Questions tagged [bosonization]
Bosonization is a mathematical procedure mapping a system of interacting fermions in 1+1 dimensions to a system of massless, bosons (excitations).
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Book recommendation for CFT in condensed matter theory
I've been looking for sources about conformal field theory (CFT) applications in condensed matter theory (CMT) like bosonization, critical phenomena, and QFT anomalies. I have studied CFT from ...
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Superfluid helium bosonic and fermionic degrees of freedom?
I have looked at
Helium Nucleus as boson
How can multiple fermions combine to form a boson?
Why are He-4 nuclei considered bosons, and He-3 nuclei considered fermions?
but I still feel like saying &...
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Bosonization at finite temperature? [closed]
Textbook for bosonization mainly focus on the zero temperature limit. I wonder that at finite temperature, if there exists the boson-fermion dictionary as well.
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Time reversal symmetry and Bosonization
Bosonization of Spin 1/2s to fields $\phi(x)$, $\theta(x)$ is defined as (Ref: 'Quantum Physics in 1-D' by Giamarchi):
$S^z(x)=\frac{-1}{\pi}\nabla\phi(x)+\frac{(-1)^x}{\pi a}\cos 2\phi(x)$,
$S^x(x)=\...
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CDW correlation function for 1D Dirac fermion in condensed matter
I am following Shankar's lecture notes on bosonization, specifically the theory of left-/right-moving fields for a low-energy 1D fermionic chain. For now, I ignore the Heisenberg time dependence of ...
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Non-local commutator $[\phi(x), \phi(y)] = i\pi \textrm{sgn}(x-y)$ of 1D chiral boson: why?
It is well-known from bosonization that 1D chiral boson has the commutation relation
$$[\phi(x), \phi(y)] = i\pi \mathrm{sgn}(x-y). \tag{1}$$
This gives the correct anticommutation relation for the ...
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Dot product of displacement vector with gradient [closed]
I have an integral like Eq. E.21 in Giamarchi's book (Appendix E, Quantum Physics in 1-D) :
$I=\int d^2R \int d^2r (r\cdot\nabla_R \phi(R))^2 e^{-f(r)}$
where, $r=r_1-r_2, R=\dfrac{r_1+r_2}{2}.$
How ...
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Magnon spectrum with in-plane Dzyaloshinski-Moria interraction
I'm attempting to derive a magnon spectra using first principles. In-plane DMI is considered in my system. $z$ axis is out of plane. First of all I wrote a Hamiltonian for interacting spins with two ...
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Spin and scale dimension of canonical spin-1/2 fields in (1+1)d
I am reading the book "Non-perturbative methods in 2 dimensional quantum field theory" by Abdalla, Abdalla and Rothe and have some questions about the Chapter 2.4 "Bosonization of ...
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How would one compute the heterotic amplitude for four gauginos using bosonization?
I'm reading through Polchinski's String Theory Volume II, and I was unsure of how to approach Problem 12.9. For posterity, the problem states:
Calculate the tree-level heterotic string amplitude with ...
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Bosonization of Fermionic theory with boundary
Consider massless Thirring model
\begin{equation}
-\psi^\dagger_R(x)\partial_x\psi_R(x)+i\psi^\dagger_L(x)\partial_x\psi_L(x)+g\psi^\dagger_R(x)\psi_R(x)\psi^\dagger_L(x)\psi_L(x)
\end{equation}
Using ...
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Question about a derivation in Field theoretical bosonization (Page 178 Altland and Simons)
I'm now reading the 'Condensed Matter Field Theory' by Altland and Simons, Chapter4.3 on page 178, and having difficulties understanding the commutation relationship (4.47) (in my opinion, there ...
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CFT Description of the 2D Ising Model as both a free fermion theory and a $\varphi^4$ Landau theory
There are numerous Stack Exchange answers that explain how to construct a free fermion CFT ($c = 1/2$) which describes the critical point of a 2D Ising model.
However there are also sources that ...
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Path from correspondence between fermionic oscillator and bosonic oscillator to free bosons from interacting fermions
This question is open to edits and corrections. I'm available to make corrections as needed.
I am attempting to understand fermion boson correspondence and bosonization.
What is the correspondence ...
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Is bosonic normal-ordering equal to fermionic normal ordering?
I'm trying to understand Jan von Delft's "Bosonization for Beginners — Refermionization for Experts", in which he uses boson normal ordering and fermion normal ordering interchangeably, and ...
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