All Questions
Tagged with correlation-functionscondensed-matter
53 questions
2votes
0answers
47views
Are there ever circumstances when exponential decay of correlations implies gappedness of the Hamiltonian?
There are by now a set of well-known results showing that if a Hamiltonian has a gap, then this implies exponential decay of correlations between spatial separated observables (e.g. https://arxiv.org/...
3votes
0answers
46views
Ergodic hierarchy and the two-point correlation function
I'm currently looking at a paper about dual unitary circuits (https://arxiv.org/pdf/1904.02140) where the authors derive an expression for the correlation function looking like $$C_{\alpha\beta} = \...
2votes
1answer
208views
How are general quantum correlation functions actually measured?
These days, the majority of work in theoretical particle, condensed matter, and AMO physics is about methods for calculating exotic correlation functions, of the rough form $$G_{ij} \sim \langle \...
- 107k
1vote
0answers
61views
What's physical meaning of 2-point correlation function in holographic condensed matter?
Background: In AdS/CFT, we can do calculations in AdS spacetime, and get the result in CFT. When we consider RN-AdS black hole/brane, 2-point correlation functions in CFT can be obtained, which are ...
- 11
2votes
1answer
175views
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 ...
- 75
3votes
1answer
130views
Green function power-law behavior in real and momentum space
Given a Green's function with pawer-law behavior in $k$-space $g(k)\sim\frac{1}{k^a}$ (at least for small $k$), what is the asymptotic form for $g(x)$ in the real space? In the paragraph above Eq. (56)...
- 3,942
3votes
1answer
75views
How to choose an appropriate value for the regularization $\eta$ in correlation functions in linear response for numerical calculations?
TL;DR How to choose an appropriate value for the regularization $\eta$ in correlation functions used in linear response for a discretized Brillouin zone? For more context, please see below. ...
- 1,098
1vote
0answers
140views
Combinatorics for Feynman Diagrams [closed]
When one wants to calculate the two-point-function for an electronic system with Coulomb-interactions in quantum many body systems with the path-integral-formalism $$ \mathscr{G}_{ \alpha , \alpha^{ \...
- 343
1vote
0answers
130views
Correlation function and Green's function
I have referred to several materials on Green's function but I found those notions pretty confusing. Now what I have tried to do is to calculate the inverse matrix of $G^+(E)=E-H+\mathrm{i}\eta$ where ...
- 153
2votes
0answers
128views
Analytic continuation of the many-body spectral density
For an observable $A$, define the real-time autocorrelation function $$ C(t) = \langle A A(t) \rangle_{\beta} = \dfrac{1}{Z} \mathrm{Tr}\left[ e^{-\beta H} A e^{i H t} A e^{-i H t}\right], $$ with $Z =...
- 1,350
2votes
1answer
117views
When is static limit ($\omega=0$ and then $q=0$) of correlation function physical and used?
For a general correlation/response function $F(q,\omega)$, it can be both frequency and momentum dependent. And there are the so-called transport limit $$q\rightarrow0 \text{ and then }\omega\...
- 3,942
2votes
2answers
1kviews
Does particle-hole symmetry always imply half-filling and real correlations $\langle c^\dagger_n c_{n+1} \rangle$?
Suppose we had a lattice Hamiltonian $H$ which was symmetric under the particle-hole transformation $$ c_n \mapsto U^\dagger c_nU=(-1)^nc^\dagger _n$$ such that $[H,U] = 0$, where $c_n$ are Fermionic ...
- 4,074
1vote
1answer
412views
Kubo identity (electrical conductivity) integration
I am deriving Kubo formula using Kubo identity and I am confused that how does the article perform the following steps. On page 8, we have a integration $$ I\equiv\int_0^\beta d\lambda Tr\bigg\{\rho_0 ...
- 1,457
1vote
1answer
934views
How do core electrons factor into the $f$-sum rule?
Kubo gives in Statistical-Mechanical Theory of Irreversible Processes section 8 the sum rules for conductivity, $$ \frac{2}{\pi} \int_{0}^{\infty} d \omega \operatorname{Re}\left(\sigma_{\mu \nu}(\...
- 583
2votes
1answer
208views
Dynamical Mean Field Theory (DMFT) does not take into account spacial correlations?
It is often said that the Dynamical Mean Field Theory (DMFT) does not take into account spacial correlations. What does this mean in layman terms? Does that mean that we assume: $$ \langle n_i n_j \...
- 1,845
