Real Time Dynamics and Confinement in the $\mathbb{Z}_{n}$ Schwinger-Weyl lattice model for 1+1 QED

Giuseppe Magnifico1,2, Marcello Dalmonte3,4, Paolo Facchi5,6, Saverio Pascazio5,6,7, Francesco V. Pepe5,6, and Elisa Ercolessi1,2

1Dipartimento di Fisica e Astronomia dell'Università di Bologna, I-40127 Bologna, Italy
2INFN, Sezione di Bologna, I-40127 Bologna, Italy
3Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
4SISSA, Via Bonomea 265, I-34136 Trieste, Italy
5Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
6INFN, Sezione di Bari, I-70126 Bari, Italy
7Istituto Nazionale di Ottica (INO-CNR), I-50125 Firenze, Italy

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Abstract

We study the out-of-equilibrium properties of $1+1$ dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian $\mathbb{Z}_{n}$ gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.

Gauge theories represent a fundamental building block of our understanding of physical laws. Despite their elegance, their real-time dynamics is often difficult to solve on classical computers, due to their complexity, that grows exponentially with the system size.

In recent years, several approaches leveraging on quantum information have enabled controlled simulations of such theories in real-time. These novel tools, based on a class of wave-functions known as tensor networks, offer unique opportunities to understand the spreading of quantum correlations, and in particular entanglement, in gauge theories.

We study here the Schwinger-Weyl lattice model, in which both space and the gauge degree of freedom are discretized, in such a way that standard quantum electrodynamics in 1+1 dimensions is reproduced in the continuum limit.

We analyze the stability of the Dirac vacuum, the mechanism of pair (particle/antiparticle) production, as well as the intriguing string breaking mechanism. Strings behave very differently, depending on the particle mass and charge (coupling), and their dynamics leaves characteristics footprints in the entanglement evolution. A number of out-of-equilibrium features are unhearted and scrutinized.

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[7] Roberto Verdel, Fangli Liu, Seth Whitsitt, Alexey V. Gorshkov, and Markus Heyl, "Real-time dynamics of string breaking in quantum spin chains", arXiv:1911.11382.

[8] Umberto Borla, Ruben Verresen, Fabian Grusdt, and Sergej Moroz, "Confined Phases of One-Dimensional Spinless Fermions Coupled to Z<SUB>2</SUB> Gauge Theory", Physical Review Letters 124 12, 120503 (2020).

[9] Nouman Butt, Simon Catterall, Yannick Meurice, Ryo Sakai, and Judah Unmuth-Yockey, "Tensor network formulation of the massless Schwinger model with staggered fermions", Physical Review D 101 9, 094509 (2020).

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[11] Bipasha Chakraborty, Masazumi Honda, Taku Izubuchi, Yuta Kikuchi, and Akio Tomiya, "Digital Quantum Simulation of the Schwinger Model with Topological Term via Adiabatic State Preparation", arXiv:2001.00485.

[12] Joseph Vovrosh and Johannes Knolle, "Confinement and Entanglement Dynamics on a Digital Quantum Computer", arXiv:2001.03044.

[13] Riccardo Javier Valencia Tortora, Pasquale Calabrese, and Mario Collura, "Relaxation of the order-parameter statistics and dynamical confinement", arXiv:2005.01679.

[14] Piotr Sierant, Maciej Lewenstein, and Jakub Zakrzewski, "Polynomially filtered exact diagonalization approach to many-body localization", arXiv:2005.09534.

[15] Gianluca Lagnese, Federica Maria Surace, Márton Kormos, and Pasquale Calabrese, "Confinement in the spectrum of a Heisenberg-Ising spin ladder", arXiv:2005.03131.

[16] Titas Chanda, Ruixiao Yao, and Jakub Zakrzewski, "Coexistence of localized and extended phases: Many-body localization in a harmonic trap", arXiv:2004.00954.

[17] Yannick Meurice, "Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories", arXiv:2003.10986.

[18] Flavia B. Ramos, Mate Lencses, J. C. Xavier, and Rodrigo G. Pereira, "Confinement and bound states of bound states in a transverse-field two-leg Ising ladder", arXiv:2005.03145.

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The above citations are from Crossref's cited-by service (last updated successfully 2020-07-13 22:24:45) and SAO/NASA ADS (last updated successfully 2020-07-13 22:24:46). The list may be incomplete as not all publishers provide suitable and complete citation data.