Dynamical quantum effects in cluster dynamics of Fermi systems

Stephan Haas

Jun’ichi Ozaki, Masaki Tezuka, Norio Kawakami

We study cluster-cluster collisions in one-dimensional Fermi systems with particular emphasis on the nontrivial quantum effects of the collision dynamics. We adopt the Fermi-Hubbard model and the time-dependent density-matrix renormalization-group method to simulate collision dynamics between two fermion clusters of different spin states with contact interaction. It is elucidated that the quantum effects become extremely strong with the interaction strength, leading to the transmittance being much more enhanced than expected from the semiclassical approximation. We propose a concise model as an application of the Bethe ansatz, which unveils the origin of the quantum effects and also explains the overall properties of the simulation results clearly. This model provides an intuitive perspective of the collision dynamics with contact interaction. Some potential applications, such as repeated collisions, are addressed.

Jagdish Prasad Singh

Jun'ichi Ozaki, Masaki Tezuka, Norio Kawakami

Recently, many experiments with cold atomic gases have been conducted from interest in the non-equilibrium dynamics of correlated quantum systems. Of these experiments, the mixing dynamics of fermion clusters motivates us to research cluster-cluster collision dynamics in one-dimensional Fermi systems. We adopt the one-dimensional Fermi-Hubbard model and apply the time-dependent density matrix renormalization group method. We simulate collisions between two fermion clusters of spin-up and spin-down and calculate reflectance of the clusters R changing the particle number in each cluster and the interaction strength between two fermions with up and down spins. We also evaluate the quasi-classical (independent collision) reflectance R qc to compare it with R . The quasi-classical picture is quantitatively valid in the limit of weak interaction, but it is not valid when interaction is strong.

Félix Fossati, E. A. Stepanov

In this work, we extend the dual triply irreducible local expansion (D-TRILEX) approach for correlated electronic systems by introducing a cluster reference system for the diagrammatic expansion. This framework allows us to consistently combine the exact treatment of short-range correlation effects within the cluster, with an efficient diagrammatic description of the long-range charge and spin collective fluctuations beyond the cluster. We demonstrate the effectiveness of our approach by applying it to the one-dimensional nano-ring Hubbard model, where the low dimensionality enhances non-local correlations. Our results show that the cluster extension of D-TRILEX accurately reproduces the electronic self-energy at momenta corresponding to the Fermi energy, in good agreement with the reliable Hirsch-Fye quantum Monte Carlo solution of the problem. We further compare this method with the more computationally demanding parquet dynamical vertex approximation and find that, our method yields substantially more accurate results at momenta associated with the Fermi surface. We show that the D-TRILEX diagrammatic extension drastically reduces the periodization ambiguity of cluster quantities when mapping back to the original lattice, compared to cluster dynamical mean-field theory (CDMFT). Furthermore, we identify the CDMFT impurity problem as the main source of the translational-symmetry breaking and propose a computational scheme for improving the starting point for the cluster-diagrammatic expansion.

Viktor Mikhaĭlovich Galit︠s︡kiĭ