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arXiv:2401.08770 · Physical review. B./Physical review. B

Percolation as a confinement order parameter in Z 2 lattice gauge theories

Simon M. Linsel, Annabelle Bohrdt, Lukas Homeier, Lode Pollet, Fabian Grusdt

Published Dec 2, 2024• 10 citations
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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 $T=\ensuremath{\infty}$ in two dimensions (critical ${T}_{c}$, i.e., finite-$T$ phase transition, in three dimensions) for any nonzero 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 three-dimensional 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.

DOI
10.1103/physrevb.110.l241101

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Exploring confinement transitions in Z2\mathbb{Z}_2Z2​ lattice gauge theories with dipolar atoms beyond one dimension
Confinement of particles into bound states is a phenomenon spanning from high-energy to condensed matter physics, which can be studied in the framework of lattice gauge theories (LGTs). Achieving a comprehensive understanding of confinement continues to pose a major challenge, in particular at finite matter density and in the presence of strong quantum fluctuations. State-of-the-art quantum simulators constitute a promising platform to address this problem. Here we study confinement in coupled chains of Z2\mathbb{Z}_2Z2​ LGTs coupled to matter fields, that can be mapped to a mixed-dimensional (mixD) XXZ model. We perform large-scale numerical matrix-product state calculations to obtain the phase diagram of this model, in which we uncover striped phases formed by the Z2\mathbb{Z}_2Z2​ charges that can be melted at finite temperature or by increasing the tunneling rate. To explore this setting experimentally, we use our quantum simulator constituted by erbium atoms with dipolar interactions in a quantum gas microscope, and observe the predicted melting of a stripe phase by increasing the particle tunneling rate. Our explorative experimental studies of thermal deconfinement of Z2\mathbb{Z}_2Z2​ charges motivate our further theoretical study of the mixD Z2\mathbb{Z}_2Z2​ LGT, in which we predict a confined meson gas at finite temperature and low magnetization where thermal fluctuations destroy stripes but enable spontaneous commensurate spin order. Overall, we demonstrate that our platform can be used to study confinement in Z2\mathbb{Z}_2Z2​ LGTs coupled to matter fields, including long-range interactions and beyond one dimension, paving the way for future research of confinement in the quantum many-body regime.
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