Journal of High Energy Physics

, 2019:225 | Cite as

Exact bosonic Matrix Product States (and holography)

  • Romuald A. JanikEmail author
Open Access
Regular Article - Theoretical Physics


We derive an exact formula for a matrix product state (MPS) representation (or a PEPS in higher number of dimensions) of the ground state of translationally invariant bosonic lattice systems in terms of a single one-dimensional Euclidean quantum mechanical path integral with sources. We explicitly evaluate the general formula in the special case of the one-dimensional Klein-Gordon harmonic chain, being a spatial discretization of 1+1 dimensional free boson QFT, obtaining an exact MPS with an infinite dimensional bond space. We analytically diagonalize the transfer matrix obtaining two Fock spaces with continuous modes and check that the exact MPS construction reproduces the correct correlation functions. We also comment on possible holographic interpretations.


AdS-CFT Correspondence Field Theories in Lower Dimensions 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute of PhysicsJagiellonian UniversityKrakówPoland

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