Tuning from fermi liquid to SYK-like non-fermi liquid via scattering momentum cutoff in a bound state system

While bound states are typically treated as long-lived quasiparticles with slow momentum and current relaxation in a Fermi liquid (FL) phase, this paper investigates their properties within a non-Fermi liquid (NFL) phase exhibiting Sachdev–Ye–Kitaev (SYK)-like ensemble behavior. We establish a fundamental relation between the UV cutoff of the relative scattering momentum, [Formula: see text], and the emergence of this SYK-like physics, a connection which has not been previously explored. We find that [Formula: see text] directly controls the statistical properties of the coupling term. In the limit [Formula: see text], the large number of momentum steps causes the coupling to behave as a Gaussian or Chi-square random variable, fulfilling the conditions for SYK-like chaos. This reveals [Formula: see text] as a tuning parameter for a phase transition: the [Formula: see text] limit corresponds to the NFL phase with ill-defined bound states, while a finite [Formula: see text] corresponds to a (disordered) FL phase with well-defined bound state quasiparticles. Furthermore, we show that pair condensation, which emerges at a critical temperature, competes with and suppresses the NFL phase. Finally, we note that in the case of large-range condensation, a homogeneous character emerges and thermalization is observed, where high-energy eigenstates show low overlap with low-entanglement states.