Thermalization in 1d many body systems

Liangsheng Zhang

I. E. Mazets, Jörg Schmiedmayer

We study the collisional processes that can lead to thermalization in one-dimensional (1D) systems. For two-body collisions, excitations of transverse modes are the prerequisite for energy exchange and thermalization. At very low temperatures, excitations of transverse modes are exponentially suppressed, thermalization by two-body collisions stops and the system should become integrable. In quantum mechanics, virtual excitations of higher radial modes are possible. These virtually excited radial modes give rise to effective three-body velocity-changing collisions, which lead to thermalization. We show that these three-body elastic interactions are suppressed by pairwise quantum correlations when approaching the strongly correlated regime. If the relative momentum k is small compared with the two-body coupling constant c , the three-particle scattering state is suppressed by a factor of ( k / c ) 12 , which is proportional to γ −12 , that is, to the square of the three-body correlation function at zero distance in the limit of the Lieb–Liniger parameter γ≫1. This demonstrates that in 1D quantum systems, it is not the freeze-out of two-body collisions but the strong quantum correlations that ensure absence of thermalization on experimentally relevant time scales.

Jin-Lou Ma, Bobo Liu, Qing Li +3 more

Disorder in one-dimensional (1D) many-body systems facilitates abundant phases such as many-body localization (MBL) and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder compared to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of a MBL phase in the JCH model that strongly violates the eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in the weak disorder regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.

Karamoko Soumahoro, Alison Valbuena, Roman Senkov

Ehud Altman

Jin-Lou Ma, Bobo Liu, Qing Li +3 more

Disorder in one-dimensional (1D) many-body systems emerges abundant phases such as many-body localization (MBL), and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, as known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder comparing to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of MBL phase in the JCH model that strongly violate eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in weak disorder or weak coupling regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.