8
votes
1answer
184 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 ...
5
votes
1answer
187 views

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 ...
1
vote
0answers
40 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
1answer
114 views

How many kinds of topological degeneracy are there?

Here I want to summarize the various kinds of topological ground-state degeneracy in condensed matter physics and want to know whether there exists any other kind of topological degeneracy. For ...
1
vote
1answer
78 views

Wave vector $\vec{k}$ vs position vector $\vec{x}$

My question is about the $k$-vectors in first Brillouin zone. If I am not misunderstood, the relation k = 2π/(Na) tells that when k goes to zero, we are very very far away from the reference atom and ...
2
votes
1answer
176 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 $\mathbf{B}=\nabla\times\mathbf{A}$ ...
5
votes
1answer
101 views

$SU(N)$ Neel manifold

I have seen multiple papers talking about the manifold, $M$ of the Neel order for an $SU(N)$ magnet is $$M~=~\frac{U(N)}{U(m)\times U(N-m)}.$$ So for instance, a $SU(2)$ magnet has manifold $$M ~=~ ...
8
votes
1answer
233 views

Chiral coupling in string-nets

In Xiao-Gang Wen's review of topological order http://arxiv.org/abs/1210.1281 , he states in footnote 52 that string-nets are so far unable to produce the chiral coupling between the SU(2) gauge boson ...
1
vote
1answer
658 views

What is the Hubbard-Holstein model?

Please explain as simply as possible what the Hubbard-Holtstein model is and what it is used for.
9
votes
1answer
137 views

Why are topological solitons present in some phases for lattice models?

Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
9
votes
1answer
356 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 ...
10
votes
1answer
119 views

Consideration of static atomic displacements in electronic structure calculations

I am hoping to discuss some details of electronic structure calculations. I am not an expert on this topic, so please forgive any abuse of terminology. It is my understanding that first principles ...
10
votes
2answers
309 views

What is known about some massive Gaussian models on a lattice?

Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle ...