Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-dimensional generalizations of the Berry curvature   A family of finite-dimensional quantum systems with a non-degenerate ground
state gives rise to a closed 2-form on the parameter space: the curvature of
the Berry connection. Its cohomology class is a topological invariant of the
family. We seek generalizations of the Berry curvature to families of gapped
many-body systems in D spatial dimensions. Field theory predicts that in
spatial dimension D the analog of the Berry curvature is a closed (D+2)-form on
the parameter space (the Wess-Zumino-Witten form). We construct such closed
forms for arbitrary families of interacting lattice systems in all dimensions.
In the special case of systems of free fermions in one dimension, we show that
these forms can be expressed in terms of the Bloch-Berry connection on the
product of the Brillouin zone and the parameter space. In the case of families
of Short-Range Entangled systems, we argue that integrals of our forms over
spherical cycles are quantized.

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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys