All Questions
Tagged with duality condensed-matter
13
questions
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17
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Symmetry group and dualities
Let's say two quantum models $M_1$ and $M_2$ are dual to each other and let their symmetry groups be $S_1$ and $S_2$ respectively. Is it necessary for $S_1$ to be isomorphic to $S_2$? (I thought so ...
- 366
2
votes
2
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122
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How to see that the Ising CFT has $c = 1/2$ while the quantum XY CFT has $c = 1$ via Jordan-Wigner?
It is well known that the CFT at the critical point of the 1+1d transverse field Ising model has central charge 1/2. This can be attributed to the fact that, after a Jordan-Wigner transformation, the ...
5
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85
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Question about the duality between 2+1 d transverse-field Ising model (TFIM) and $\mathbb{Z}_2$ gauge theory
I was reading McGreevy's Lecture notes Where do QFTs come from?
, and on chapter 5 he talks about a duality between the $2+1d$ transverse-field Ising model (TFIM) and the $\mathbb{Z}_2$ gauge theory, ...
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2
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449
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Is the self-dual point always a critical point?
I was studying duality maps in my Advanced Stat. Mech. class and it was told that all self-dual points need not correspond to critical point. I understand that critical points are points where ...
- 904
1
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82
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Duality between topological order and SPT in $K$-matrix formalism
It is a well-known fact that the low energy effective theory of intrinsic topological order is multi-components Chern-Simons theory $\frac{K_{I J}}{4 \pi} \int_{\mathcal{M}} d t d^{2} x \epsilon^{\mu \...
- 11
4
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130
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How to calculate the "vortex" correlation function in 2D free system?
I want to calculate the following correlation function in 2D square lattice:
$$G(i, j, \tau) \equiv\left\langle e^{-\frac{i}{2}\left[\hat{\Phi}_{i}(\tau)-\hat{\Phi}_{j}(0)\right]}\right\rangle_{0}$$
$\...
- 1,602
4
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Why is the Jordan-Wigner transformation an example of an S-duality?
The Jordan-Wigner transformation allows one to map a spin theory to a fermionic theory and, according to wikipedia, it is an example of an S-duality. In turn, according to the wiki page for the S-...
- 1,544
3
votes
1
answer
836
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Kramers-Wannier duality high and low temperature expansions confusion
I am reading the section on the 2D Ising model Krammer-Wannier duality in the book Exactly Solved Models in Statistical Mechanics (pg. ~76) by R.J. Baxter. I have two questions:
What was the ...
- 1,544
5
votes
1
answer
534
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Charge-Vortex Duality for Bosons
Consider a (2+1)d continuum field theory with the Minkowski action
$$\mathcal{L}=|\partial\phi|^2-r|\phi|^2-u|\phi|^4,$$
where $\phi$ is a complex field. The theory undergoes a quantum phase ...
- 131
4
votes
1
answer
2k
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Wilson-Fisher Fixed Point in 2+1 Dimensions
In the paper by y Nathan Seiberg, T. Senthil, Chong Wang and Edward Witten,
A Duality Web in 2+1 Dimensions and Condensed Matter Physics
it is claimed on page 1 that the two theories
$$|D_{B}\phi|^...
- 2,923
3
votes
1
answer
289
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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 ...
- 464
8
votes
1
answer
399
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Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?
Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
- 11.9k
29
votes
2
answers
4k
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Confusion about duality transformation in 1+1D Ising model in a transverse field
In 1+1D Ising model with a transverse field defined by the Hamiltonian
\begin{equation}
H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x
\end{equation}
There is a duality transformation which ...
- 1,566