Licentiate seminar: Density Matrix Renormalization Group approach to anisotropic 3-dimensional bosons

I welcome you to attend (on Zoom) my Licentiate seminar (subject in title).
The opponent is Dr. Salvatore Manmana from the Georg-August University of Göttingen

The microscopic origin of electron pairing in Unconventional Superconductivity (USC) and in particular for USC at high critical temperature remains one of the great challenges in condensed matter physics. One large difficulty lies in the numerical simulation of such theoretical systems which are hypothesized to exhibit USC. In particular, there is still contention as to what is the ground state of the 2D Hubbard model, believed to represent USC in cuprates. As a result it is difficult to predict which systems showing USC have high critical temperatures. The related 1D Hubbard ladder does allow for high-quality, quasi-exact solutions using the Density Matrix Renormalization Group (DMRG) algorithm, and repulsively mediated electron pairing is known to occur. However, despite the appearance of such pairing these ladders cannot exhibit USC as quantum fluctuations in 1D are too strong even at zero temperature to allow for spontaneous breaking of a continuous symmetry (Mermin-Wagner theorem). Curing this deficiency can be done by connecting the 1D system to a reservoir and in particular letting the reservoir be an infinite array of such 1D systems. In this licentiate a method named MPS+MF, which utilizes DMRG and mean field theory, has been developed for solving such systems. The low-energy sector of Hubbard ladders can be realized by a Bose-Hubbard model with hard-core restrictions. Such a system is itself interesting due to its possibility of being simulated with an ultra-cold atomic gas. The validity of MPS+MF is tested against the established gold standard of Quantum Monte Carlo (QMC) which has no issues in hard-core boson systems. It is found that MPS+MF obtains a first order quantum phase transition from a 3D superfluid (SF) to a largely one-dimensional array of 1D charge-density waves (CDWs) when interaction strength is tuned which occurs at the same level as QMC. Furthermore, critical temperatures for the on-set of superfluidity in the system are found to be substantially improved from full mean field approaches. Additionally, the deviation that does occur seems independent of microscopic parameters. The results show dimensional cross-over being particularly pronounced around the SF-CDW transition, verifying the approachs validity further.


Meeting ID: 651 8687 5419