Our next talk in the series QM Talks@CBPF will be delivered by Alexandre B. Tacla (Glasgow). Alexandre has many interests, and a broad knowledge. In this talk he will tell us about his recent results on how to deal with complex many-body systems in an efficient way.
Note that this week, due to the holiday celebrating the Proclamation of the Republic in Brazil on Wednesday, the talk will be on Monday. See the full info below, and be sure to not miss this talk!
Title: Particle-correlated states: A non-perturbative treatment beyond mean field
Speaker: Alexandre B. Tacla (Glasgow)
Coordinates: room 601C, CBPF. 13.11 (Monday), 16h00
Abstract: Many useful properties of dilute Bose gases at ultralow temperatures are predicted precisely by the (mean-field) product-state Ansatz, in which all particles are in the same single-particle state. However, in situations where particle-particle correlations become important, this technique fails and more sophisticated methods are required. In this talk, I will introduce a new set of states that include quantum correlations nonperturbatively: The particle-correlated state (PCS) of N = l × n particles is derived by symmetrizing the n-fold product of an l-particle quantum state. Quantum correlations of the l-particle state “spread out” to any subset of the N bosons by symmetrization. Specifically, I will present the PCS theory for the ground-state of bosonic systems constructed from a two-particle pure state (l=2) [Phys. Rev. A 96, 023621 (2017)]. In particular, I will show (i) how to simulate PCS efficiently for large systems and (ii) how to calculate analytically the reduced density matrices (correlation functions) directly from the PCS normalization factor. Lastly, I will discuss the efficacy of PCS when applied to the two-site Bose-Hubbard model. The key result is that the PCS Ansatz can faithfully represent the exact ground-state over the entire parameter region from a superfluid to a Mott insulator.