Lattice is a way of discretizing a quantum field theory for numerical simulations.
Questions tagged [lattice-model]
474 questions
41
votes
3 answers
Why is high temperature superconductivity so hard to solve?
The phenomenon of high temperature superconductivity has been known for decades, particularly layered cuprate superconductors. We know the precise lattice structure of the materials. We know the band theory of electrons and how electronic orbitals…
quack
- 411
34
votes
3 answers
Continuum theory from lattice theory
I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can obtain the Ising chiral CFT from a lattice…
Pieter Naaijkens
- 1,088
26
votes
3 answers
What is the fundamental reason of the fermion doubling?
Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds themselves with an additional amount (precisely…
Marek
- 23,981
22
votes
6 answers
Mean field theory Vs Gaussian Approximation?
I am getting confused about the distinction between Mean-field theory (MFT) and the Gaussian approximation (GA). I have being told on a number of occasions (in the context of the Ising model) that the Gaussian approximation is at the same level as…
21
votes
2 answers
Hilbert Space of (quantum) Gauge theory
Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something more rich/subtle than just saying the Hilbert Space…
user32229
21
votes
1 answer
Continuum Field Theory for the Ising Model
My problem is to take the $d$-dimensional Ising Hamiltonian,
$$H = -\sum_{i,j}\sigma_i J_{i,j} \sigma_j - \sum_{i} \tilde{h}_i \sigma_i$$
where $J_{ij}$ is a matrix describing the couplings between sites $i$ and $j$. Applying a Hubbard-Stratonovich…
Kai
- 3,930
- 1
- 15
- 29
21
votes
5 answers
Home-made lattice calculation?
The topic of Lattice QCD or Lattice gauge theory or even Lattice field theory is quite old now. And the main reason for the interest in the topic is the ability to calculate nonperturbative stuff on a computer.
It seems that to do research with…
Kostya
- 20,288
19
votes
2 answers
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). Lets assume there are scientists living in such…
Pavlo. B.
- 2,605
19
votes
1 answer
What are Griffiths effects in the context of condensed matter physics?
From a cursory examination of the literature I've gathered the following: it seems that ordered systems have a "clean" critical point, at which the system makes a sharp phase transition, and that disordered systems have a "dirty" critical point…
Arun Nanduri
- 876
18
votes
1 answer
How to determine if an emergent gauge theory is deconfined or not?
2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are deconfined. However in general, $\mathbb{Z}_N$ gauge…
Everett You
- 12,228
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17
votes
2 answers
Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
The 1D transverse field Ising model,
\begin{equation}
H=-J\sum_{i}\sigma_i^z\sigma_{i+1}^z-h\sum_{i}\sigma^x_i,
\end{equation}
can be solved via the Jordan-Wigner (JW) transformation (for further reference about the explicit form of the JW…
VanillaSpinIce
- 1,458
17
votes
2 answers
Jordan-Wigner transformation v.s. Bosonization
Jordan-Wigner transformation is a powerful tool, mapping between models with spin-1/2 degrees of freedom and spinless fermions. The key idea is that there is a simple mapping between the Hilbert space of a system with a spin-1/2 degree of freedom…
wonderich
- 8,086
17
votes
2 answers
Mean-field theory : variational approach versus self-consistency
I have a general question concerning mean-field approaches applied to quantum or classical statistical mechanics.
Does determining the mean-field by a variational approach always imply that the self-consistency is satisfied ? Moreover are there some…
VanillaSpinIce
- 1,458
15
votes
3 answers
Critical 2d Ising Model
The 2d Ising model is extremely well studied, nevertheless I have encountered two facts which seem to contradict one another, and I have not been able to find the resolution in the literature. The puzzle is the following.
The critical Ising model is…
Surgical Commander
- 4,057
14
votes
1 answer
Anomalies for not-on-site discrete gauge symmetries
If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in general there are discrete symmetries that…
Ryan Thorngren
- 8,254