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arXiv:2504.17000

Bosonic vs. Fermionic Matter in Quantum Simulations of $2+1$D Gauge Theories

N. S. Srivatsa, Jesse J. Osborne, Debasish Banerjee, Jad C. Halimeh

Published Apr 23, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum link models extend lattice gauge theories beyond the traditional Wilson formulation and present promising candidates for both digital and analog quantum simulations. Fermionic matter coupled to $U(1)$ quantum link gauge fields has been extensively studied, revealing a phase diagram that includes transitions from the columnar phase in the quantum dimer model to the resonating valence bond phase in the quantum link model, potentially passing through a disordered liquid-like phase. In this study, we investigate the model coupled to hardcore bosons and identify a similar phase structure, though with a more intricate mixture of phases around the transition. Our analysis reveals that near the transition region, a narrow and distinct ordered phase emerges, characterized by gauge fields forming plaquette configurations with alternating orientations, which is then followed by a thinner, liquid-like regime. This complexity primarily stems from the differences in particle statistics, which manifest prominently when the matter degrees of freedom become dynamic. Notably, our findings suggest that bosons can effectively replace fermions in lattice gauge theory simulations, offering solutions to the challenges posed by fermions in both digital and analog quantum simulations.

DOI
10.48550/arxiv.2504.17000

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The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a \mathrm{U}(1) U ( 1 ) quantum link lattice gauge theory where the gauge fields, represented by spin- \frac{1}{2} 1 2 operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in (2+1) ( 2 + 1 ) -d. This model allows us to smoothly tune between the \mathrm{U}(1) U ( 1 ) quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.
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Quantum link models have attracted a lot of attention in recent times as a generalization of Wilson's lattice gauge theories, and are particularly suitable for realization on quantum simulators and computers. These models are known to host new phases of matter and act as a bridge between particle and condensed matter physics. In this paper, we study the Abelian U(1)\text{U}(1)U(1) lattice gauge theory in (3+1)D(3+1)\mathrm{D}(3+1)D tubes using large-scale exact diagonalization. We are then able to motivate the phase diagram of the model with finite-size scaling techniques, and in particular propose the existence of a Coulomb phase. Furthermore, we introduce models involving fermionic quantum links, which generalize the gauge degrees of freedom to be of fermionic nature. We prove that while the spectra remain identical between the bosonic and the fermionic versions of the U(1)\text{U}(1)U(1)-symmetric quantum link models in (2+1)D(2+1)\mathrm{D}(2+1)D, they are different in (3+1)D(3+1)\mathrm{D}(3+1)D. We discuss the prospects of realizing the magnetic field interactions as correlated hopping in quantum simulator experiments.