Related papers: On the set of reduced states of translation invariant, infinite quantum systems

On the set of reduced states of translation invariant, infinite quantum systems

URL: http://arxiv.org/abs/2308.14585v2
Date: Sun, 27 Oct 2024 16:24:28 GMT
Title: On the set of reduced states of translation invariant, infinite quantum systems
Authors: Vjosa Blakaj, Michael M. Wolf,
Abstract summary: We show that the set of reduced states of translation invariant, infinite quantum spin chains is not semialgebraic. We also provide evidence that additional elementary transcendental functions cannot lead to a finitary description.
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Abstract: The set of two-body reduced states of translation invariant, infinite quantum spin chains can be approximated from inside and outside using matrix product states and marginals of finite systems, respectively. These lead to hierarchies of algebraic approximations that become tight only in the limit of infinitely many auxiliary variables. We show that this is necessarily so for any algebraic ansatz by proving that the set of reduced states is not semialgebraic. We also provide evidence that additional elementary transcendental functions cannot lead to a finitary description.

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