arXiv : Out-of-Equilibrium Dynamics in a U(1) Lattice Gauge Theory via Local Information Flows: Scattering and String Breaking

Artiaco, Claudia; Barata, João; Rico, Enrique

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Preprint
Report number	CERN-TH-2025-191 ; arXiv:2510.16101
Title	Out-of-Equilibrium Dynamics in a U(1) Lattice Gauge Theory via Local Information Flows: Scattering and String Breaking
Author(s)	Artiaco, Claudia (Royal Inst. Tech., Stockholm) ; Barata, João (CERN) ; Rico, Enrique (CERN ; Basque U., Bilbao ; Donostia Intl. Phys. Ctr., San Sebastian)
Document contact	Contact: arXiv
Imprint	2025-10-17
Number of pages	32
Note	32 pages, 17 figures
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-lat ; Particle Physics - Lattice ; quant-ph ; General Theoretical Physics
Abstract	We introduce local information flows as a diagnostic tool for characterizing out-of-equilibrium quantum dynamics in lattice gauge theories. We employ the information lattice framework, a local decomposition of total information into spatial- and scale-resolved contributions, to characterize the propagation and buildup of quantum correlations in real-time processes. Focusing on the Schwinger model, a canonical $(1+1)$-dimensional U(1) lattice gauge theory, we apply this framework to two scenarios. First, in the near-threshold scattering of two vector mesons, we demonstrate that the emergence of correlations at a longer length scale in the information lattice marks the production of heavier scalar mesons. Second, in the dynamics of electric field strings, we clearly distinguish between the confining regime, which evolves towards a steady state with a static correlation profile, and the string-breaking sector. The latter is characterized by dynamic correlation patterns that reflect the sequential formation and annihilation of strings. This information-centric approach provides a direct, quantitative, and interpretable visualization of complex many-body phenomena, offering a promising tool for analyzing dynamics in higher-dimensional gauge theories and experiments on quantum hardware.
Other source	Inspire
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0)

$(a) Information lattice for a product state of qubits, e.g., $\ket{\Omega_\mathrm{s.c.}}$ in Eq.~\eqref{eq:vac_SC}. (b) Illustration of the formula for local information in Eq.~\eqref{eq:local_info_formula} for $i(3.5,3)$; red denotes positive contributions and blue negative ones. The underlying green area shows the subsytem $\mathcal{C}^{3}_{3.5}$. (c) Information per scale for the ground state $\ket{\Omega_{\mathrm{s.c.}}}$ and first excited states $\ket{1_{\mathrm{V,S}}}$ of the Schwinger model in the strong coupling limit in Eqs.~\eqref{eq:vac_SC} and \eqref{eq:vector_meson_strong_coupling}, respectively, with $N=20$. Only scales $\ell < 7$ are shown.$ $\textbf{Left:} Mass spectrum as a function of the expectation value of the squared pseudo momentum operator $P =-i \sum_n \left( \sigma_{n}^- \sigma^z_{n+1} \sigma^+_{n+2}- {\rm h.c.} \right)$ for $ga=1$. Here, $\mathcal{M}_i= E_i-E_{\rm vac}$ is the energy gap to the vacuum of the $i$-th state. The vector ($i=1$) and scalar ($i=20$) states (gold stars) are identified by having the minimal momentum and exhibiting a mass gap. Their identification was further confirmed by checking their parity. Blue circular markers denote finite momentum excitations of the vector meson, which appear only in the lattice theory. The results for mass gaps of the identified states agree quantitatively with those reported in Ref.~\cite{Papaefstathiou:2024zsu}. \textbf{Right:} $I(\ell)$ distribution for the vacuum, vector, and scalar meson states identified in the left panel. $I(\ell)$ is also shown for the same states at $ga=2$, which are identified through the same DMRG procedure. Note that for $ga=2$ the curves of the vector and scalar meson states overlap. We set $ma=10^{-5}$ and $N=40$ in both panels.$ $\textbf{Left:} Mass spectrum as a function of the expectation value of the squared pseudo momentum operator $P =-i \sum_n \left( \sigma_{n}^- \sigma^z_{n+1} \sigma^+_{n+2}- {\rm h.c.} \right)$ for $ga=1$. Here, $\mathcal{M}_i= E_i-E_{\rm vac}$ is the energy gap to the vacuum of the $i$-th state. The vector ($i=1$) and scalar ($i=20$) states (gold stars) are identified by having the minimal momentum and exhibiting a mass gap. Their identification was further confirmed by checking their parity. Blue circular markers denote finite momentum excitations of the vector meson, which appear only in the lattice theory. The results for mass gaps of the identified states agree quantitatively with those reported in Ref.~\cite{Papaefstathiou:2024zsu}. \textbf{Right:} $I(\ell)$ distribution for the vacuum, vector, and scalar meson states identified in the left panel. $I(\ell)$ is also shown for the same states at $ga=2$, which are identified through the same DMRG procedure. Note that for $ga=2$ the curves of the vector and scalar meson states overlap. We set $ma=10^{-5}$ and $N=40$ in both panels.$ Show more plots

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Record created 2025-10-22, last modified 2025-10-24

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