Exact bosonic Matrix Product States (and holography)

Abstract

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.

28 pages, 3 figures; v2: various explanations added, journal version

References in corpus (6)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix product states represent ground states faithfully
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Path-Integral Complexity for Perturbed CFTs
• Towards holography for quantum mechanics

Cited by in corpus (2)

• On the generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions
• Entanglement distillation toward minimal bond cut surface in tensor networks