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arXiv · 1808.00976

Continuous Tensor Network States for Quantum Fields

Antoine Tilloy·J. Ignacio Cirac
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Abstract

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean invariant, and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending Projected Entangled Pair States (PEPS), we propose a generalization bearing similarities with the continuum Multi-scale Entanglement Renormalization Ansatz (cMERA).

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Antoine Tilloy, J. Ignacio Cirac. 2018-08-02. Continuous Tensor Network States for Quantum Fields. https://doi.org/10.1103/physrevx.9.021040

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