Questions tagged [lattice-gauge-theory]
The study of (particle physics) gauge theories on a spacetime that has been discretized into a lattice.
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How to update $SU(2)$ Higgs fields with Heat Bath algorithm?
I'm trying to update the Higgs field coupled with a pure gauge $SU(2)$ theory through Heat Bath algorithm. Pure gauge and Higgs configurations should be updated separately. For the pure gauge part the ...
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The "overlap function" of a $Z_2$ gauge theory
Consider a $Z_2$ gauge theory on a square lattice (Ising spins on edges) with classical degrees of freedom, i.e.
\begin{equation}
E = -\sum_{\square} \sigma_i\sigma_j\sigma_k\sigma_l
\end{equation}
...
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Lattice gauge theory with $A_\mu$ instead of $E_\mu$ or $B_\mu$
In most formulations of the lattice gauge theory one uses the Hilbert space basis defined by the eigenstates of the electric or magnetic field. For example, in the "electric basis" on one ...
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Path integral in Lattice gauge theory with fixed gauge really the same as without fixing the gauge?
In 1 the question why in lattice gauge theories with gauge group $G$, there was no need for gauge fixing to obtain finite path integrals was answered. Thus observables could be calculated as
\begin{...
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Does the existence of the monopole in a 2+1D $U(1)$ gauge theory require the gauge field compact?
I find the monopole is allowed in a 2+1D compact $U(1)$ gauge theory in lattice (Hermele, PRB 69,064404 (2004)), there the gauge field $A$ is also compact and takes value in $[0,2\pi)$, so there is a ...
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Wilson action equations of motion
Let $S_W$ be a Wilson action of $1\times 1$ plaquettes for a gauge group $G$:
\begin{equation*}
S_W = \beta a^4 \sum_P \left( 1-\frac{1}{N_G} \text{Re Tr}(U_P) \right),
\end{equation*}
where $\beta$ ...
- 2,613
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Question about the measure in the partition function of a lattice Yang-Mills theory
This can seem like a dumb question but the partition function of a lattice pure gauge field theory in euclidean space is:
\begin{equation}
Z=\int \prod_{x,\mu} dU_\mu(x)\,e^{-S_W[U_\mu(x)]}\,\,\,,\,\,\...
- 2,613
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"Axial" gauge in the $Z_2$ lattice gauge theory
I am reading the paper by Fradkin and Susskin on the lattice gauge theory (Order and disorder in gauge systems and magnets). In section III. C, where they were trying to introduce the duality ...
- 1,181
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Equivalence between rotation and magnetic flux in lattice models
I am trying to understand the presence of complex hopping amplitudes in Hubbard-like lattice models. The hopping term features the so called "Peierls phase":
$$
- t\sum_{j=1}^L \left( c_{...
- 1,232
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Degenerate link variable configuration in $Z_2$ lattice gauge theory (Wen's QFT book)
I'm reading through Xiao-Gang Wen's Quantum Field Theory of Many-body Systems, and I just begin reading $Z_2$ lattice gauge theory.
In page 255, the author constructed a four-fold denegerate (in the ...
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2D toric code intuition
I’m trying to self-learn QFT in condensed matter and I’ve hit a stumbling block with gauge theory and toric code. I’m trying to solve problem 2 from this webpage http://www.its.caltech.edu/~motrunch/...
- 301
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What's wrong with lattice quantum gravity?
Assume one can write the metric field on a lattice, so on each lattice point one has a value of $g^{\mu\nu}$. Similar to the way lattice QCD is formulated. Then later taking the distance between ...
user84158
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Parity of a 1d Ising model, and with higher order terms
I don't know if this should be asked here or in a math stack exchange, but I'll try here first.
Consider the classical 1d Ising model with periodic boundary condition:
\begin{equation}
H_2 (\vec{\...
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What is the reverse operation of gauging a global symmetry?
As far as I understand, gauging a global symmetry means taking a model with a global symmetry and transforming it into a model such that the previous symmetry group is now the gauge symmetry of your ...
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What means charge-$N$ scalar field $\varphi$?
Let $G = \oplus_{i=1}^N (\mathbb{Z}/N_i)$ be an Abelian group, for sake of simplicity eg a cyclic group $\mathbb{Z}/N$ . We consider abstract $G$- gauge theories.
What is in this context the precise ...
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