All Questions
Tagged with quantum-field-theory statistical-mechanics
304
questions
3
votes
3
answers
608
views
Path integral at large time
From the path integral of a QFT:
$$Z=\int D\phi e^{-S[\phi]}$$
What is a nice argument to say that when we study the theory at large time $T$, this behaves as:
$$ Z \to e^{-TE_0} $$
where $E_0$ is the ...
- 411
2
votes
1
answer
48
views
Precise relation between theromdynamic beta and coupling constant in Euclidean QFT
In statistical mechanics, the thermodynamic is inverse of the temperature: $\beta \propto T^{-1}$.
In Euclidean QFT, I have often run into the expression like $\beta \propto g^{-2}$ where $g$ is the ...
- 1,669
1
vote
0
answers
76
views
physical interpratation of partition function in Quantym field theory
Partition function in Statistical mechanics is given by
$$ Z = \sum_ne^{-\beta E_n} $$
For QFT, it is defined in terms of a path integral:
$$ Z = \int D\phi e^{-S[\phi]} $$
How can we see the relation ...
- 411
1
vote
0
answers
70
views
Intuition for imaginary time Greens function
I understand that $$G^M(0,0^+) = \operatorname{tr}\{\rho O_2 O_1\}$$ (I am not putting hats on the operators here because they don't render in the correct position) is simply the expectation value of ...
- 21
0
votes
0
answers
78
views
Operator Product Expansion (OPE) coefficients of free massless theory
Consider the action of the free massless bosonic theory in $2+1D$
$$
S = \int d^3x \partial_{\mu}\phi(x) \partial^{\mu} \phi(x).
$$
The single-particle spectrum (on the surface of a sphere) is given ...
- 11
1
vote
0
answers
36
views
Does the changes of flow regimes of the renormalization group flow diagram imply always that a symmetry has been broken?
Usually we can use RG flow diagrams to understand that a phase transition has happened. Because they are intimately related to a broken symmetry, does that imply that it always implies that a symmetry ...
- 11
3
votes
1
answer
125
views
Why can't bosonic systems have fermionic excitations?
When reading Abrikosov's book AGD, there is a statement that 'It is obvious only that a Bose system can not have excitations with half-integral spins' (page 5).
I don't understand why this is the case....
- 51
2
votes
0
answers
76
views
Different ways to understand fermions [closed]
I first learned about fermions in my atomic physics class, where the teacher said that electrons obey the Pauli exclusion principle. Later, in my quantum mechanics class, I learned about identical ...
- 368
0
votes
0
answers
38
views
Calculation of conformal dimension for Ising model in two dimensional space
Recently I was reading Ph. Di Francesco's book, "Conformal Field Theory", and in section 7.4.2 where it discussed about Ising model, conformal dimensions $(h,\bar{h})$ are deduced from ...
0
votes
1
answer
62
views
Chern-Simons theory: Connection between Thermal and Quantum Partition Function
I have been reading the Quantum Hall Effect from Prof. David Tong's notes. In the section on Chern-Simons theory, he describes the connection between the Thermal Partition Function and the Quantum ...
- 1
0
votes
0
answers
29
views
How to relate the two expressions of thermal spectrum?
I am reading a proof of the fact that if there exists a monochromatic plane electromagnetic wave for an observer in frame $S$, an observer in a frame $S'$, which is uniformly accelerated with respect ...
- 108
3
votes
1
answer
83
views
Is RG fixed point always related to a second-order phase transition?
In practice, usually one of the parameters is tuned (for example temperature in 3D Ising model, which is a relevant parameter) so that it coincides with the value of RG fixed point, then RG flow make ...
- 619
2
votes
0
answers
97
views
What is the action of fermionic Hamiltonian $\mu_1 n_1 + \mu_2 n_2 + U n_1 n_2$
Problem
Consider a Hamiltonian
\begin{equation}
H(c^\dagger, c) = \mu_1 c_1^\dagger c_1 + \mu_2 c_2^\dagger c_2 + U c_1^\dagger c_1 c_2^\dagger c_2\,,
\end{equation}
where $c_i$ are fermionic ...
- 191
2
votes
0
answers
172
views
Is there any renormalization group with infinite number of generators that does not satisify a renormalization group equation?
A generating set of a semigroup(monoid) is a subset of the semigroup set such that every element of the semigroup can be expressed as a combination (under the semigroup operation) of finitely many ...
2
votes
1
answer
121
views
Thermal ground state?
Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$, described by the Hamiltonian
$$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i< j}V(x_{i}-x_{j}) \...
- 1,131
0
votes
0
answers
69
views
Zero temperature Green function as limit of finite temperature Green function
Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$. The Hamiltonian of the system is:
$$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i< j}V(x_{i}-x_{...
- 1,131
0
votes
0
answers
32
views
Schwinger function with and without temperature
I have always been confused with the differences and relation between many-body theory with and without temperature. Suppose I have a theory described by some Hamiltonian $H = H_{0} + V$, where $H_{0}$...
- 1,131
6
votes
1
answer
355
views
Can we define topological order in the context of QFT?
Topological order is defined to be a phase that has ground state degeneracy (GSD) not described by the Landau SSB paradigm but exhibits some Long Range Entanglement property. Mathematically, it is ...
- 141
2
votes
1
answer
176
views
Examples of Path integral $\neq$ Partition function?
Are there any systems we know of whose partition function is not simply Wick rotation of the path integral? Does anyone know of any examples?
- 1,200
0
votes
0
answers
41
views
Partition function in Non-equilibrium field theory in statistical mechanics
Consider a system that described by the Hamiltonian $H(t)$, contains non-adiabatic time-dependent external fields and the evolution drives the system away from equilibrium.
Now the partition function ...
- 177
4
votes
0
answers
109
views
What is the relationship between the renormalization schemes in quantum field theory and statistical field theory
Consider the $\phi^4$ theory for example.
In QFT, we do renormalized perturbation theory by defining the theory at a particular scale, see for example, eq. 12.30 of Peskin and Schroeder:
Then we can ...
- 51
1
vote
0
answers
85
views
Gaussian approximation of Landau Ginzburg and Renoramalization Group
I am studing an introduction to the Renormalization Group (RG); during my course my prof. came up saying that:
Landau-Ginzburg (LG) theory truncated at Gaussian order is exact at the critical point.
...
1
vote
0
answers
56
views
Landau Ginzburg path integral (PI) for the Ising model at gaussian order
I am stick with a problem in computing explicitely the gaussian PI in the Landau-Ginzburg theory for the Ising model.
If we do a procedure of coarse graining, we can define $m(x)$ as a continuous ...
1
vote
0
answers
65
views
System interacting with Fermi Gas
My question denoted by a reduced dynamic for a system interacting with a reservoir.
Before asking the question, for completeness I will write in detail the statement of the problem and notation.
...
- 33
1
vote
1
answer
143
views
Feynman diagrams in statistical physics
Feynman diagrams were, to my understanding, first developed in QED to calculate things such as scattering amplitudes and the running of the coupling constants.
They have later been adopted to ...
- 577
2
votes
0
answers
53
views
Are there universality classes not found through a Ginzburg-Landau like free energy expansion
Usually the real free energy of a system is too complex to be exactly computed, thus one either expands it in power/gradient series or simply builds it from symmetry considerations. For example:
$$F[\...
- 1,168
3
votes
0
answers
104
views
Critical exponent from powercounting of the action through the renormalization group
This will be a very basic question. For example, when we write down a $\phi^4$ action in condensed matter, let's say for an Ising magnet:
$$F[\phi] = \int d^Dx \dfrac{1}{2}(\nabla \phi)^2 + \dfrac{1}{...
- 1,168
2
votes
2
answers
214
views
Gibbs state and creation and annihilation operators
Let's consider quantum Fermi or Bose gas. Let $a(\xi)$, $a^{\dagger}(\xi)$ are standard annihilation and annihilation operators. Hamiltonian of system is denoted as
$$
\hat{H} = \int_{R^3} \frac{p^2}{...
- 33
3
votes
1
answer
167
views
Generating functional for fields with non-zero expectation value
When doing QFT or statistical field theory of, say $N$ scalar fields $\varphi_i$, we consider the the generating functional
$$
W[J] = - \ln Z[J], \quad Z[J] = \int \mathcal D \varphi \, e^{-S[\varphi] ...
- 577
1
vote
0
answers
87
views
Spontaneous breaking of discrete symmetry in d=1+1 at finite temperature and infinite volume
I came across the question of SSB of a discrete symmetry (say, $\mathbb{Z}_2$) symmetry in a QFT in d=1+1 dimensions, at finite temperature, and I have trouble making sense of two different viewpoints ...
