On Matrix Product States for Periodic Boundary Conditions

Details On Matrix Product States for Periodic Boundary Conditions On Matrix Product States for Periodic Boundary Conditions

1999-10-27

arxiv.org/abs/cond-mat/9910452v1

Physics

Condensed Matter

7 pages, latex

Scientific paper

10.1088/0305-4470/33/14/102

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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