Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories (2409.17142v2)

Abstract: Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. Here, we investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics via a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent excitations and string dynamics.

• The paper introduces a variational circuit, WALA, to efficiently prepare low-energy states in a (2+1)D Z2 lattice gauge theory.
• It simulates charge dynamics by distinguishing confined and deconfined regimes, evidenced by oscillatory behavior in particle separations.
• The study visualizes string dynamics, revealing strong vs. weak confinement regimes and providing insights into string breaking phenomena.

Overview of Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories

The paper "Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories" presents a detailed investigation into the dynamics of lattice gauge theories (LGTs) using a superconducting quantum processor. The primary focus of this research is understanding the behavior of strings and particles in a $\mathbb{Z}_2$ LGT framework, particularly the transition between deconfined and confined dynamics.

Lattice gauge theories serve as a versatile framework to analyze high-energy particle interactions and many-body phenomena in condensed matter physics. However, solving the non-equilibrium dynamics within these systems remains challenging, primarily due to the inadequacies of perturbative methods and the limitations of classical numerical approaches like Monte Carlo simulations and tensor network methods. The authors propose leveraging quantum hardware to simulate LGTs, a promising approach given the potential of quantum processors to manage the complexity of these systems.

Main Contributions

The paper introduces an experimental realization of a (2+1)D $\mathbb{Z}_2$ lattice gauge theory using a two-dimensional grid of superconducting qubits. The researchers focus on several key contributions:

1. Variational Ground State Preparation: The authors develop a variational circuit, termed the Weight Adjustable Loop Ansatz (WALA), to efficiently prepare low-energy states approximating the ground state of the LGT. The circuit's performance is benchmarked across various parameters of the LGT, showing its efficacy in reducing energy error compared to other standard state preparation methods.
2. Simulation of Particle Dynamics: The paper investigates the dynamics of charge excitations by monitoring their separation and spatial distribution over time using quantum simulations. Data indicates a clear distinction between confined and deconfined dynamics, corroborating theoretical predictions of phase transitions in LGTs.
3. String Dynamics: The experiment successfully images string dynamics in the confined phase, revealing two distinct regimes: strong confinement, where transverse fluctuations of strings are frozen, and weak confinement, characterized by significant transverse string fluctuations.
4. String Breaking Phenomena: The researchers explore the resonance condition where string breaking is enhanced, linking it to the interplay between the strength of the magnetic field and electric field parameters. This is crucial for understanding pair production and dynamics in quantum chromodynamics analogs.

Results and Implications

• Phase Transition Dynamics: This experimental work offers quantitative insights into the deconfinement-to-confinement phase transition, demonstrated by the dynamics of separations between charge excitations. The observed oscillatory behavior of charge separation in strong magnetic fields corroborates theoretical models of confined particle dynamics.
• Visualization of String Dynamics: The paper enriches the understanding of string dynamics by providing real-time visualization of string vibrations and breaking, which are otherwise challenging to simulate using classical computational methods.
• Verification through Quantum Simulations: The utilization of a quantum processor for simulating LGTs is an essential step towards validating theoretical models and could act as a prototype for future quantum simulations in more complex gauge theories.

Future Directions

The experimental methodologies established in this research pave the way for further exploration into other types of gauge groups and higher-dimensional lattice gauge theories using quantum processors. Additionally, there is potential for studying real-time dynamics and non-equilibrium phenomena in quantum systems of increasing complexity, fundamentally advancing our understanding of strongly correlated quantum systems.

In summary, this paper presents a significant experimental endeavor in visualizing and understanding the dynamics of charges and strings in lattice gauge theories using quantum computing platforms. The insights gained from this paper hold promise for future developments in both quantum computing and theoretical physics, particularly in the realms of quantum field theories and condensed matter physics.