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:2609.04114

Real-Time String Dynamics in $3+1$D Lattice Quantum Electrodynamics

Helen Zwölfer, Giovanni Cataldi, Umberto Borla, Jad C. Halimeh

hep-latcond-mat.quant-gashep-phhep-thquant-phSubmitted Sep 3, 2026• Announced Sep 4, 2026• 0 citations
arXivHTMLPDF

Abstract

Understanding real-time string dynamics in three spatial dimensions is essential for connecting quantum simulations of lattice gauge theories (LGTs) to the physical dimensionality of QED and QCD, where transverse fluctuations and competing local processes proliferate. We present the first real-time simulations of string breaking in $3+1$D lattice quantum electrodynamics. Using tree tensor networks, we simulate the quench dynamics of electric flux strings in a $3\!+\!1$D U(1) LGT with dynamical matter. At strong coupling, the string breaks resonantly at a sharp resonance condition of mass and gauge couplings, converting electric energy into matter--antimatter pairs that screen the static charges. Off resonance, we classify all competing channels---pair production, string deformations and extensions, and flux loops---whose multiplicity, extensive for pair production and flux loops, depletes the string sector even far from resonance. A channel-resolved perturbation theory quantitatively reproduces these dynamics and their Fourier spectrum. Our results establish diagnostics and benchmarks for upcoming quantum simulators of higher-dimensional LGTs.

Comments
$10+2+5$ pages, $4+0+4$ figures

Related papers

String Breaking Dynamics and Glueball Formation in a $2+1$D Lattice Gauge Theory

Kaidi Xu, Umberto Borla, Sergej Moroz +1 more

With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the $2+1$D $\mathbb{Z}_2$ LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.

arXiv:2507.01950•Jul 2, 2025•0 citations

String Breaking and Glueball Dynamics in $2+1$D Quantum Link Electrodynamics

Jiahao Cao, Rohan Joshi, Yizhuo Tian +2 more

At the heart of quark confinement and hadronization, the physics of flux strings has recently become a focal point in the field of quantum simulation of high-energy physics (HEP). Despite considerable progress, a detailed understanding of the behavior of flux strings in quantum simulation-relevant lattice formulations of gauge theories has remained limited to the lowest truncations of the gauge field, which are severely limited in their ability to draw conclusions about the quantum field theory limit. Here, we employ tensor network simulations to investigate the behavior of flux strings in a quantum link formulation of $2+1$D quantum electrodynamics (QED) with a spin-$1$ representation of the gauge field. We first map out the ground-state phase diagram of this model in the presence of two spatially separated static charges, revealing distinct microscopic processes responsible for string breaking, including a two-stage breaking mechanism not possible in the spin-$\frac{1}{2}$ formulation. Starting in different initial product state string configurations, we then explore far-from-equilibrium quench dynamics across various parameter regimes, demonstrating genuine $2+1$D real-time string breaking and glueball-like bound state formation, with the latter not possible in the spin-$\frac{1}{2}$ formulation. In and out of equilibrium, we consider different values and placements of the static charges. Finally, we provide efficient qudit circuits for a quantum simulation experiment in which our results can be observed in state-of-the-art ion-trap setups. Our findings lay the groundwork for quantum simulations of flux strings towards the quantum field theory limit.

hep-latCross-listedarXiv:2601.16166•Jan 23, 2026•0 citations

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

String-Breaking Mechanism in a Lattice Schwinger Model Simulator

Ying Liu, Wei-Yong Zhang, Zi-Hang Zhu +3 more

String breaking is a fundamental concept in gauge theories, describing the decay of a flux string connecting two charges through the production of particle-antiparticle pairs. This phenomenon is particularly important in particle physics, notably in quantum chromodynamics, and plays a crucial role in condensed matter physics. However, achieving a theoretical understanding of this nonperturbative effect is challenging, as conventional numerical approaches often fall short and require substantial computational resources. On the experimental side, studying these effects necessitates advanced setups, such as high-energy colliders, which makes direct observation difficult. Here, we report an experimental investigation of the string breaking mechanism in a one-dimensional U(1) lattice gauge theory using an optical lattice quantum simulator. By deterministically preparing initial states of varying lengths with fixed charges at each end, and adiabatically tuning the mass and string tension, we observed in situ microscopic confined phases that exhibit either string or broken-string states. Further analysis reveals that string breaking occurs under a resonance condition, leading to the creation of new particle-antiparticle pairs. These findings offer compelling evidence of string breaking and provide valuable insights into the intricate dynamics of lattice gauge theories. Our work underscores the potential of optical lattices as controllable quantum simulators, enabling the exploration of complex gauge theories and their associated phenomena.

arXiv:2411.15443•Physical Review Letters•Jun 26, 2025•9 citations

Realizing string breaking dynamics in a Z 2 lattice gauge theory on quantum hardware

Constantia Alexandrou, Andreas Athenodorou, Kostas Blekos +2 more

We investigate static and dynamical aspects of string breaking in a Z 2 lattice gauge theory coupled to Kogut-Susskind staggered fermions. Using tensor network simulations, we demonstrate that the static potential as well as the site-resolved configuration of the matter sites and gauge links allows us to identify the regimes in which string breaking occurs. Furthermore, we develop a variational quantum eigensolver that allows for reliably preparing the ground state of the theory in both the absence and presence of static charges and to capture the static aspects of the phenomenon. Carrying out state preparation on real quantum hardware for up to 19 qubits, we demonstrate its suitability for current quantum devices. In addition, we study the real-time dynamics of a flux tube between two static charges using both tensor networks and quantum hardware. Using a trotterization for the time-evolution operator, we are able to show that the breaking process starts with the creation of charges inside the string. These eventually redistribute toward the static charges and screen them, which leads to the breaking of the flux tube.

arXiv:2504.13760•Physical review. D/Physical review. D.•Nov 12, 2025•8 citations

U(1) lattice gauge theory and string roughening on a triangular Rydberg array

Lisa Bombieri, Torsten V. Zache, Hannes Pichler +1 more

Lattice gauge theories (LGTs) describe fundamental interactions in particle physics. A central phenomenon in these theories is confinement, which binds quarks and antiquarks into hadrons through the formation of string-like flux tubes of gauge fields. Simulating confinement dynamics is a challenging task, but recent advances in quantum simulation are enabling the exploration of LGTs in regimes beyond the reach of classical computation. For analog devices, a major difficulty is the realization of strong plaquette interactions, which generate string fluctuations that can drive a roughening transition. Understanding string roughening -- where strong transversal functions lead to an effective restoration of translational symmetry at long distances -- is of central importance in the study of confinement. In this work, we show that string roughening emerges naturally in an analog Rydberg quantum simulator. We first map a triangular Rydberg array onto a (2+1)D U(1) LGT where plaquette terms appear as first-order processes. We study flux strings connecting static charges and demonstrate that, near a deconfined quantum critical point, the string exhibits logarithmic growth of its transverse width as the separation between charges increases, along with the universal Lüscher correction to the confining potential -- both signatures of string roughening. Finally, we investigate the real-time dynamics of an initially rigid string, observing large fluctuations after quenching into the roughening regime, as well as string breaking via particle-pair creation. Our results indicate that rough strings can be realized in experimentally accessible quantum simulators, opening the door to detailed studies of how strong fluctuations influence string-breaking dynamics.

quant-pharXiv:2602.06123•Feb 9, 2026•0 citations
Real-Time String Dynamics in 3+13+13+1D Lattice Quantum Electrodynamics
Understanding real-time string dynamics in three spatial dimensions is essential for connecting quantum simulations of lattice gauge theories (LGTs) to the physical dimensionality of QED and QCD, where transverse fluctuations and competing local processes proliferate. We present the first real-time simulations of string breaking in 3+13+13+1D lattice quantum electrodynamics. Using tree tensor networks, we simulate the quench dynamics of electric flux strings in a 3 ⁣+ ⁣13\!+\!13+1D U(1) LGT with dynamical matter. At strong coupling, the string breaks resonantly at a sharp resonance condition of mass and gauge couplings, converting electric energy into matter--antimatter pairs that screen the static charges. Off resonance, we classify all competing channels---pair production, string deformations and extensions, and flux loops---whose multiplicity, extensive for pair production and flux loops, depletes the string sector even far from resonance. A channel-resolved perturbation theory quantitatively reproduces these dynamics and their Fourier spectrum. Our results establish diagnostics and benchmarks for upcoming quantum simulators of higher-dimensional LGTs.
String Breaking Dynamics and Glueball Formation in a 2+12+12+1D Lattice Gauge Theory
With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the 2+12+12+1D Z2\mathbb{Z}_2Z2​ LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.
String Breaking and Glueball Dynamics in 2+12+12+1D Quantum Link Electrodynamics
At the heart of quark confinement and hadronization, the physics of flux strings has recently become a focal point in the field of quantum simulation of high-energy physics (HEP). Despite considerable progress, a detailed understanding of the behavior of flux strings in quantum simulation-relevant lattice formulations of gauge theories has remained limited to the lowest truncations of the gauge field, which are severely limited in their ability to draw conclusions about the quantum field theory limit. Here, we employ tensor network simulations to investigate the behavior of flux strings in a quantum link formulation of 2+12+12+1D quantum electrodynamics (QED) with a spin-111 representation of the gauge field. We first map out the ground-state phase diagram of this model in the presence of two spatially separated static charges, revealing distinct microscopic processes responsible for string breaking, including a two-stage breaking mechanism not possible in the spin-12\frac{1}{2}21​ formulation. Starting in different initial product state string configurations, we then explore far-from-equilibrium quench dynamics across various parameter regimes, demonstrating genuine 2+12+12+1D real-time string breaking and glueball-like bound state formation, with the latter not possible in the spin-12\frac{1}{2}21​ formulation. In and out of equilibrium, we consider different values and placements of the static charges. Finally, we provide efficient qudit circuits for a quantum simulation experiment in which our results can be observed in state-of-the-art ion-trap setups. Our findings lay the groundwork for quantum simulations of flux strings towards the quantum field theory limit.
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.
String breaking is a fundamental concept in gauge theories, describing the decay of a flux string connecting two charges through the production of particle-antiparticle pairs. This phenomenon is particularly important in particle physics, notably in quantum chromodynamics, and plays a crucial role in condensed matter physics. However, achieving a theoretical understanding of this nonperturbative effect is challenging, as conventional numerical approaches often fall short and require substantial computational resources. On the experimental side, studying these effects necessitates advanced setups, such as high-energy colliders, which makes direct observation difficult. Here, we report an experimental investigation of the string breaking mechanism in a one-dimensional U(1) lattice gauge theory using an optical lattice quantum simulator. By deterministically preparing initial states of varying lengths with fixed charges at each end, and adiabatically tuning the mass and string tension, we observed in situ microscopic confined phases that exhibit either string or broken-string states. Further analysis reveals that string breaking occurs under a resonance condition, leading to the creation of new particle-antiparticle pairs. These findings offer compelling evidence of string breaking and provide valuable insights into the intricate dynamics of lattice gauge theories. Our work underscores the potential of optical lattices as controllable quantum simulators, enabling the exploration of complex gauge theories and their associated phenomena.
We investigate static and dynamical aspects of string breaking in a Z 2 lattice gauge theory coupled to Kogut-Susskind staggered fermions. Using tensor network simulations, we demonstrate that the static potential as well as the site-resolved configuration of the matter sites and gauge links allows us to identify the regimes in which string breaking occurs. Furthermore, we develop a variational quantum eigensolver that allows for reliably preparing the ground state of the theory in both the absence and presence of static charges and to capture the static aspects of the phenomenon. Carrying out state preparation on real quantum hardware for up to 19 qubits, we demonstrate its suitability for current quantum devices. In addition, we study the real-time dynamics of a flux tube between two static charges using both tensor networks and quantum hardware. Using a trotterization for the time-evolution operator, we are able to show that the breaking process starts with the creation of charges inside the string. These eventually redistribute toward the static charges and screen them, which leads to the breaking of the flux tube.
Lattice gauge theories (LGTs) describe fundamental interactions in particle physics. A central phenomenon in these theories is confinement, which binds quarks and antiquarks into hadrons through the formation of string-like flux tubes of gauge fields. Simulating confinement dynamics is a challenging task, but recent advances in quantum simulation are enabling the exploration of LGTs in regimes beyond the reach of classical computation. For analog devices, a major difficulty is the realization of strong plaquette interactions, which generate string fluctuations that can drive a roughening transition. Understanding string roughening -- where strong transversal functions lead to an effective restoration of translational symmetry at long distances -- is of central importance in the study of confinement. In this work, we show that string roughening emerges naturally in an analog Rydberg quantum simulator. We first map a triangular Rydberg array onto a (2+1)D U(1) LGT where plaquette terms appear as first-order processes. We study flux strings connecting static charges and demonstrate that, near a deconfined quantum critical point, the string exhibits logarithmic growth of its transverse width as the separation between charges increases, along with the universal Lüscher correction to the confining potential -- both signatures of string roughening. Finally, we investigate the real-time dynamics of an initially rigid string, observing large fluctuations after quenching into the roughening regime, as well as string breaking via particle-pair creation. Our results indicate that rough strings can be realized in experimentally accessible quantum simulators, opening the door to detailed studies of how strong fluctuations influence string-breaking dynamics.