All Questions
Tagged with gauge-theory condensed-matter
75
questions
2
votes
0
answers
50
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The notion of "stable mean-field state" of a spin liquid
I have some issues understanding X-G. Wen's notion of stable mean-field states of spin liquids.
I understand that the slave-boson mean-field theory is reliable when fluctuations on top of it are weak (...
- 400
2
votes
1
answer
70
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What is parity of charge?
In the book Field Theories of Condensed Matter Physics by Fradkin:
When discussing the gauge-invariant operators of $Z_2$ lattice gauge theory in Page 299, the author says
Owing to the $Z_2$ symmetry,...
- 776
0
votes
0
answers
62
views
What is an imaginary gauge potential?
This paper considers a generalised Strum-Liouville equation, that is equations of the form
$$
\left[-\frac{d}{dx}p(x)\frac{d}{dx}-\frac{i}{2}\left(\lambda_1(x)\frac{d}{dx}+\frac{d}{dx}\lambda_2(x)\...
- 121
0
votes
0
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29
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Spinon is charge neutral or has a unit charge?
I have studied that spinons are charge neutral particles and have spin 1/2. But in XG Wen’s book (quantum field theory for many body system), it is mentioned that spinon coupled to gauge field carries ...
- 358
1
vote
0
answers
85
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Global form of flavour symmetry groups in gauge theories
How do we work out the global nature of a flavour symmetry group? To be concrete, consider the simplest example of QED, preferably in D dimensions, with $N$ flavours of fermions with Lagrangian
$$\...
- 51
1
vote
1
answer
212
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What is a "statistical" gauge field?
In the Fractional Quantum Hall Effect (FQHE), one introduces a Chern-Simons (CS) gauge field and it is called statistical. Why? Another main question is below (*), but maybe I should state some things ...
- 393
5
votes
0
answers
130
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Flux Quantization in a Compact $U(1)$ Gauge Theory in 2+1D
I was reading through the Gauge Theory section on Xiaogang Wen's textbook on Quantum Field Theory of Many Body Systems.
In this chapter, he talks about a compact $U(1)$ gauge theory in $2+1 D$, where ...
- 51
3
votes
3
answers
669
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‘Proof’ that non-Abelian Berry phase vanishes identically
For a degenerate system with Hamiltonian $H =H(\mathbf{R})$ and eigenstates $\left|n(\mathbf{R})\right\rangle$ the non-Abelian Berry connection is
$$A^{(mn)}_i=\mathrm{i}\left\langle m|\partial_in\...
- 2,157
3
votes
0
answers
76
views
Could there exist gauge-symmetry-protected topological order?
More precisely, let $\hat{H}_1, \hat{H}_2$ be locally-interacting, translation-invariant quantum many-body Hamiltonians (defined on the same quantum system) that both has a gauge symmetry $G$, and ...
- 883
2
votes
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28
views
How to understand degeneracy and singularity of field
In the online lecure given by Professor Wu Yongshi https://www.koushare.com/video/videodetail/4619 1:30‘, he says:
Suppose we have a state $|m,R(t)\rangle$, where $R(t)$ is controlled parameters ...
- 776
3
votes
0
answers
58
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Properties of Topologically Ordered States
From what I've read so far, all topologically ordered states seem to possess the following properties:
Gapped excitations with fractionalized statistics (anyons)
Gauge theory structure (which may be &...
- 93
3
votes
0
answers
143
views
In the Kitaev honeycomb model, is it possible to get a ground state that is completely 'unphysical' when working with Majorana representation?
Kitaev's way of exactly solving his honeycomb model described here is to describe the system using Majorana fermions, a description that introduces a lot of unphysical degrees of freedom. The up shot ...
- 919
0
votes
0
answers
97
views
Quantum gauge transformation definition
I have always thought that a gauge transformation of a quantum Hamiltonian $H(\Psi,\Psi^{\dagger},A)$ ($A$ is the vector potential and $\Psi$ a matter field) is given by:
$$\Psi(r) \rightarrow \Psi(r) ...
- 192
9
votes
1
answer
2k
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Why is Kitaev's toric code a $Z_2$ gauge theory?
I am reading Kitaev's 2003 paper. In the literature, it is often said that the model proposed in this paper is a $Z_2$ gauge theory. I don't quite see why it is the case. Where is the $Z_2$ gauge ...
- 508
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vote
0
answers
74
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How to write the gauge-invariant anomalous Nambu Green's function for 2D square lattice with uniform $\pi$ flux?
For the free fermion system in two-dimensional square lattice, we add the $\pi$ flux in each plateau:
$$H=-t \sum_{\langle i, j\rangle} e^{i A_{i, j}} c_{i}^{\dagger} c_{j}+h . c .$$
where
$$\sum_{\...
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