Theoretical Studies on Spin-Orbit-Coupled Fermi Superfluids and Many-Body Localization in Low Dimensions

Abstract

We investigate Gorkov--Melik-Barkhudarov (GM) correction to the superfluid transition temperature in two-dimensional interacting Fermi gases with Rashba spin-orbit coupling (SOC). We find that the spin-mixing effect of SOC induces the conventional screening effect and additional antiscreening effect. The contributions of each term interplay significantly in the strong SOC regime. While the GM correction lowers the estimation of the transition temperature, the ratio between the estimates with and without correction exhibits a crossover behavior as the strength of SOC increases at a fixed weak interaction. The ratio first decreases with SOC and becomes insensitive to SOC when it goes into the strong SOC regime. Applying the correction to estimate the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, the ratio between the estimates without correction presents a similar crossover with the mean-field estimation. The zero-temperature condensate fraction applying the GM correction is consistent with the result calculated in recent quantum Monte Carlo results. We investigate the typical growth behavior of the out-of-time-ordered (OTO) commutator in the many-body localized (MBL) quantum spin chains. In the MBL phase of the Heisenberg XXZ chain, we find that the disorder average of the OTO commutator is physically meaningless at the intermediate time of the main growth due to the large fluctuation with the disorder realizations. We argue that the characteristic behavior of the OTO commutator growth can still be shown in the level of individual disorder realization. After a disorder-dependent relaxation period, a typical growth appears in a power-law type, which is close to the $t^2$ form derived in the effective Hamiltonian of a full MBL system. Our tests with various state preparations verified the robustness of the characteristic growth behavior at an individual disorder realization. The typical growth is confirmed in another MBL system of the random-transverse-field quantum Ising chain in a uniform longitudinal field.