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.

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1answer
153 views

What is the etale homotopy type of the Witt group of braided fusion categories?

The Witt group $\mathcal{W}$ of braided fusion categories (see also the sequel paper) can be defined over any field; I am happy to restrict to characteristic $0$ if it matters. Is $\mathbb k \...
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1answer
369 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\} ...
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3answers
315 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
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1answer
135 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
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0answers
174 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-...
7
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1answer
212 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
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0answers
153 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
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316 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
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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
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1answer
773 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
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1answer
328 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
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1answer
248 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,...