Matrix product states for gauge field theories

Abstract

The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study non-equilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.

expanded discussion on real-time evolution, matching the published version

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• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Ab-initio Determination of Light Hadron Masses
• The iTEBD algorithm beyond unitary evolution
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• Light Hadron Masses from Lattice QCD
• Entanglement renormalization and gauge symmetry
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• S matrix from matrix product states

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