Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2509.10835

Collective motion in the massive Schwinger model via Tensor Network

Shao, Haiyang, Shile Chen, Shuzhe Shi

Published Sep 13, 2025• 0 citations
arXivHTMLPDF

Abstract

We simulate the real-time dynamics of a massive Schwinger model using the Time-Evolving Block Decimation tensor network algorithm. Starting from a non-equilibrium initial state with localized energy excitation on top of vacuum, we track the subsequent evolution to investigate two distinct physical phenomena. First, by analyzing the system's energy-momentum tensor, we show that this system exhibits hydrodynamic behavior analogous to Bjorken flow at large coupling-to-mass ratio, a signature that diminishes as the coupling weakens, or mass increases. Second, by examining the evolution of the electric field and charge density, we observe the signal of spontaneous parity symmetry breaking phase transition in a dynamical system. The parity-restored regime is marked by ''string breaking'' and efficient charge screening, while the parity-broken regime displays stable propagation of nearly free charges and persistent electric fields connecting them.

DOI
10.48550/arxiv.2509.10835

Related papers

Onset of Bjorken Flow in Quantum Evolution of the Massive Schwinger Model

Shao, Haiyang, Shile Chen, Shuzhe Shi

The onset of hydrodynamics in the hot medium created in relativistic heavy-ion collisions is a crucial theoretical question. A first-principle simulation requires a real-time, non-perturbative calculation of the quantum system. In this Letter, we perform such simulations using the tensor network method, which enables large-scale quantum many-body simulations by retaining only the most essential quantum states for collective behaviors. We focus on the massive Schwinger model, a low-dimensional analog of quantum chromodynamics (QCD), as they share important properties such as confinement and chiral symmetry breaking. Starting from an initial state that puts a localized excitation atop the vacuum and mimics the energy deposition from colliding nuclei, we observe hydrodynamic behavior consistent with Bjorken flow in all relevant degrees of freedom: energy density, fluid velocity, and bulk pressure. The time scale for hydrodynamic onset aligns with the thermalization time of the quantum distribution function.

arXiv:2509.10855•Sep 13, 2025•0 citations

Onset of quantum hydrodynamics in high energy collisions

Haiyang Shao, Shile Chen, Shuzhe Shi

In this work, we perform quantum many-body simulations of the massive Schwinger model. Starting from putting local excitation atop vacuum, we observe the onset of Bjorken-flow-like behavior in the case of strong coupling. Moreover, we observe the signal of the well-known phase transition but in the dynamical evolution of an excited state. The current proceeding focuses on the details of exploring the phase transition with low electric field cut-off.

•Aug 5, 2026•0 citations

Onset of quantum hydrodynamics in high energy collisions

Haiyang Shao, Shile Chen, Shuzhe Shi

In this work, we perform quantum many-body simulations of the massive Schwinger model. Starting from putting local excitation atop vacuum, we observe the onset of Bjorken-flow-like behavior in the case of strong coupling. Moreover, we observe the signal of the well-known phase transition but in the dynamical evolution of an excited state. The current proceeding focuses on the details of exploring the phase transition with low electric field cut-off.

EPJ Web of Conferences•Jan 1, 2026•0 citations

Collective Organization of String Fragmentation

Romuald A. Janik, Maciej A. Nowak, Marek M. Rams +1 more

How coherent confining strings reorganize into hadronic matter is a central open problem in nonequilibrium gauge dynamics. Using real-time tensor-network simulations of the massive Schwinger model, we identify a collective organization underlying string fragmentation. For intermediate masses, the dynamics simplifies and more than $99\%$ of the temporal evolution of the electric-field probability distribution is governed by a single collective mode whose decay tracks the survival probability of the parent string. The extracted survival law exhibits the same Gaussian dependence implied by the Lund world-sheet area law, providing microscopic support for its characteristic area law dependence without assuming the Lund fragmentation mechanism. The same mode controls the transition from the coherent string to the produced mesons, explains the universal non-thermal effective fluid equation of state, and essentially controls the growth of bipartite entanglement through the causal propagation of massive pairs. These results identify collective fragmentation as an organizing principle of coherent string breaking and provide a microscopic perspective on the dynamical origin of a central ingredient of Lund hadronization.

hep-phCross-listedarXiv:2610.20793•Oct 16, 2026

Real-Time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks

Thomas Pichler, Marcello Dalmonte, Rico Ortega, Enrique +2 more

Tensor network algorithms provide a suitable route for tackling real-time-dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1 + 1) dimensions in the presence of dynamical matter for different mass and electric-field couplings, a theory akin to quantum electrodynamics in one dimension, which displays string breaking: The confining string between charges can spontaneously break during quench experiments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric-field and particle fluctuations. We determine a dynamical state diagram for string breaking and quantitatively evaluate the time scales for mass production. We also show that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, thus demonstrating that the Schwinger mechanism is tightly linked to entanglement spreading. To present a variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we test the quality of quantum simulations of these dynamics, quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entanglement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.

•Jan 1, 2016•147 citations

Emergent Nonthermal Fluid from Jets in the Massive Schwinger Model Using Tensor Networks

Romuald A. Janik, Maciej A. Nowak, Marek M. Rams +1 more

We analyze the correlation between the energy, momentum, and spatial entanglement produced by two luminal jets in the massive Schwinger model. Using tensor network methods, we show that for m/g>1/π, in the vicinity of the strong- to weak-coupling transition, a nearly perfect and chargeless effective fluid behavior appears around the midrapidity region with a universal energy-pressure relationship. The evolution of energy and pressure is strongly correlated with the rise of the spatial entanglement entropy, indicating a key role of quantum dynamics. Some of these observations may be used to analyze high multiplicity jet fragmentation events, energy-energy and energy-charge correlators at current collider energies.

arXiv:2502.12901•Physical Review Letters•Nov 20, 2025•6 citations
We simulate the real-time dynamics of a massive Schwinger model using the Time-Evolving Block Decimation tensor network algorithm. Starting from a non-equilibrium initial state with localized energy excitation on top of vacuum, we track the subsequent evolution to investigate two distinct physical phenomena. First, by analyzing the system's energy-momentum tensor, we show that this system exhibits hydrodynamic behavior analogous to Bjorken flow at large coupling-to-mass ratio, a signature that diminishes as the coupling weakens, or mass increases. Second, by examining the evolution of the electric field and charge density, we observe the signal of spontaneous parity symmetry breaking phase transition in a dynamical system. The parity-restored regime is marked by ''string breaking'' and efficient charge screening, while the parity-broken regime displays stable propagation of nearly free charges and persistent electric fields connecting them.
The onset of hydrodynamics in the hot medium created in relativistic heavy-ion collisions is a crucial theoretical question. A first-principle simulation requires a real-time, non-perturbative calculation of the quantum system. In this Letter, we perform such simulations using the tensor network method, which enables large-scale quantum many-body simulations by retaining only the most essential quantum states for collective behaviors. We focus on the massive Schwinger model, a low-dimensional analog of quantum chromodynamics (QCD), as they share important properties such as confinement and chiral symmetry breaking. Starting from an initial state that puts a localized excitation atop the vacuum and mimics the energy deposition from colliding nuclei, we observe hydrodynamic behavior consistent with Bjorken flow in all relevant degrees of freedom: energy density, fluid velocity, and bulk pressure. The time scale for hydrodynamic onset aligns with the thermalization time of the quantum distribution function.
How coherent confining strings reorganize into hadronic matter is a central open problem in nonequilibrium gauge dynamics. Using real-time tensor-network simulations of the massive Schwinger model, we identify a collective organization underlying string fragmentation. For intermediate masses, the dynamics simplifies and more than 99%99\%99% of the temporal evolution of the electric-field probability distribution is governed by a single collective mode whose decay tracks the survival probability of the parent string. The extracted survival law exhibits the same Gaussian dependence implied by the Lund world-sheet area law, providing microscopic support for its characteristic area law dependence without assuming the Lund fragmentation mechanism. The same mode controls the transition from the coherent string to the produced mesons, explains the universal non-thermal effective fluid equation of state, and essentially controls the growth of bipartite entanglement through the causal propagation of massive pairs. These results identify collective fragmentation as an organizing principle of coherent string breaking and provide a microscopic perspective on the dynamical origin of a central ingredient of Lund hadronization.
Tensor network algorithms provide a suitable route for tackling real-time-dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1 + 1) dimensions in the presence of dynamical matter for different mass and electric-field couplings, a theory akin to quantum electrodynamics in one dimension, which displays string breaking: The confining string between charges can spontaneously break during quench experiments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric-field and particle fluctuations. We determine a dynamical state diagram for string breaking and quantitatively evaluate the time scales for mass production. We also show that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, thus demonstrating that the Schwinger mechanism is tightly linked to entanglement spreading. To present a variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we test the quality of quantum simulations of these dynamics, quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entanglement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.
We analyze the correlation between the energy, momentum, and spatial entanglement produced by two luminal jets in the massive Schwinger model. Using tensor network methods, we show that for m/g>1/π, in the vicinity of the strong- to weak-coupling transition, a nearly perfect and chargeless effective fluid behavior appears around the midrapidity region with a universal energy-pressure relationship. The evolution of energy and pressure is strongly correlated with the rise of the spatial entanglement entropy, indicating a key role of quantum dynamics. Some of these observations may be used to analyze high multiplicity jet fragmentation events, energy-energy and energy-charge correlators at current collider energies.