Unanswered Questions
1,799 questions with no upvoted or accepted answers
6
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Do we know the exact ground state of the Antiferromagnetic Heisenberg Model?
I've been reading about the Heisenberg Model:
\begin{equation}
H=-J\sum_{\langle i, j\rangle } \hat{\vec{S}}_i .\hat{\vec{S}}_j = -J\sum_{\langle i, j\rangle}\left[\hat{S}^z_i \hat{S}^z_j + \frac{1}{2}...
- 980
6
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2
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Wiedemann-Franz law
The Wiedemann-Franz law states that the ratio of thermal conductivity $\kappa$ and electrical conductivity $\sigma$ for metals fairly accurately obeys $\kappa/\sigma = LT$, where $T$ is the ...
- 206k
6
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853
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What is the reason for chiral anomalies in condensed matter systems?
If you consider a massless relativistic fermion theory and you perform a chiral transformation, then you realize that while the classical action remains invariant under this transformation the ...
- 206k
6
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281
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Detailed Balance for Quantum Master Equations from System Hamiltonians with Degenerate Spectrum
Kossakowski, Andrzej, et al. ("Quantum detailed balance and KMS condition." Communications in Mathematical Physics 57.2 (1977): 97-110) gave a proof that the stationary state of a quantum dynamical ...
6
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785
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How is Laughlin's gauge argument explaining integer quantum hall effect(IQHE)?
It seems essential in Laughlin's gauge argument that the sample has to be cylindrical(or with similar toplogy), so that we can "thread" a thin solenoid through to control the gauge function on the ...
- 3,995
6
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324
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Third-order topological quantum phase transition in p+ip superfluid
A two-dimensional spinless non-relativistic p+ip superfluid undergoes a quantum phase transition between the BCS (weakly-coupled) and BEC (strongly-coupled) regimes. This transition is driven by ...
- 581
6
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311
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Finding difficulties in taking continuum limit in nonlinear sigma model
I am learning nonlinear sigma model from Assa Auerbach's book "Interacting Electrons and Quantum Magnetism" and getting some difficulties in taking continuum limit. I am following chapter 12: The ...
- 363
6
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1
answer
454
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Quantum description of Raman effect
In the classical description of the Raman effect the object of study is the electric polarizability of the system.
I'm interested in learning the quantum description of the Raman effect and in Bernath'...
- 2,646
5
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0
answers
140
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Handling zero eigenvalues in Dyson Series for calculating Green's function at zero frequency numerically
I am working on calculating the Green's function for a Hamiltonian $H = H_0 + V$ numerically, where I'm specifically interested in $G(\omega) = \frac{1}{\omega - H + i\epsilon}$ at $\omega = 0$.
A ...
- 466
5
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84
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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, ...
- 206k
5
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111
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Evaluating integral that include Fermi distribution function using residue theorem
$$
I=\int_{-\infty}^{+\infty} \frac{d\epsilon}{2\pi} f(\epsilon)
\left[
\frac{1}{(\epsilon-\epsilon_n +i0^+)^2(\epsilon-\epsilon_m +i0^+)} - \frac{1}{(\epsilon-\epsilon_n -i0^+)^2(\epsilon-\epsilon_m ...
- 206k
5
votes
0
answers
143
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Confusion about Friedel sum rule
In Mahan's "Many-Particle Physics" (3rd edition, page 197), the so-called Friedel sum rule is of the form
$$Z = \frac{2}{\pi} \sum_l (2l+1) \delta_l (k_F) , \tag{4.72}\label{4.72}$$
where $Z$...
- 16k
5
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165
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Inverse Participation Ratio (IPR) a predictor for quantum phase transition?
In a typical quantum quench protocol, a Hamiltonian is considered of the form
$$H = H_{0} + g H_{1}$$
where $g>g_{c}$, system will be in one phase and $g<g_{c}$, system will be in another phase. ...
- 626
5
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answers
97
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Does the path integral of Cooper pairs have a Berry-phase term?
In a BCS superconductor, by Hubbard-Stratonovich transformation, we can integrate out the electrons and get an effective theory for Cooper pairs like
$$
S = \int \mathrm{d} \tau \mathrm{d}^3 x \left( (...
- 2,646
5
votes
0
answers
130
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Flux Quantization in a Compact $U(1)$ Gauge Theory in 2+1D
I was reading through the Gauge Theory section on Xiaogang Wen's textbook on Quantum Field Theory of Many Body Systems.
In this chapter, he talks about a compact $U(1)$ gauge theory in $2+1 D$, where ...
- 3,710