Questions tagged [lattice-model]

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

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Solving some equations from lattice and boltzmann paper

i have solved equation 1 in this way I am a student of mathematics I am solving some equations from the lattice Boltzmann paper, but I can't please help you solve them. I want help to solve equation ...
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Question on computation in the paper "Objective interpretations of quantum mechanics and the possibility of a deterministic limit" from A. Sudbery

At the moment I am reading the paper: "Objective interpretations of quantum mechanics and the possibility of a deterministic limit", from A. Sudbery, and I am struggling to understand a ...
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$R$ projection operator in entanglement entropy

I was reading a paper about entanglement entropy. The author introduced a real space cutoff operator $R$ which he claimed to project onto a real space subregion. Then he used $\bar P:=RPR$ as an ...
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The reason why the Nielsen-Nimiya Theorem doesn't have to hold true in the Floquet system?

According to the Nielsen-Ninomiya (NN) theorem, under appropriate assumptions, the number of right-handed and left-handed particles must be equal in a lattice system. On the other hand, in recent ...
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What is a basis actually is and how it differs from primitive unit cell?

I have some questions about primitive unit cell and basis. These are: Is the basis the smallest identical fragment of a crystal which repeats in a pattern throughout the crystal? Or can it be an ...
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Response function in a honeycomb lattice

My doubt is the following: If we calculate the response function of a honeycomb lattice in the three spatial directions, the xx components will be always equal to yy. I imagine that it is because of ...
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Spin correlation function in a Heisenberg model and its relationship to Green function in Hubbard model

Consider the Hubbard model on a lattice: $$\hat{H} = -t\sum_{\langle i,j \rangle, \sigma}\hat{c}^\dagger_{i\sigma}\hat{c}_{j\sigma}+U\sum_i \hat{n}_{i\uparrow}\hat{n}_{i\downarrow}.$$ Downfolding ...
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Bells jump process on the lattice, simple example

At the moment i am reading the paper of Vink, "Quantum mechanics in terms of discrete beables". (http://www.psiquadrat.de/downloads/vink93.pdf) Here, in section III, Vink uses Bells beable ...
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Bohms equation of motion on the lattice

Consider a simple model with one particle on a one-dimensional lattice $\varepsilon \mathbb{Z}$ with lattice distance $\varepsilon$. At every time $t$, the particle has a position $Q(t)\in \varepsilon\...
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Why do we need to make sense of QED in continuous spacetime anyway?

QED is an approximate description of reality. Even if it did give finite predictions in the continuum limit, those predictions would've been incorrect anyway! Newtonian gravity does give finite ...
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Can a diamond lattice be deformed to have a site-avoiding mirror symmetry?

I'm working on an argument that relies heavily on the presence of site-avoiding mirror symmetries, i.e. mirror symmetries that do not fix any lattice sites. It's possible to deform the lonsdaleite ...
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Is the continuum limit equivalent to the low-energy limit?

It is frequently stated that the continuum limit of a lattice model is equivalent to the low-energy limit, e.g. here, here and section IIB of this. I do not know how to show this for myself. Take for ...
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(In)finite lattice in quantum statistical mechanics: validity of phase classifications and TQFT [closed]

I would like to understand the motivation for studying quantum statistical mechanics, such as spin models, on an infinite lattice, or in other word, in the operator algebraic framework. I learned that ...
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Applications of real-space renormalizaton group (RG)

I'm looking for lattice models on which real-space RG can be applied fairly simply to get decent results. In particular, I'm looking for something like the classical 2D Ising model on a triangular ...
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What is the order of the transition for a 2D Ising model?

I have been running around the block trying to find answers for this question, and I keep running into caveats. So, I just want to write down the list of things I want to know: Given that the order ...
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What is the difference between lattice models and tight-binding simulations?

In condensed-matter physics, people use different methods to solve the many-particle Schrödinger equation. I was wondering about two of those methods, the lattice model and tight-binding simulation. ...
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Dispersion relation for a lattice: Why the optics branch disappear?

I have a linear chain of two atoms type connected by springs and a lattice's constant $a$. Let said that mass is $m_1=m_2=m$ and the spring's constant $C_1$ and $C_2$. I have found the dispersion ...
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Energy current in a quantum chain

I have seen in (e.g. this paper) the definition of the energy current in a chain with $H = \sum_{j=1}^L h_j$ where $H_j$ has support on the $k$ sites $j,j+1,j+2,...,j+(k-1)$ as $$J_j - J_{j+1} = i[H, ...
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How to determine the distance between any two sites of a finite lattice subjected to periodic boundary conditions?

I want to study the Ising model on a finite kagome lattice assuming periodic boundary conditions (PBC) and long range interactions. More specifically, all spin pairs contribute to the total energy, so ...
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Derivative of Function of Unitary matrices

I need some help in understanding derivative of function of matrices, Unitary matrices in my case. I am studying lattice-qcd, there i need to take derivative of Wilson gauge action, $S[U]$ w.r.t link $...
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Holomorphicity of Functions of unitary matrices

I am studying lattice QCD and there I encounter functions of unitary matrices. For ex. The action, $S = \sum$Tr( plaquettes), where each plaquette, $P$ is written as, $$ P = U_{\mu}(x)U_{\nu}(x+\mu){U}...
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Interpretation of "pressure" as the logarithm of the partition function

Consider the Ising model on a subset $\Lambda\subset\mathbb{Z}^d$, with partition function $Z_{\Lambda; \beta , h}$ where $\beta$ is the inverse temperature and $h$ the external magnetic field. The ...
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Dispersion of finite 2D lattice

Following problem: I have the coupling matrix for an $N$-by-$N$ finite lattice of coupled masses (only nearest-neighbour coupling, periodic until terminated). I would like to numerically calculate its ...
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Coulomb interaction in 2D crystal

My question is very simple. What is the correct way of modelling a Coulomb interaction on a 2D lattice? Usually for a system that is infinitely big $(N\to\infty)$ and not discrete $(a_0\to 0)$, the ...
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How to calculate lattice hamiltonian?

I was watching White's DMRG introduction video on youtube, where he was showing the 1D lattice model as an example. He said that it's hamiltonian is (ignoring the constant factors) $$H = -\frac{\...
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What are some good resources to learn about perturbative and non-perturbative approaches to QCD, for example Lattice QCD, at an introductory level?

I am writing at an introductory level about the anomalous magnetic moment of the muon and part of that is the subsequent Lattice QCD that potentially verifies the results from the experiments that ...
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Nearly Free Electron Approximation for 3D Lattice

I have been learning the Nearly-Free Electron approximation method and its application in one dimensional lattices. Since nearly all real-world lattices are three-dimensional, I am trying to apply ...
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Can we determine when the lowest-energy state cannot be annihilated by any local operator, just by inspection of the Hamiltonian?

Relativistic quantum field theory (QFT) has the property that the lowest-energy state cannot be annihilated by any operator that is localized in a finite region of space (references 1,2,3). In other ...
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Triagulations of 4D Euclidean Lattice

I am interested in Euclidean gravity models such as Regge's simplicial gravity model. These models use triangulations of $\mathbb{R}^4$ with periodic boundary conditions. While there are many papers ...
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Why can we choose spin-1/2 degrees of freedom to commute?

Edit 2: The previous title of this question was "Why are qubits bosonic?" Thanks to the answers that have been provided so far, I now realize I asked my question in a sloppy way. The ...
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Action of $\phi^4$ theory in lattice field theory

Euclidian action of $\phi^4$ thory is given by: \begin{equation} \int d^Dx L_E=\int d^Dx\left ( \frac{1}{2}(\partial_\mu \phi)^2 +\frac{m_0 ^2}{2}\phi^2+\frac{g_0}{4!} \phi^4\right), \end{equation} ...
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Integration over first Brillouin zone

I have the following lattice and reciprocal lattice and Brillouin zone: There is such integral $\frac{1}{V_{first~BZ}}\int_{first~BZ} f(k_1,k_2)dk_1dk_2$, where $k_1 = \vec{k} \cdot \hat{n}_1$ and $...
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Could higher-dimensional quantum field theories be obtained as continuum limits of lattice models?

Traditional lore, based mostly on lagrangians and perturbation theory, said that nontrivial quantum field theories exist only in $d$-dimensional spacetime with $d\leq 4$. Now the lore is changing: at ...
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Planck-scale curvature in covariant LQG and quantization of length: does LQG apply also to the Planck-regime?

In the covariant approach of loop quantum gravity (see http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf ), the theory is defined on a "lattice", similar to lattice QCD. In this case ...
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How does flux on a lattice model translate to the continuum

Consider a square lattice with bipartite hopping terms (e.g., nearest neighbor hopping) $t_{xy}$. Then a magnetic field can be modeled by complex $t_{xy}$ so that the flux enclosed by some closed path ...
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How to calculate spin texture in $k$-space?

I have a triangular lattice model. In $k$-space, it is written as: $$ H = \sum_k\sum_\sigma \Psi_{k\sigma}^+ h_k\Psi_{k\sigma} $$ where $\Psi_{k\sigma} = [a_{k\uparrow}, b_{k\uparrow}, c_{k\uparrow},...
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Spin glass observables in Monte Carlo simulations

I am currently simulating an Edwards-Anderson spin glass using standard Metropolis Monte Carlo techniques. The spins are placed on a 3D cubic lattice with periodic boundaries and take on Ising values (...
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Analog Is Digital (Discrete)?

As I started reading a bit about analog vs digital signals, I keep returning to this thought. This could be something pretty obvious to the pros out there, but is it safe to assume that underneath it ...
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How to find energy dispersion in weak potential model in 3D (FCC)?

I have a problem with finding the energy of an electron in an FCC lattice using the weak potential method. We did that for a one-dimensional lattice during class, and I know that there was a double ...
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Book for lattice field theory for somebody with basic understanding of Quantum Field Theory [duplicate]

I have finished a first course in Quantum Field theory and I'm looking to get into lattice field theory (mostly QCD on the lattice). What are some resources for somebody wanting to learn how things ...
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Proof that the self-energy is an inverse lifetime

My question concerns the self-energy of a diagonal propagator for a single-particle lattice problem. The context is Anderson Localisation, but really it's a problem of complex analysis. I would like ...
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Large-scale rotational invariance in lattice space

It is often claimed among physicists that rotational invariance can emerge at large scales in lattice space. Let's focus on quantum mechanics for now. I interpret this claim as follows (I am a ...
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Could someone help me understand the connection between these two wikipedia entries? (reciprocal lattice)

The Brillouin zone is a primitive cell (more specifically a Wigner-Seitz cell) of the reciprocal lattice, which plays an important role in solid state physics due to Bloch's theorem. A Wigner–Seitz ...
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Are there solvable lattice field theories? [closed]

In lattice QCD, correlations functions are calculated by Monte Carlo integration of the path integral. Are there other field theories whose discretized versions allow lattice correlators to be ...
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Physical meaning of quartic observable in abelian Higgs model

Consider the $\mathrm{U}(1)$ gauge-Higgs model defined by the lagrangian \begin{equation} \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+D^\mu\phi^\dagger D_\mu\phi-V(\phi^\dagger\phi), \end{equation} ...
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Lattice Gas Automata and Galilean Invariance

I have been studying Lattice Gas Automata methods (also this), and every time I read up on their drawbacks, I see that they are not Galilean invariant and that the simulations have statistical noise. ...
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Hilbert space of toric code on a lattice

Kitaev mentions that if one places a $k\times k$ square lattice on a torus, and place a qubit on each edge of the lattice then there are $n=2k^2$ total qubits. Why is this so? Shouldn't there only be $...
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How to write lattice $\phi^4$ hamiltonian in terms of Pauli matrices?

I want to decompose lattice~$\phi^4$ hamiltonian in terms of Pauli matrices. Particularly, how can I decompose $$ H_\text{Lattice}=a^d\sum_{{n}\in{Z}}\left[\frac{1}{2}\Pi_{n}^2+\frac{1}{2}\left(\...
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Are observables in QFT actually observable?

Consider some interacting QFT on a lattice (just to avoid infinitely large momentums). The size of the lattice is assumed to be much smaller than the size of the emergent particles (like in our world)....
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Continuum limit of tight-binding models

Suppose I had a simple $1D$ tight-binding Hamiltonian $$ H = -t \sum_i a^\dagger_n a_{n +1} + \text{h.c.}$$ with $N$ sites and lattice spacing $a$. This Hamiltonian can be diagonalised with a discrete ...
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