Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes

Abstract

Quantum link models (QLMs) have attracted a lot of attention in recent times as a generalization of Wilson's lattice gauge theories (LGT), 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 article, we study the Abelian $U(1)$ lattice gauge theory in $(3+1)$-d tubes using large-scale exact diagonalization (ED). We are then able to motivate the phase diagram of the model with finite size scaling techniques (FSS), and in particular propose the existence of a Coulomb phase. Furthermore, we introduce the first 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 $U(1)$-symmetric quantum link models in $(2+1)$-d, they are different in $(3+1)$-d. We discuss the prospects of realizing the magnetic field interactions as correlated hopping in quantum simulator experiments.

arXiv comment19 pages, 15 figures

References in corpus (35)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Ground state overlap and quantum phase transitions
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Many-body localization: an introduction and selected topics
• Fidelity approach to quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Fractons
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• QCD as a Quantum Link Model
• Three dimensional resonating valence bond liquids and their excitations
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Quench Dynamics of a Fermi Gas with Strong Non-Local Interactions
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Quantum Simulation of the Abelian-Higgs Lattice Gauge Theory with Ultracold Atoms
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Minimal model for Hilbert space fragmentation with local constraints
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality
• Numerical approach to low-doping regime of the t-J model
• Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model
• A qubit regularization of the $O(3)$ sigma model
• From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories
• Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
• Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
• Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States
• Scalable cold-atom quantum simulator for two-dimensional QED
• Low-Energy Effective Theories of Quantum Link and Quantum Spin Models
• A quantum liquid with deconfined fractional excitations in three dimensions
• Three-dimensional isometric tensor networks

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