All Questions
Tagged with correlation-functionsmany-body
27 questions
4votes
1answer
142views
Why is this an out-of-time-order (OTOC) correlator?
I am trying to understand operator growth through the paper Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK by Qi and Streicher. It has equation 3.7, which is: $$ -\frac{1}{N}\sum_{j=1}...
- 57
6votes
1answer
116views
Expansion of $(S_{I}[\bar{\alpha},\alpha])^n$ in the proof of the linked-cluster theorem
On P.192 of Piers Coleman's "Introduction to many body physics", he uses Sam Edwards' replica trick to show that Green's function $$G(1-2)=\sum{\text{two-leg linked-cluster diagram}}\tag{7....
2votes
1answer
124views
Long distance correlation among particles
Given a many-body particle system, let's define the particle-particle correlation function as $F_{i,j} = \langle O_i O_j\rangle - \langle O_i\rangle\langle O_j\rangle$, for a certain operator $O$, and ...
- 334
1vote
1answer
91views
Greens Function formalism for the independent boson model
This may be a very specific question, but since almost everyone seems to be quoting this book, I want to understand the derivation(s) of the solution for the independent boson model (IBM) from Mahan's ...
- 163
2votes
1answer
174views
Transformations on correlation functions
Let $\hat{U}$ be a unitary transformation that acts on fermionic fields (defined on a lattice) as $$\hat\psi_j \rightarrow \hat{U}\hat\psi_j\hat{U}^{-1},$$ $$\hat\psi_j^\dagger \rightarrow \hat{U}\hat\...
- 689
3votes
0answers
46views
Ergodic hierarchy and the two-point correlation function
I'm currently looking at a paper about dual unitary circuits (https://arxiv.org/pdf/1904.02140) where the authors derive an expression for the correlation function looking like $$C_{\alpha\beta} = \...
3votes
1answer
204views
What is the signal of a spin wave?
From what I understand, for example in the Ising model, we can probe the correlation function via neutron scattering, and the correlation function gives the magnetic susceptibility for the system. Is ...
- 720
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
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
4votes
2answers
282views
Dyson equation from the equation of motion of the one-body Green's function
Starting from the equation of motion of the one-body Green function is: $$\left[ {i\hbar {\partial \over {\partial {t_1}}} - {h_0}\left( 1 \right)} \right]G\left( {12} \right) - \int {\Sigma \left( {...
- 233
2votes
1answer
354views
Un-equal time correlation via non-interacting tight-binding Hamiltonian
Let's assume we have a model, which is initially defined by the tight-binding Hamiltonian with a random on-site energy $f_n$, as follows: $$H^i=-J\sum_n^{L-1}\left(a_n^\dagger a_{n+1}+h.c\right)+\...
- 23
1vote
1answer
92views
Momentum conservation in correlation functions
In Mahan "Many particle physics" the following Hamiltonian is considered in studying electron tunnelling through a junction \begin{equation} H_t = \sum_{kp} T_{kp} c^\dagger_k c_p + h.c. \...
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
2votes
0answers
110views
What exactly is effective interaction with regards to Feynman diagrams?
What does it actually mean to calculate to calculate the effective interaction using Feynman diagrams? To be concrete, let us consider the example of random phase approximation (RPA) calculation of ...
- 2,263
2votes
1answer
437views
Many-body Green Functions equation
In many-body physics the concept of Green Functions is essential especially when you deal with things like superconductivity that are strictly linked to the presence of off-diagonal long-range order ...
- 168
