String breaking refers to flux strings breaking, resulting in the production of particle-antiparticle pairs. Now, investigators quantitatively analyze the real-time evolution of string breaking and study the growth of the system entanglement.
Real-Time String Dynamics in 3+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+1D lattice quantum electrodynamics. Using tree tensor networks, we simulate the quench dynamics of electric flux strings in a 3+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 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.
String breaking is at the core of hadronization models of relevance to particle colliders. Yet, studies of string-breaking dynamics rooted in quantum chromodynamics remain fundamentally challenging. Tensor networks enable sign-problem-free studies of static and dynamical properties of lattice gauge theories. In this work, we develop and apply a tensor-network toolkit based on the loop-string-hadron formulation of an SU(2) lattice gauge theory in 1+1 dimensions with dynamical fermions. We apply this toolkit to study static and dynamical aspects of strings and their breaking in this theory. The simple, gauge-invariant, and local structure of the loop-string-hadron states and constraints removes the need to impose non-Abelian constraints in the algorithm, and allows for a systematic computation of observables at increasingly large bosonic cutoffs, and toward the infinite-volume and continuum limits. Our study of static strings yields a determination of the string tension in the continuum and thermodynamic limits. Our study of dynamical string breaking, performed at a fixed lattice spacing and system size, illuminates underlying processes at play during the quench dynamics of a string. The loop, string, and hadron description offers a systematic and intuitive way to diagnose these processes, including string expansion and contraction, endpoint splitting and particle shower, chain scattering events, and inelastic processes resulting from string dissociation and recombination, and particle production. We relate these processes to several features of the dynamics, such as energy transport, entanglement-entropy production, and correlation spreading. This work opens the way to future tensor-network studies of string breaking and particle production in increasingly complex lattice gauge theories.
String Breaking Dynamics and Glueball Formation in a 2+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+1D Z2 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.
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.
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.