# Bond dimension witnesses and the structure of homogeneous matrix product states

@article{Navascus2015BondDW, title={Bond dimension witnesses and the structure of homogeneous matrix product states}, author={Miguel Navascu{\'e}s and Tam'as V'ertesi}, journal={arXiv: Quantum Physics}, year={2015} }

For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b… CONTINUE READING

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