Percolation as a confinement order parameter in ${\mathbb{Z}}_2$ lattice gauge theories

Abstract

Lattice gauge theories (LGTs) were introduced in 1974 by Wilson to study quark confinement. These models have been shown to exhibit (de-)confined phases, yet it remains challenging to define experimentally accessible order parameters. Here we propose percolation-inspired order parameters (POPs) to probe confinement of dynamical matter in ${\mathbb{Z}}_2$ LGTs using electric field basis snapshots accessible to quantum simulators. We apply the POPs to study a classical ${\mathbb{Z}}_2$ LGT and find a confining phase up to temperature $T=\infty$ in 2D (critical $T_c$, i.e. finite-$T$ phase transition, in 3D) for any non-zero density of ${\mathbb{Z}}_2$ charges. Further, using quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice Fradkin-Shenker phase diagram at $T=0$ and explore the phase diagram at $T>0$. The correlation length exponent coincides with the one of the 3D Ising universality class and we determine the POP critical exponent characterizing percolation. Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators, making them suitable as a probe for quantum spin liquids.

5+9 pages, 4+6 figures

References in corpus (24)

• Fault-tolerant quantum computation by anyons
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Phase diagram of the toric code model in a parallel magnetic field
• Diagnosing Deconfinement and Topological Order
• The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
• The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality
• Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• Self-Correcting Quantum Memories Beyond the Percolation Threshold
• A Derivation of the Fradkin-Shenker Result From Duality: Links to Spin Systems in External Magnetic Fields and Percolation Crossovers
• Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model
• Random percolation as a gauge theory
• Dynamical signatures of thermal spin-charge deconfinement in the doped Ising model
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Quantum percolation of monopole paths and the response of quantum spin ice
• Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes
• Broken Symmetry and Fractionalized Flux Strings in a Staggered U(1) Pure Gauge Theory

Cited by in corpus (8)

• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• Approximately-symmetric neural networks for quantum spin liquids
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• Percolation renormalization group analysis of confinement in ${\mathbb{Z}}_2$ lattice gauge theories
• Independent e- and m-anyon confinement in the parallel field toric code on non-square lattices
• Mass-Assisted Local Deconfinement in a Confined ${\mathbb{Z}}_2$ Lattice Gauge Theory
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions