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Matrix product states for Hamiltonian lattice gauge theories

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arxiv 1411.0020 v1 pith:NHVYJSS5 submitted 2014-10-31 hep-lat cond-mat.str-el

Boye Buyens , Karel Van Acoleyen , Jutho Haegeman , Frank Verstraete This is my paper · ORCID
classification hep-latcond-mat.str-el
keywords gaugestatesquantumsimulationdimensionalfullfurthermorehamiltonian
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Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.

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Cited by 2 Pith papers

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  1. Developing techniques for Simulation of SU(3) Quantum Field Theories on State-of-the-Art Quantum Devices

    quant-ph 2025-02 conditional novelty 6.0 of 10

    A compilation of NISQ-era circuit designs for SU(3) lattice QCD and 3-flavor neutrino oscillations, plus a numerical finding that all-three-flavor initial neutrino states maximize persistent quantum magic.

  2. Critical behavior of the Schwinger model via gauge-invariant VUMPS

    hep-lat 2024-12 conditional novelty 6.0 of 10

    The gauge-invariant VUMPS algorithm determines the continuum critical mass of the Schwinger model as (m/g)c = 0.333556(5) and produces data collapse consistent with Ising critical exponents.

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