Session W30: Quantum Gases in Low Dimension

New results in 1D repulsive Hubbard model: Quantum liquid, criticality and transport

The Hubbard model, although extensively studied for a long time, has found renewed interest and become increasingly important in condensed matter physics, ultracold atoms and quantum metrology. In this talk, we will present new results of one-dimensional repulsive Hubbard model in the presence of a magnetic field. Using Bethe ansatz solution, we rigorously show that the fractional spin and holon excitations display different features of spin-charge separation in various phases regimes. We determine universal behavior of such spin-coherent and -incoherent liquids, Tan's contact and the interaction-driven criticality in and near different phases. In particular, analytical and general results on spin and charge Drude weights are obtained for the ground state, the Luttinger liquid and the quantum critical region at both zero and finite temperatures, showing deep insights into ballistic and diffusive quantum transports in strongly correlated systems in one dimension. References: Jia-Jia Luo, Han Pu and Xi-Wen Guan, Physical Review B 107, L201103 (2023); Jia-Jia Luo, Han Pu and Xi-Wen Guan, arXiv:2307.00890 Jia-Jia Luo, Han Pu, Xi-Wen Guan in preparation, 2023   

Strongly interacting 1D quantum gases

Understanding the effect of correlations in interacting many-body systems is one of the main challenges in quantum mechanics. While the general problem can only be addressed by approximate methods and numerical simulations, in some limiting cases, it is amenable to exact solutions. I will present a family of exact solutions for strongly interacting 1D quantum gases in arbitrary external potential, valid for bosons, multicomponent fermions and mixtures. It allows us to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillation regime yielding the collective modes of the system and the large quench regime where the system parameters are changed considerably. The solution can be extended to describe finite-temperature conditions, spin, and magnetization effects. In particular I will present large-size calculations of the frequency- and momentum-resolved spectral function of strongly repulsive lattice bosons and a symmetry-breaking exact solution for a Bose-Bose mixture. Our approach directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved.   

Out-of-equilibrium 1D Bose gases and generalized hydrodynamics

The theory of generalized hydrodynamics (GHD) takes advantage of nearly perfect conservation laws in nearly integrable systems to accomplish the otherwise difficult task of predicting their dynamical behavior. We will describe experiments with quenched 1D Bose gases that validate GHD. We will then show how certain sudden quenches can temporarily invalidate the assumptions that underly GHD. For very short times "hydrodynamization" occurs, during which energy rapidly redistributes among different modes and GHD does not work. At somewhat longer times "local prethermalization" occurs, during which GHD can still work quite well although the nominal GHD assumptions do not hold. Finally, we will illustrate, with new experimental and theoretical evidence, the conditions needed for there to be distinct hydrodynamization and local prethermalization time scales. We suspect that these considerations qualitatively hold for energetic quenches in all many-body quantum systems, integrable or not.