Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [tomonaga-luttinger-liquid]

Tomonaga-Luttinger liquid, more often referred to as simply a Luttinger liquid, is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor (e.g. quantum wires such as carbon nanotubes). Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension.

1
vote
0answers
6 views

Gapping out edge modes by backscattering

I was reading this paper by Michael Levin about protected edge states without symmetry. In the introduction, he makes the argument that backscattering terms or other perturbations gap out left and ...
2
votes
1answer
108 views

The correct definition of Klein Factor

Klein factors are the operators which make sure that the anticommutation between the different species is correct during the bosonization procedure. According to this famous review by Jan Von Delft, ...
0
votes
0answers
26 views

Co-propagating fermions with tunneling

When we have coupled fermions with an opposite chirality, the existence of the tunneling term will effectively act as a mass term and opens up the gap. When we bosonize the theory this mass term ...
8
votes
2answers
211 views

“$\theta$-$\phi$ duality” and $T$-duality

When bosonizing an interacting spinless Luttinger liquid, the action can be written as \begin{equation} S=\frac{K}{2\pi}\int dx d\tau\ (\partial_\mu\phi)^2 = \frac{1}{2\pi K}\int dx d\tau\ (\partial_\...
1
vote
0answers
18 views

Stability conditions for the Luttinger liquid

I came across an interesting question and was not able to find an answer in the internet, so let's see whether someone of you can help. I was working on a problem using the bosonization method and ...
2
votes
0answers
81 views

What's the relation between SDW/CDW and spinon/holon in the one dimensional repulsive Hubbard model?

As is well known, spin-charge separation occurs in the one dimensional repulsive Hubbard model. This phenomenon can be well understood by the Luttinger liquid theory, where spin density wave(SDW) and ...
1
vote
1answer
50 views

Occupation Number of Tomonaga-Luttinger Liquid away from the Fermi Wavevector

I have read that, near $k_F$, the occupation number of a Tomonaga-Luttinger liquid goes as $ n(k)\sim -\textrm{sgn}(k-k_F)|k-k_F|^{(K+1/K)/2-1}$ where $K=\left(1+\frac{Uv_F}{\pi}\right)^{-1/2}$ ...
2
votes
0answers
60 views

The validity of infinite many Conformal Field Theories on the Fermi surface

The naive $2$-dimensional Fermi sea in $k$-space (with a convex structure and positive Gaussian curvature, some nice properties, etc) in $2+1$-dimensional spacetime may be viewed as an infinite ...