Continuous Tensor Network States for Quantum Fields

2018/08/31 by Antoine Tilloy, J. Ignacio Cirac · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Euclidean geometry #Invariant (physics) #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum state #Renormalization #Tensor (intrinsic definition) #Tensor contraction #Tensor field #Tensor product #cond-mat.str-el #hep-lat #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevx.9.021040

published as Phys. Rev. X 9, 021040 (2019) · 16 pages, 5 figures, close to published version

openalex publication_date 2019/05/28 · arxiv created 2019/06/08 · arxiv updated 2019/06/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/06

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 to spatial dimensions d 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, we propose a generalization bearing similarities with the continuum multiscale entanglement renormalization ansatz.

Citations

• Approximating Gibbs states of local Hamiltonians efficiently with projected entangled pair states
• Colloquium: Area laws for the entanglement entropy
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• Solving gapped Hamiltonians locally
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• Entropy and Area
• Entanglement spectrum of a topological phase in one dimension
• Class of Quantum Many-Body States That Can Be Efficiently Simulated
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
• Entanglement Renormalization for Quantum Fields in Real Space
• The density-matrix renormalization group
• Nonabelions in the fractional quantum hall effect

Cited by

• Pushing Tensor Networks to the Limit

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• Continuum limit of gauged tensor network states