vec{\mu}, \vec{\nu})\...
QFTheorist's user avatar
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Physical meaning of Laue's condition for diffraction from crystals

The Laue's condition for diffraction is that scattering vector is equal to reciprocal lattice vectors $\mathbf{G}$. But how can a 'particular vector' equal a set of vectors? The reciprocal lattice ...
Mr. Wayne's user avatar
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Particle number in lattice field theory

Is it even possible to calculate a particle number of some field in lattice field theory? After all, it's implemented in the formalism of imaginary time path integrals, here's no such concepts as ...
Peter's user avatar
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Does the following generalization of the Ashkin-Teller model make sense

Ashkin-Teller (AT) model has interesting properties. I learned this from some threads here on PhysSE, particularly the recent one. In short, the AT model can be described as two layers of Ising spins. ...
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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 ...
Bradley Martin's user avatar
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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?
Solidification's user avatar
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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 ...
Dinesh Katoch's user avatar
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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: \...
Seira Asakawa's user avatar
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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 ...
Peter's user avatar
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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 ...
Humberto Emiliano's user avatar
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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 ...
Cha's user avatar
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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. ...
Snpr_Physics's user avatar
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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 ...
Olandelie's user avatar
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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. ...
Satoshi Nawata's user avatar
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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 ...
PhysFan's user avatar
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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 ...
chen jiiong's user avatar
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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 ...
TopoLynch's user avatar
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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 ...
User1396's user avatar
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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 ...
FIREREED's user avatar
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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 ...
Kostas's user avatar
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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(\...
Wild Feather's user avatar
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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 ...
Justin Lien's user avatar
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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-...
Sudipta Nayak's user avatar
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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 ...
Areen's user avatar
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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},$...
Qwertuy's user avatar
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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 ...
Rescy_'s user avatar
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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 ...
Simplyorange's user avatar
7 votes
1 answer
213 views

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 ...
Brian Bi's user avatar
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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.
王庆轩's user avatar
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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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