All Questions
26
questions
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
2
votes
0
answers
54
views
Interpretations of wave numbers between open and periodic boundary conditions
I'm curious about the difference in physical interpretation between open and periodic boundary conditions (OBC and PBC) although they are identical in the thermodynamic limit.
For simplicity, let's ...
- 165
1
vote
0
answers
63
views
Computational problem in Altland & Simons p.184
While try to understand functional field integral I encountered this problem on Altland & Simons page 184. The question is: Employ the free fermion field integral with action (4.43) to compute the ...
- 33
1
vote
0
answers
53
views
Particle density and current in terms of Green function
Consider a non-relativistic free-fermion system. I am wondering how to calculate observables like average particle density and average current in terms of momentum-space Green functions. I know that ...
- 59
0
votes
1
answer
73
views
Units in Actions (Functional Field Integrals)
When one rewrites the partition function of a grand-canonical ensemble (quantum version) as functional field integral
$$
Z = \operatorname{Tr}_{ \mathscr{F}} \mathrm{e}^{ - \beta \left( H - \mu N \...
- 324
4
votes
0
answers
116
views
Is it possible to express any quadratic fermionic system in terms of a quadratic majorana system and viceversa?
Can one always write, for some suitable matrix $M$
$$
H= \sum^N_{jk}(A_{jk}c^\dagger_jc_k+B_{jk}c_jc_k+h.c.)=i\sum^{2N}_{jk} M_{jk} \gamma_j\gamma_k,
$$
for any $A,B$? And viceversa, can one always ...
- 1,544
0
votes
0
answers
110
views
Technique for diagonalising this free spinless fermionic Hamiltonian?
How does one diagonalise the following Hamiltonian?
$$
H = \sum_n \epsilon_n c^\dagger_n c_n + g \sum_n (c^\dagger_n c^\dagger_{-n} + c_{-n}c_n),
$$
where $c_n$ is a spineless fermionic op. Clearly we ...
- 1,544
1
vote
1
answer
300
views
How to diagonalise this free fermionic Hamiltonian?
I have the following $1$D fermionic Hamiltonian $H$, given by
$$
H = H^A_0+H
_0^B+H_I^{AB}=\sum_{jk\in A} H_{jk}^Ac^\dagger_j c_k + \sum_{jk\in B} H_{jk}^Bc^\dagger_j c_k + \lambda \sum_{j\in A, \ k \...
- 1,544
5
votes
1
answer
901
views
Proof that the reduced density matrix of free fermions is thermal?
I found this question here but it was partly unanswered. The question remains, namely:
Given a free theory of fermions in a bi-partite system $S=A\cup B$ with Hamiltonian
$$
H = \sum_{ij} t_{ij}a^{\...
- 1,544
0
votes
0
answers
138
views
Calculating the residue as part of Matsubara summation
On page no. $166$ of "Many-body quantum theory in
condensed matter physics" by Henrik Bruus & Karsten Flensberg, while explaining the summation of Matsubara frequency, the following ...
- 405
4
votes
1
answer
350
views
Time reversal symmetry implies that fermions are massless?
In TASI Lectures on Emergence of
Supersymmetry, Gauge Theory and String in
Condensed Matter Systems some continuous limit of lattice model with fermions considered. And on page 6 there is a statement:
...
- 5,707
5
votes
0
answers
262
views
Random Fermion Hopping Model
Consider a random, all to all, complex fermion hopping model on $N$ sites with quenched (Gaussian) disorder, that has a well defined large $N$ limit (aka the SYK2 model). So, we start with free ...
- 814
7
votes
2
answers
2k
views
Anomaly inflow mechanism
I know very simple example of anomaly inflow. See section 4.4 in David Tong: Lectures on Gauge Theory. As I read, such mechanism have some applications in condensed matter and in quantum field theory, ...
- 5,707
3
votes
1
answer
118
views
Relativistic Dispersion In One Space Dimension
I'm now reading Three Lectures On Topological Phases Of Matter by
Edward Witten and face some statements that are unclear to me.
According to lectures:
As I understand, electronic excitations in ...
- 5,707
5
votes
1
answer
1k
views
The correct definition of Klein Factor
Klein factors are the operators which make sure that the anticommutation between the different species is correct during the bosonization procedure. According to this famous review by Jan Von Delft, ...
- 161