Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Matrix Product States for Periodic Boundary Conditions   The possibility of a matrix product representation for eigenstates with
energy and momentum zero of a general m-state quantum spin Hamiltonian with
nearest neighbour interaction and periodic boundary condition is considered.
The quadratic algebra used for this representation is generated by 2m operators
which fulfil m^2 quadratic relations and is endowed with a trace. It is shown
that {\em not} every eigenstate with energy and momentum zero can be written as
matrix product state. An explicit counter-example is given. This is in contrast
to the case of open boundary conditions where every zero energy eigenstate can
be written as a matrix product state using a Fock-like representation of the
same quadratic algebra.

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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas