4
votes
3answers
291 views

Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of ...
1
vote
0answers
57 views

Should Brillouin zone be a continuous object rather than a discrete one in the thermodynamic limit?

For example, just consider a 1D atom chain with $N$ sites and lattice constant $a=2\pi$, under periodic boundary conditions, the crystal momentum reads as $k=\frac{n}{N}\frac{2\pi}{a}=\frac{n}{N}$, ...
1
vote
1answer
167 views

Relative Change of Volume

Simple question, in materials publications I often see the relative change of volume in a system reported as $$ \Delta \left (V \right )/V $$ is the denominator volume supposed to be initial or the ...
5
votes
3answers
861 views

Entanglement spectrum

What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
3
votes
1answer
442 views

What are Low-lying energy levels?

I am reading about some canonical transformations of the Hamiltonian (of a system consisting of an electron interacting with an ionic lattice) due to Tomanaga and Lee, Low and Pines. One of the ...
17
votes
5answers
4k views

What does it mean for a Hamiltonian or system to be gapped or gapless?

I've read some papers recently that talk about gapped Hamiltonians or gapless systems, but what does it mean? Edit: Is an XX spin chain in a magnetic field gapped? Why or why not?