Abstract
The formalism of matrix product states is used to perform a numerical study of 1+1 dimensional QED -- also known as the (massive) Schwinger model -- in the presence of an external static `quark' and `antiquark'. We obtain a detailed picture of the transition from the confining state at short interquark distances to the broken-string `hadronized' state at large distances and this for a wide range of couplings, recovering the predicted behavior both in the weak and strong coupling limit of the continuum theory. In addition to the relevant local observables like charge and electric field, we compute the (bipartite) entanglement entropy and show that subtraction of its vacuum value results in a UV-finite quantity. We find that both string formation and string breaking leave a clear imprint on the resulting entropy profile. Finally, we also study the case of fractional probe charges, simulating for the first time the phenomenon of partial string breaking.
Highlights
The confinement of color charge in quantum chromodynamics is one of the beautiful key mechanisms of the standard model
In addition to the relevant local observables like charge and electric field, we compute the entanglement entropy and show that subtraction of its vacuum value results in a UV-finite quantity. We find that both string formation and string breaking leave a clear imprint on the resulting entropy profile
We do this for the simplest nontrivial quantum gauge field theory: (1 þ 1)-dimensional quantum electrodynamics (QED2), known as the Schwinger model [23]
Summary
The confinement of color charge in quantum chromodynamics is one of the beautiful key mechanisms of the standard model. We study how confinement and string breaking show up in the Hamiltonian setup, as opposed to the Euclidean path integral setup of lattice Monte Carlo simulations We do this for the simplest nontrivial quantum gauge field theory: (1 þ 1)-dimensional quantum electrodynamics (QED2), known as the Schwinger model [23]. The direct access to the quantum state allows for a relatively easy calculation of all local observables In this way we could extract the static interquark potential, and, for instance, determine the detailed spatial profile of the electric string or the precise charge distribution of the light fermions around the probe charges.
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