Questions tagged [condensed-matter]

Condensed matter physics deals with properties of condensed phases of matter, seeking to understand these phases by using the fundamental laws, e.g. quantum statistical mechanics, etc. The familiar condensed phases are solids and liquids while more exotic condensed phases include the superconducting phase, the ferromagnetic and antiferromagnetic phases of spins on atomic lattices, and the Bose–Einstein condensate in cold atomic systems.

Filter by
Sorted by
Tagged with
5
votes
1answer
343 views

Are framed manifolds cubulatable?

Let's say an $n$-manifold is cubulated if it is glued out of cubes $[0,1]^n$ in a way that looks locally like the standard cubulation of $\mathbb R^n$. For instance, the face $[0,1]^{k-1} \times \{1\} ...
10
votes
3answers
255 views

Generalization of Drinfeld double to comodule algebras

Let $ \mathcal C $ be a monoidal category. Then $ \mathcal C $ is both a left and right module category over itself. Moreover, the Drinfeld centre of $ \mathcal C $ can be defined as the category of ...
6
votes
1answer
117 views

Relationship between irreducible representations of the Schur covering group and elements of $H^2(G,U(1))$

Let $G$ be a finite group and let $D(g)$ be a projective representation of $G$ i.e. \begin{equation} D(g) D(h) = e^{i \omega(g,h)} D(gh) \end{equation} These can be classified by the equivalence ...
7
votes
0answers
156 views

Why are Levin-Wen/Turaev-Viro models said to be non-chiral?

I'd like to bring together the following two notions of "non-chiral": On the abstract algebraic side, a modular fusion category describing the anyon content of some physical system is said to be non-...
6
votes
1answer
190 views

Is there a simple argument that shows that two unitary fusion categories are Morita equivalent if their Drinfeld centers are equal?

By Morita equivalent I mean that there is an invertible bi-module between the two fusion categories. [Feel free to replace the Drinfeld centers being "equal" by an appropriate categorial notion of "...
6
votes
0answers
149 views

Are 2d gauge anomalies determined by genus-one data?

Let $G$ be a (finite, say) group and $\alpha \in \mathrm{H}^3(\mathrm{B}G; \mathrm{U}(1))$ a 3-cohomology class. For each oriented 3-manifold $X^3$ equipped with a $G$-bundle $P : X \to \mathrm{B}G$, ...
5
votes
0answers
282 views

A property of slant product in group cohomology

Recently I have encountered a problem concerning the property of slant product in group cohomology. The problem is as follows: Consider a finite group G (can have anti-unitary operations). And there ...
9
votes
2answers
1k views

Relation between the homotopy classes of maps on a torus, and maps on a sphere

In modern condensed matter physics, one is often interested in the homotopy classes of mappings from a $d$-dimensional torus $$\mathbb{T}^d=\underbrace{S^1\times\ldots \times S^1}_d$$ (corresponding ...
6
votes
1answer
688 views

What is a Fermi surface?

I posted this question on the physics site, but then received immediately the sense that I won't be able to understand answers even if they come. So I hope it's all right if I post it here, since ...
7
votes
1answer
319 views

Regularizing divergent sums over lattices

Vertex-models and nearest-neighbor models with translation-invariant local energy functions on an infinite lattice have the troublesome feature that the sum of the local energies diverges. A standard ...
5
votes
1answer
247 views

Vorticial ground states for the O(2) rotor model

Is there a sensible notion of a ground state for the classical $O(2)$ rotor model "frustrated at infinity by a single unit of counterclockwise vorticity"? Here is a picture of the kind of thing I mean,...