Quantum Charge-4e Superconductivity and Deconfined Pseudocriticality in the Attractive SU(4) Hubbard Model

Unlike conventional charge-2e superconductors, a charge-4e superconductor exhibits long-range coherence of electron quartets rather than Cooper pairs. Clear zero-temperature realizations of charge-4e superconductivity remain rare. Here, we investigate the zero-temperature phase diagram of the attractive SU(4) Hubbard model with numerically exact, large-scale quantum Monte Carlo (QMC) simulations overcoming major technical hurdles. We identify both charge-2e and charge-4e superconducting phases. Upon increasing interaction, charge-2e correlations are suppressed and eventually vanish, while the charge-4e correlations remain robust and converge with system size, signaling the onset of a quartet-condensed phase. Interestingly, across the charge-2e--charge-4e transition, single electrons remain gapped, while charge-2e correlations exhibit a scaling behavior inconsistent with a conventional Landau description. These features are naturally captured by a fractionalized framework in which the physical charge-2e order parameter is a composite field coupled to an emergent non-Abelian gauge structure. We formulate an Sp(4) gauge-Higgs theory that realizes deconfined quantum pseudocriticality between the Higgs (charge-2e) phase and the confined (charge-4e) phase. The Sp(4) gauge-Higgs theory yields pseudocriticality through a fixed-point collision, and its one-loop collision-point exponents quantitatively track the QMC results. Our results establish charge-4e superconductivity as a bona fide zero-temperature phase, provide a simple model for future studies in a numerically exact framework, and reveal an unconventional route to superconducting criticality.