Abstract
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.
Highlights
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions
We have shown that Tensor Networks (TN) methods can simulate Lattice Gauge Theories (LGT) in three spatial dimensions, in the presence of matter and charge imbalance, exploring those regimes where other known numerical strategies struggle
We have investigated collective phenomena of lattice Quantum Electrodynamics (QED) which stand at the forefront of the current research efforts, including quantum phase diagrams, confinement issues, and the string breaking mechanism at equilibrium
Summary
(upper panel), for the system undergoes a transition between two regimes, analogously to the (1 + 1)D and (2 + 1)D cases[25,37,47]: for large positive masses, the system approaches the bare vacuum, while for large negative masses, the system is arranged into a crystal of charges, a highly degenerate state in the semiclassical limit (t → 0) due to the exponential number of electric field configurations allowed We track this transition by monitoring the average matter density ρ where n^x. We expect that for small positive masses m, the vacuum inside the plates will spontaneously polarize to an effective dielectric, by creating particle and antiparticle pairs to screen the electric field from the plates, into an energetically favorable configuration We observe this phenomenon by monitoring the charge density function along the direction μx orthogonal to the plates qcðdÞ 1⁄4. For large negative m, the charge distribution is roughly uniform
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