Questions tagged [lattice-model]

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

Filter by
Sorted by
Tagged with
2
votes
1answer
62 views

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. ...
1
vote
1answer
23 views

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 ...
1
vote
1answer
36 views

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, ...
0
votes
1answer
39 views

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 ...
1
vote
0answers
39 views

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 $...
1
vote
1answer
61 views

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}...
2
votes
1answer
86 views

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 ...
2
votes
1answer
59 views

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 ...
0
votes
1answer
43 views

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 ...
0
votes
1answer
45 views

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{\...
0
votes
1answer
50 views

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 ...
0
votes
0answers
78 views

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 ...
6
votes
0answers
78 views

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 ...
1
vote
1answer
31 views

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 ...
6
votes
3answers
849 views

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 ...
0
votes
0answers
49 views

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} ...
3
votes
0answers
108 views

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 $...
5
votes
0answers
72 views

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 ...
3
votes
0answers
174 views

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 ...
0
votes
0answers
22 views

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 ...
0
votes
1answer
70 views

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},...
2
votes
0answers
54 views

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 (...
2
votes
1answer
71 views

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 ...
0
votes
0answers
10 views

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 ...
3
votes
0answers
36 views

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 ...
2
votes
1answer
60 views

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 ...
3
votes
0answers
77 views

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 ...
0
votes
1answer
63 views

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 ...
2
votes
0answers
31 views

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 ...
0
votes
0answers
14 views

On the number of independent Bravais lattices

Let's consider the $2D$ case for simplicity. The Bravais lattices are defined as follow, in terms of the length of the edges and the angle between them: $a\neq b$ and $\theta=90^{\circ}$ (simple and ...
5
votes
1answer
178 views

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} ...
0
votes
0answers
51 views

What symmetry breaks in exciton condensation?

Recently the possibility of exciton condensates have shown up in some lattice TQFT models we've been studying, and I've been trying to learn more about them. Suppose that we have a band insulator with ...
1
vote
0answers
23 views

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. ...
-1
votes
1answer
27 views

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 $...
1
vote
1answer
51 views

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(\...
18
votes
2answers
959 views

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)....
3
votes
1answer
175 views

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 ...
1
vote
0answers
52 views

Einstein-Hilbert action on lattice

I am wondering how the Einstein-Hilbert action is written on lattice in Euclidean spacetime, and if the metric will still be diagonal if it is possible to write Einstein-Hilbert action on lattice.
5
votes
0answers
219 views

1D transverse-field Ising model - what is the difference between its classical and quantum treatment?

The 1D transverse field Ising model: $$ H(\sigma)=-J\sum_{i\in Z} \sigma^x_i \sigma^x_{i+1} -h \sum_{i \in Z} \sigma^z_i$$ is usually solved in quantum way, but we can also solve it classically - ...
1
vote
0answers
52 views

What is the state space of fermions in lattice QFT, in position space, in the Schrödinger picture?

Let me motivate this question by analogy: In classical mechanics with $N$ particles in $d$ dimensions, trajectories are $\mathbf{r}: \mathbb{R} \to \mathbb{R}^{2d \cdot N}$, and the state at time $t$ ...
0
votes
1answer
90 views

What is the relationship between 'taste' and 'flavor' in particle physics?

This paper, among others, discusses 'taste symmetry.' What is it talking about, and how does it relate to flavor? Reference: Borsanyi, S., Fodor, Z., Guenther, J.N. et al. Leading hadronic ...
2
votes
1answer
73 views

A potential well with 3-fold reflection symmetry

When we are talking about Bloch's theorem and also the tight-binding approximation, we can use them to help finding eigenstates of a system. However, I am so confused how to apply it in this case (...
0
votes
1answer
86 views

Is spin-1 Ising model exactly solvable (one dimension and two dimension)?

I am working on spin-1 Ising model and I am new in this field. it seems that spin-1 Ising model in one dimension can be exactly solved by transfer matrix similar with spin 1/2 Ising model, am I right ...
0
votes
0answers
27 views

Open source software for lattice quantum theory with Wick rotation

I am trying to learn more about numerical calculations in QFT and in particular the reconstruction of real time quantum observables from numerical results on a Euclidean lattice. Is there any open ...
3
votes
0answers
38 views

Different ways to defining Fourier transform of a lattice model

I have a Kagome 2D lattice as shown in the figure below: There are three atoms in one unit-cell A, B, and C (shown in circle). An interaction Hamiltonian can be $$H = H_1+H_2+H_3\equiv -t\sum_{\...
2
votes
0answers
216 views

Dirac equation for the Kagome lattice

Background To model graphene we often use a nearest-neighbour tight-binding Hamiltonian $$H = - t \sum_{<ij>} c^{\dagger}_i c_j$$ embedded on a hexagonal lattice. By performing a Fourier ...
2
votes
1answer
101 views

Discrete Fourier transforms of Hubbard hoppings: a contradiction?

It's well known that condensed matter Hamiltonians of the form $$\mathcal{H} = t\sum_{\langle i j \rangle} a_i^\dagger a_j + a_j^\dagger a_i$$ where $a_i$ are bosonic creation/annihilation operators, ...
0
votes
1answer
40 views

Bibliography and basic resources to get started in the finite element method

This is my first question in this medium, which has helped me at many times. Perhaps, for that reason, it is not well posed or formulated. I would be interested in starting, on my own, in the finite ...
0
votes
0answers
21 views

Software for mean field calculations with fermions on a lattice

I know there is lots of software for practical calculations with DFT method, but I am more interested in toy models here. Is there any software for calculating mean-field phase transitions for ...
1
vote
0answers
36 views

Integrable Lattice Lieb Liniger Model

Is there a model of the 1D Bose gas (aka the Lieb Liniger Model) on a lattice that retains integrability? As a naive guess, I had thought that the Bose Hubbard model would fit this criterion, since ...

1
2 3 4 5
8