1
vote
0answers
13 views

Mean-field approach to quantum phase transitions in Fermi systems

I have a basic confusion concerning the mean-field theory of quantum phase transitions in Fermi systems. Consider as an example the BCS theory of superconductivity in a Dirac fermion system, ...
5
votes
1answer
121 views

What do we mean when we say Bose condensation? And why can't fermions condense if they don't pair?

In common textbooks, we are told that bosons can condense in a single-particle state because of bose statistics and when the system undergoes a bose condensation, the bose field operator obtains a ...
2
votes
1answer
69 views

Hamiltonian for the Periodic Kitaev Model

The Hamiltonian for a system of spinless fermions on a 1D chain (with chemical potential $\mu=0$) is given by $$ H=-\sum_j\left( c^\dagger_{j+1} c_j+h.c.\right)+\Delta \sum_j \left( ...
2
votes
1answer
128 views

Solving the BCS Hamiltonian via the Bogoliubov Transformation

I was doing a calculation in Giamarchi's Introduction to Many Body Physics, chapter 3, on BCS theory and second quantization, and ran into some confusion with the BCS Hamiltonian. The pdf is here for ...
4
votes
1answer
157 views

Entanglement entropy of 1D chiral Fermion

I was told that the entanglement entropy $S_E$ on the ground state of a (1+1)D conformal field theory (CFT) follows the logarithmic behavior $S_E=\frac{c}{12}\ln L$ where $L$ is the length scale ...
6
votes
0answers
340 views

Exact diagonalization by Bogoliubov transformation

I am developing a model of multiple gaps in a square lattice. I simplified the associated Hamiltonian to make it quadratic. In this approximation it is given by, $$ H = \begin{pmatrix} \xi_\mathbf{k} ...
6
votes
1answer
124 views

Does the Fermi surface make sense for “Fermi liquids” with non-uniform charge density?

For a Fermi liquid, the Fermi momentum is determined by the singularity of the Green's function at $\omega=0$, i.e., $G(\omega=0,{\bf k}={\bf k}_F)\to\infty$. Suppose due to an external field or ...
5
votes
2answers
409 views

Why is the Fermi surface stable?

As a condensed matter physicist, I take it for granted that a Fermi surface is stable. But it is stable with respect to what? For instance, Cooper pairing is known as an instability of the Fermi ...
4
votes
2answers
315 views

Imposing anti-commutation relations on fermionic quasi-particles

In many theories of CMT, we assume the nature of quasi-particles (without giving proper justifications). For example, we assume nature of quasi-particles to be fermionic in case of a interacting ...
2
votes
1answer
313 views

Intuitive description of what a “Fermi Gas” really is?

This question is based in the area of material equations of state. I am wanting to know what a Fermi Gas really is. I have searched in several places for a decent description, but I have not found ...
4
votes
2answers
383 views

Has BCS Cooper pair condensate been observed in experiment?

Feshbach resonance in s-wave scattering states a BCS Cooper pair condensation at B-field just above the resonance where the scattering length a <0. Just wondering if the condensation has been ...
3
votes
1answer
169 views

How is the dynamic equilibrium nature of fermi-dirac distribution of particles facilitated?

I read this in Kittel: Introduction to Solid State Physics about deriving that product of electron and hole concentration as independent at a given temperature by the law of mass action. For this ...
4
votes
1answer
901 views

Do derivatives anticommute with Grassmann variables and complex numbers in a many-body path integral?

I'm trying to learn how to do a many-body path integral for both fermions and bosons, and I'm stuck. I'm following Altland and Simons - Condensed Matter Field Theory, chapter 4. On page 167, equation ...
8
votes
2answers
1k views

How do Dirac fermions arise in graphene, and, what significance (if any) does this have for high-energy physics?

Graphene has a honeycomb lattice (in the absence of defects and impurities). By considering the low-energy limit of the half-filled Hubbard model used to model the strongly interacting electron gas we ...