Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. In this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system's von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity ($CP$) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors.
Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. In this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system's von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity (CP) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors.
Open-system lattice gauge theory (LGT) has so far been developed predominantly in Abelian settings, leaving open how genuinely non-Abelian gauge structure reshapes dissipative real-time dynamics. Here, we study a 1+1D SU(2) Yang--Mills LGT with dynamical matter coupled to a thermal scalar environment through a gauge-preserving Lindblad evolution, which we solve using tensor networks. Starting from a quark--antiquark pair connected by a chromoelectric flux string, we find that the thermal medium melts the string by delocalizing the color charges and screening the flux; on resonance, this dissipative melting competes with and delays coherent string breaking. The thermalization time is non-monotonic in the environment coupling, decreasing through environment-assisted transport at weak dissipation before increasing in a quantum-Zeno regime. In the strong-dephasing limit, a Schrieffer--Wolff expansion maps the dynamics to a classical exclusion process and yields the Liouvillian thermalization time analytically. Beyond these generic open-system effects, the non-Abelian matter structure produces a systematic mesonic bias in the steady state, while the thermalization time decreases with temperature, in contrast to the Abelian Schwinger model trend and in qualitative agreement with pNRQCD studies of the quark--gluon plasma. These results establish a gauge-preserving framework for thermalization and string dynamics in open non-Abelian lattice gauge theories.
Quantum field theories treated as open quantum systems provide a crucial framework for studying realistic experimental scenarios, such as quarkonia traversing the quark-gluon plasma produced at the Large Hadron Collider. In such cases, capturing the complex thermalization process requires a detailed understanding of how particles evolve and interact with a hot medium. Considering the open lattice Schwinger model and using tensor network algorithms, we investigate the thermalization dynamics of mesonic particles in a hot medium, such as the Schwinger boson or the electric flux string. We simulate systems with up to 100 lattice sites, achieving accurate preservation of the electric field parity symmetry, demonstrating the algorithm's robustness and scalability. Our results reveal that the thermalization time increases with stronger dissipation from the environment, increasing environment temperature, higher background electric field and heavier fermion masses. Further, we study the quantum mutual information between the two halves of the flux string connecting a meson's constituent particles and analyze its relation to relevant dynamical observables.
A bstract Quantum field theories treated as open quantum systems provide a crucial framework for studying realistic experimental scenarios, such as quarkonia traversing the quark-gluon plasma produced at the Large Hadron Collider. In such cases, capturing the complex thermalization process requires a detailed understanding of how particles evolve and interact with a hot medium. Considering the open lattice Schwinger model and using tensor network algorithms, we investigate the thermalization dynamics of mesonic particles in a hot medium, such as the Schwinger boson or the electric flux string. We simulate systems with up to 100 lattice sites, achieving accurate preservation of the electric field parity symmetry, demonstrating the algorithm’s robustness and scalability. Our results reveal that the thermalization time increases with stronger dissipation from the environment, increasing environment temperature, higher background electric field and heavier fermion masses. Further, we study the quantum mutual information between the two halves of the flux string connecting a meson’s constituent particles and analyze its relation to relevant dynamical observables.
Abstract The spontaneous formation of particle pairs is one of the most intriguing phenomena in nature. A canonical example is when the potential energy between two elementary particles increases with their separation, as if the particles were confined to one another by a tense string. When the separation exceeds a critical value, new particle pairs can form, which causes the string to break. String-breaking dynamics in quantum chromodynamics, the theory of the strong force, play a fundamental role in high-energy particle collisions and the evolution of matter in the early universe. Simulating the evolution of strings and the formation of composite particles, or hadrons, is a grand challenge of modern physics. Quantum simulators are well suited to study dynamical processes. They are, therefore, expected to provide an edge over conventional methods based on classical computing. However, the experimental capabilities required to simulate the string-breaking phenomenon have not yet been demonstrated, even for simpler prototypical models of the strong force. In this work, we probe, for the first time on a quantum simulator, the spatiotemporally-resolved dynamics of string breaking in a (1+1)-dimensional Z2 lattice gauge theory, a theory that also exhibits confinement of charges. We employ a fully programmable trapped-ion quantum simulator, and emulate the effects of external static charges and strings via site-dependent control of magnetic fields, using a dual array of tightly focused laser beams targeting individual ions. First, we study the effect of confinement on the evolution of isolated charges. We find that these charges freely spread in the absence of string tension, but exhibit localized coherent oscillations as the string tension is increased. Then, we observe and characterize the breaking dynamics of a string initially stretched between two static charges, following an abrupt increase of the string tension. We find that charge pairs appear near the string edges and then spread out into the bulk, thereby identifying a route to dynamical string breaking that is distinct from the conventional Schwinger mechanism. This work, therefore, demonstrates that analog quantum simulators have achieved the control needed to uncover features of string-breaking dynamics, which may ultimately be relevant to nuclear and high-energy physics.
The possible link between entanglement and thermalization, and the dynamics of hadronization are addressed by studying the real-time response of the massive Schwinger model coupled to external sources. This setup mimics the production and fragmentation of quark jets, as the Schwinger model and quantum chromodynamics (QCD) share the properties of confinement and chiral symmetry breaking. By using simulations of quantum dynamics on classical hardware, we study the entanglement between the produced jets, and observe the growth of the corresponding entanglement entropy in time. This growth arises from the increased number of contributing eigenstates of the reduced density matrix with sufficiently large and close eigenvalues. We also investigate the physical nature of these eigenstates, and find that at early times they correspond to fermionic Fock states. We then observe the transition from these fermionic Fock states to mesonlike bound states as a function of time. In other words, we observe how hadronization develops in real time. At late times, the local observables at midrapidity (such as the fermion density and the electric field) approach approximately constant values, suggesting the onset of equilibrium and approach to thermalization. Published by the American Physical Society 2024
Spontaneous particle-pair formation is a fundamental phenomenon in nature. It can, for example, appear when the potential energy between two particles increases with separation, as if they were connected by a tense string. Beyond a critical separation, new particle pairs can form, causing the string to break. String-breaking dynamics in quantum chromodynamics play a vital role in high-energy particle collisions and early universe evolution. Simulating string evolution and hadron formation is, therefore, a grand challenge in modern physics. Quantum simulators, well-suited for studying dynamics, are expected to outperform classical computing methods. However, the required experimental capabilities to simulate string-breaking dynamics have not yet been demonstrated, even for simpler models of the strong force. We experimentally probe, for the first time, the spatiotemporal dynamics of string-breaking in a (1+1)-dimensional Z2 lattice gauge theory using a fully programmable trapped-ion quantum simulator. We emulate external static charges and strings via site-dependent magnetic-field control enabled by a dual array of tightly focused laser beams targeting individual ions. First, we study how confinement affects isolated charges, finding that they freely spread without string tension but exhibit localized oscillations when tension is increased. Then, we observe and characterize string-breaking dynamics of a string stretched between two static charges after an abrupt increase in string tension. Charge pairs appear near the string edges and spread into the bulk, revealing a route to dynamical string-breaking distinct from the conventional Schwinger mechanism. Our work demonstrates that analog quantum simulators have achieved the necessary control to explore string-breaking dynamics, which may ultimately be relevant to nuclear and high-energy physics.