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.
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Is the Luttinger liquid a limit of the Kitaev chain model?
From what I understand, they are both models of electrons on a nanowire, but the Hamiltonian is different, just in the pairing term. When I look up the connection between them, there's surprisingly ...
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Renormalization-group approach to half-filling charge density wave
In Shankar's noted review paper on the renormalization group (RG) approach to many-body physics, Sec. IV deals with RG in a 1D lattice nearest-neighbour (quartically) interacting model, which leads to ...
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Interaction Term in Tomonaga-Luttinger Model
I am studying Tomonaga-Luttinger Model from Altland and Simon's textbook called Condensed Matter Field Theory.
From the derivation, I am stuck with showing that the contribution to the interaction ...
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How do you bosonise the spin-$1/2$ operator $S_z$?
Consider a 1D spin-$1/2$ chain. After a Jordan-Wigner transformation, the spin-$1/2$ operator $S^z_i$ takes the form
$$ S^z_i = c^\dagger_i c_i - \frac{1}{2} \equiv \rho_i - \frac{1}{2}$$
where $\{ ...
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Can Fermi liquid be obtained by a canonical transformation?
The basic assumption of the Ferm-liquid theory is the one-to-one correspondence between the states of an interacting Fermi gas to those of a gas of non-interacting quasiparticles. The question is ...
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Compact or non-compact boson from bosonization?
In some discussions of bosonization, it is stressed that the duality between free bosons and free fermions requires the use of a compact boson. For example, in a review article by Senechal, the ...
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Excitations in Luttinger liquids
It's not clear to me what are the elementary excitations of Luttinger liquids. Quoting from Giamarchi's book Quantum Physics in One Dimension:
In one dimension, [...], an electron that tries to ...
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What's the meaning of these pseudo-momentum and pseudo-position operators?
Consider the following hamiltonian, describing a system of independent bosons:
$$ \hat H = \sum_{q \neq 0} \hbar c_q |q|\hat \beta^\dagger_q \hat \beta_q \tag{1}$$
where $\hat \beta_q$ and $\hat \...
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$\cos(\sqrt{8} \phi_\sigma)$ term when bosonizing the Luttinger Hamiltonian
I am currently reading "Fermi liquids and Luttinger liquids" by Schulz (https://arxiv.org/abs/cond-mat/9807366). In page 27 it says the following:
My question is about how
$$\frac{g_1}{(2\pi\alpha)^...
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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 ...
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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, ...
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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 ...
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"$\theta$-$\phi$ duality" and $T$-duality -- is the free fermion theory self-dual?
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_\...
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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 ...
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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 ...
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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
$K=\left(1+\frac{Uv_F}{\pi}\right)^{-1/2}$
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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 ...
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