All Questions
Tagged with mathematical-physics condensed-matter
56
questions
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
7
votes
1
answer
220
views
Is IQHE a degenerate case of FQHE? What is the role of topological orders?
(As suggested by Tobias, I shall indicate that I will write "IQHE" for "Integer quantum Hall effect" and "FQHE" for "Fractional quantum Hall effect" below.)
I ...
- 73
0
votes
1
answer
114
views
Why the symmetry is not $Pin(1,3)$ or $Pin(3,1)$ in condensed matter physics?
In usual electron systems (or condensed matter physics), it is well known that $T^2=-1$ and $M^2=-1$, where $T$ and $M$ are time reversal and reflection along some axis. But in general, the symmetry ...
- 51
0
votes
0
answers
60
views
How to compute the Chern number of a quantum dot (zero-dimensional topological insulator) in AI class?
Looking at the periodic table of topological insulators, the AI class (only time reversal symmetry is preserved) has a $\mathbb{Z}$ invariant for zero-dimensional topological insulators. In the review ...
- 39
3
votes
1
answer
135
views
$\rm Tr[log( )]$ calculation to go from BCS to Ginzburg-Landau
It seems like calculating the effective action $|\Delta|^2 + Tr[ln(G^{-1})]$ give the Ginzburg Landau action.
\begin{equation}
G^{-1} =\begin{pmatrix} i\partial_t - H & \Delta \\
\Delta^* & i\...
- 31
2
votes
0
answers
347
views
Mathematically Rigorous Introductory Resources for Condensed Matter Physics
I am looking for textbooks, lecture notes, lecture videos on rigorous introductions to condensed matter physics. I'd prefer to not be referred to monographs for an introduction as they tend to be ...
6
votes
1
answer
482
views
Operators and periodic boundary conditions
Background:
In Ref. 1, a system of $N$ (identical) fermions is considered. The system is enclosed in a cubic box of volume $\Omega=L^3$ and periodic boundary conditions are employed, that is (I'll ...
- 8,094
2
votes
0
answers
61
views
(In)finite lattice in quantum statistical mechanics: validity of phase classifications and TQFT [closed]
I would like to understand the motivation for studying quantum statistical mechanics, such as spin models, on an infinite lattice, or in other word, in the operator algebraic framework. I learned that ...
- 115
4
votes
0
answers
92
views
Extension to excited states of Lieb's Theorem for the Hubbard model
Lieb's theorem shows that for the Hubbard model,
$$\hat{H} = -t \sum_{ \langle \mu,\nu \rangle, \sigma} \hat{c}^\dagger_{\mu \sigma}\hat{c}_{\nu \sigma} + U \sum_\mu \hat{n}_{\mu \uparrow}\hat{n}_{\mu ...
- 1,262
6
votes
0
answers
92
views
Can we determine when the lowest-energy state cannot be annihilated by any local operator, just by inspection of the Hamiltonian?
Relativistic quantum field theory (QFT) has the property that the lowest-energy state cannot be annihilated by any operator that is localized in a finite region of space (references 1,2,3). In other ...
- 54.5k
2
votes
0
answers
103
views
Equivalence between Hamiltonians of different dimensions
Consider a 2D lattice Hamiltonian $H_2$ of symmetry class A and a 1D ladder Hamiltonian $H_1$ of class AIII having the same number of bands and the same TKNN number for each band.
Can $H_2$ and $H_1$ ...
- 29
1
vote
1
answer
152
views
Fourier transform in crystallography: why do the bounds of the fourier integral have to be symmetric about the origin?
When analyzing the diffraction patterns of x-rays on crystals, we utilize the formula for the scattering intensity ($I(\vec{K})$):
$I(\vec{K})\propto \left|\sum_G \rho_G\int_V e^{i(\vec{G}-\vec{K})\...
- 1,581
4
votes
0
answers
148
views
Difficulties in proving the area-law conjecture in higher dimensions
A very famous and important open conjecture in condensed matter physics is the area law of entanglement entropy, which claims that in a locally-interacting quantum many body system, if the ground ...
- 883
1
vote
0
answers
17
views
A conjecture on energy distribution of product states in locally interacting systems
Let $\hat{H}$ be a locally-interacting quantum many body Hamiltonian, for example the nearest-neighbor interacting quantum Heisenberg model or Hubbard model, and let $|\psi \rangle$ be an arbitrary ...
- 883
1
vote
0
answers
91
views
Rigorous Hall conductance
I have been trying to understand the rigorous argument for calculating the hall conductance by averaging over two fluxes by reading this paper {1}. I think I understand the entire derivation, except ...
- 2,123