All Questions

0
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0answers
39 views

Gauge theory in Condensed Matter physics

Always come across these two jargons, namely Matter Field and Gauge Field, please explain what is the difference between them and why it is important in condensed matter physics? There are many ...
1
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0answers
32 views

How can I compute the spin texture for a $SU(2)$ gauge model?

I am trying to determine the helicity of 4 Dirac cones in my model, and one way I want to approach it is by plotting the spin-texture. However, I am unsure of how one would calculate the spin-texture ...
1
vote
0answers
75 views

On string-like excitations in (3+1)d discrete gauge theory

(3+1)d discrete $G$-gauge theory (untwisted Dijkgraaf-Witten theory) has both point-like and loop-like excitations; Point-like excitation is an electric charge labeled by an irreducible ...
3
votes
0answers
59 views

What is the topological data for $(\mathbb Z_n)_p$ theories?

Consider the 3d TQFT described by the Lagrangian (Dijkgraaf-Witten with gauge group $\mathbb Z_n$ at level $p$): $$ \mathcal L=\frac{n}{2\pi} B\wedge\mathrm dA+\frac{p}{4\pi}A\wedge\mathrm dA $$ with $...
8
votes
1answer
251 views

Anyon condensation – what's the precise definition?

Say I have an anyonic system modelled as a Chern-Simons system with group $G$. If the centre of $G$ is non-trivial, one may also study the system described by $G/\Gamma$, where $\Gamma$ is a discrete ...
3
votes
1answer
117 views

Can there be an emergent non-compact gauge field?

Emergent compact gauge fields are ubiquitous in condensed matter theory (like $U(1)$). Are there any examples of an emergent non-compact gauge field, in which case there won't be any quantization ...
5
votes
0answers
91 views

Path integral and gauge redundancy for slave particle

In the slave boson, we have $c^\dagger = b f^\dagger$ where $b$ is boson and $f$ is fermion. There is also a local constraint $b^\dagger b+f^\dagger f=1$ to retrict the Hilbert space and a $U(1)$ ...
2
votes
1answer
102 views

Peskin's duality in XY model (Mandelstam-'t Hooft duality in abelian lattice models)

I am studying the old paper by Peskin (1978): Mandelstam-'t Hooft duality in abelian lattice models (https://doi.org/10.1016/0003-4916(78)90252-X). However, I am confused about some details of ...
3
votes
1answer
78 views

Large gauge transformation and intersection form

I am reading this paper and on pp.19-20 it states the following relation between large gauge transformation and intersection form: for the action on a 4-manifold $M^4$ $$S[A,B] = \int_{M^4}{\sum_{I=1}...
2
votes
0answers
83 views

Toric Code model with an extra projector? (Levin-Gu)

In the seminal work by Levin and Gu in 2012 ( Braiding statistics approach to symmetry-protected topological phases ) they give a concrete prescription for how to gauge a global symmetry to a local ...
3
votes
1answer
158 views

Why is it that in presence of a long-range force Goldstone excitations are absent?

Page 15 of this note states, If a continuous symmetry of the Lagrangian is spontaneously broken, and if there are no long-range forces, then exists a zero-frequency excitation at zero momentum....
4
votes
1answer
350 views

Perturbative Results Kitaev Model with Magnetic Field

I am curious if there are results available for the Kitaev model with a magnetic field -- in his 2006 paper, Kitaev obtains the form of the effective hamiltonian (Eq. 46 in https://arxiv.org/abs/cond-...
4
votes
1answer
163 views

How should I think of monopoles in a 3+1D lattice $U(1)$ gauge theory?

The Hamiltonian for 3+1D compact $U(1)$ gauge theory on a cubic lattice is of the form \begin{equation} H = J\sum_{\text{links}\ l}E^2_{l}+ g \sum_{\text{plaquettes}\ P}\cos(\Phi_P), \end{equation} ...
1
vote
0answers
23 views

Nonlocality of gauge-charged particle?

On pp.24 left-hand side of this paper there is a statement saying: the vortex insertion operator is of course a nonlocal object, which reflects the fact that one cannot insert a gauge-charged ...
2
votes
1answer
104 views

Integral of a gauged topological term as a map from principal bundles

I am reading this paper and on pp.14 left-hand side eqn (63) reads $$\int_{M^d}{W_{top}^d(A)} \in U(1)$$ where $W_{top}^d(A)$ is a topological term obtained by integrating out the matter field $g$ ...
0
votes
0answers
170 views

Is there a U(1) version of the Toric Code?

I know of $\mathbb{Z}_n$ versions of the 2D Toric Code and also 3D versions, but I was wondering if there's a simple lattice gauge theory model with rotors instead of spins placed on each link of a ...
4
votes
1answer
202 views

Can the synthetic gauge field be dynamical?

Can the synthetic gauge field be dynamical gauge field? Early idea of Wilczek and Zee stated that (non-Abelian) gauge fields arise in the adiabatic development of simple quantum mechanical systems. ...
2
votes
0answers
119 views

“Mixed anomaly” in Weyl semimetal and its cancellation

The introduction to the problem Suppose the Weyl semimetal (read please briefly the definition before reading the question). Because of the effective nature of the chirality the parameters $b_{0}, \...
1
vote
1answer
182 views

Low dim physics: Examples of confinement-deconfinement phases of U(1) gauge theory in 2 dimensions

Please provide some examples of confinement-deconfinement phases of U(1) gauge theory in 2 spacetime dimensions (Low dimwnsional physics). U(1) gauge theory can be: pure U(1) gauge theory, or U(1) ...
6
votes
2answers
331 views

When do gauge theories have protected gapless excitations?

Goldstone's theorem states that a system in which a continuous symmetry is spontaneously broken necessarily has gapless excitations. (A hand-waving "proof" of Goldstone's theorem can be given by ...
1
vote
0answers
203 views

$U(1)$ gauge symmetry in superfluid

The conventional superfluid phase in a Bose-Hubbard ground state has $U(1)$ symmetry. In the presence of spin-orbit coupling (SOC), the superfluid ground state has non-uniform phases. Why do people in ...
3
votes
0answers
160 views

In string-net condensation, what does the quantized charge means? [closed]

The electrical charge is quantized strictly for elementary particles. What kind constraints does this fact applied to string-net theory? For the this question, I want to understand why electrical ...
3
votes
0answers
268 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ($f_{\sigma}...
6
votes
1answer
492 views

How to see the ground state degeneracy (GSD) from a $BF$ theory in $2+1$ $d$?

I have seen many times the $BF$ theory has non-trivial ground state degeneracy (typically on torus), but I can not see how the conclusion come out. Recently I found a paper by Hansson, Oganesyan and ...
1
vote
1answer
179 views

A formula in Sung-Sik Lee's paper

I want to ask if anyone has gone through the derivation of the second equality in the following formula which comes from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102.
6
votes
1answer
268 views

Will all physical quantities unchanged by this transformation?

I am reading an article about Bloch-Floquet state. My questions is in Part II.B and Appendix A of this paper, I will describe them below. The original Schordinger equation we consider is: $$i\hbar\...
11
votes
2answers
2k views

Understanding Elitzur's theorem from Polyakov's simple argument?

I was reading through the first chapter of Polyakov's book "Gauge-fields and Strings" and couldn't understand a hand-wavy argument he makes to explain why in systems with discrete gauge-symmetry only ...
4
votes
1answer
224 views

Does the projected spin state of the $d+id$ mean-field Hamiltonian on a triangular lattice has time-reversal(TR) symmetry?

Consider the following $d+id$ mean-field Hamiltonian for a spin-1/2 model on a triangular lattice $$H=\sum_{<ij>}(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$$, with $\chi_{ij}=\begin{pmatrix} 0 & \...
3
votes
2answers
1k views

Why does the $\pi$-flux state have time-reversal symmetry?

It's known that the $\pi$-flux state of the antiferromagnetic Heisenberg model on the square lattice is an important concept. The $\pi$-flux state is described by the (simplified) mean-field ...
2
votes
0answers
58 views

What's the necessary and sufficient condition for gauge equivalence in the projective construction?

The definition of gauge equivalence and notations used here is the same as those in my previous question. As we know, the condition $\chi_{ij}'=G_i\chi_{ij}G_j^\dagger$(where $G_i\in SU(2)$) is a ...
1
vote
0answers
61 views

Some question on the definition of flux in the projective construction?

Here I have some confusing points about the definition of flux in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ ...
2
votes
0answers
197 views

Some questions on the Wilson loop in the projective construction?

Based on the previous question and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij}'\psi_j+H.c.)$, we ...
3
votes
0answers
187 views

Is the $SU(2)$ flux defined in the context of Projective Symmetry Group(PSG) an observable quantity?

The $SU(2)$ flux defined in the context of PSG is as follows: Consider the mean-field Hamiltonian $H_{MF}=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ description of a 2D lattice spin-model, the ...
4
votes
1answer
372 views

A naive question on the Quantum Hall Effect(QHE) and the confinement in gauge theory?

The non-interacting 2D lattice QH system is described by the Hamiltonian $H=\sum t_{ij}e^{iA_{ij}}c_i^\dagger c_j+H.c$ My confusion is: Does this imply that the $2D$ lattice QHE is described by the $...
2
votes
1answer
493 views

A naive question on the $U(1)$ gauge transformation of electromagnetic field?

For simplicity, in the following we set the electric charge $e=1$ and consider a lattice spinless free electron system in an external static magnetic field $\mathbf{B}=\nabla\times\mathbf{A}$ ...
4
votes
1answer
296 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
1
vote
1answer
188 views

By saying a physical state has some 'symmetry', what do we really mean?

Here our arguments are restricted to the realm of the Projective Symmetry Group(PSG) proposed by Prof. Wen, Quantum Orders and Symmetric Spin Liquids. Xiao-Gang Wen. Phys. Rev. B 65 no. 16, 165113 (...
3
votes
2answers
467 views

Two puzzles on the Projective Symmetry Group(PSG)?

Recently I'm studying PSG and I felt very puzzled about two statements appeared in Wen's paper. To present the questions clearly, imagine that we use the Shwinger-fermion $\mathbf{S}_i=\frac{1}{2}f_i^\...
3
votes
1answer
171 views

Are the symmetry operators well defined in the context of Projective Symmetry Group(PSG)?

Consider the Schwinger-fermion approach $\mathbf{S}_i=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$ to spin-$\frac{1}{2}$ system on 2D lattices. Just as Prof.Wen said in his seminal paper on PSG, the ...
1
vote
1answer
301 views

Different invariant gauge groups (IGG) on different lattices with the same form mean-filed Hamiltonian?

Suppose that we use the Schwinger-fermion ($\mathbf{S_i}=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$) mean-field theory to study the Heisenberg model on 2D lattices, and now we arrive at the mean-field ...
1
vote
2answers
447 views

A simple question on $SU(2)$ gauge transformations in Wen's papers on projective symmetry group (PSG)?

Recently I am studying the projective symmetry group (PSG) and the associated concept of quantum order first proposed by prof.Wen. In Wen's paper, see the last line of Eq.(8), the local SU(2) gauge ...
2
votes
0answers
212 views

From Berry's phase to artificial Gauge potential

How a nonzero geometric phase in a loop is used to generate artificial gauge potentials? If possible, can you also tell how to generate the non-abelian artificial gauge potentials.
3
votes
1answer
317 views

How to justify matter-field interaction for non-gauge-invariant Hamiltonian?

I'm wondering how can one formally justify the electromagnetic response of a system which does not verify local U(1) gauge invariance. A good example of what I would like to consider is given by the ...
4
votes
0answers
123 views

Is there a critical order of the Abelian gauge theory in (2+1)D

In (2+1)D spacetime, it is known that the $U(1)$ gauge theory is always confined (according to Polyakov), while the $\mathbb{Z}_2$ gauge theory can support a deconfined phase. Now consider a generic ...
15
votes
1answer
1k views

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 ...