Continuum limits of Matrix Product States

Abstract

We determine which translationally invariant matrix product states have a continuum limit, that is, which can be considered as discretized versions of states defined in the continuum. To do this, we analyse a fine-graining renormalization procedure in real space, characterise the set of limiting states of its flow, and find that it strictly contains the set of continuous matrix product states. We also analyse which states have a continuum limit after a finite number of a coarse-graining renormalization steps. We give several examples of states with and without the different kinds of continuum limits.

7 pages, 2 figures. New version: somewhat expanded, some explanations added. Close to published version

References in corpus (5)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Assessing non-Markovian dynamics
• Continuous Matrix Product States for Quantum Fields
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Irreducible forms of Matrix Product States: Theory and Applications

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