Motivated by the pseudogap–Fermi liquid transition in doped Mott insulators, we examine the excitations of a $t\text{−}J$ model with random and all-to-all hopping and exchange. The stability of quasiparticles such as spin-$1/2$ fermions (Landau quasiparticles), spin-1 magnons, and emergent Jordan-Wigner (JW) fermions is cast as a problem of localization in the many-body Hilbert space, which is studied by the FEAST eigensolver algorithm. At low dopings, magnons and JW fermions are stable and better defined than Landau quasiparticles, which are unstable. Upon crossing a critical value of doping around $p_c=1/3$, the stabilities of Landau quasiparticles and the other two are interchanged. Near the critical doping, these quasiparticles are all found to be ill defined. The critical point is thus associated with a localization transition in the many-body Hilbert space. We discuss the possible role of the JW fermions in the anomalously large thermal Hall response of the cuprates.

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• Fractionalization
• Quantum phase transitions
• Cuprates
• Mott insulators
• Strongly correlated systems
• Exact diagonalization
• Non-Fermi-liquid theory
• Sachdev-Ye-Kitaev model