M.Sc Student | Neumann Oren |
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Subject | Calculating the Hall Anomaly in the t-J Model DMRG |

Department | Department of Physics |

Supervisor | Professor Assa Auerbach |

Full Thesis text |

We study in this work the t-J model
which is believed to to be a model able to describe the phenomenon of high-T_{c}
superconductivity in cuprate materials, an effect that is yet to receive a full
explanation. We use this model to simulate another phenomenon, the Hall
anomaly, an effect where the Hall conductivity of high-T_{c}
superconducting materials changes its sign when electron filling is increased
before reaching half-filling. we also calculate the change in energy of the
ground state in order to measure the appearance of pair binding. Since an exact
calculation of the t-J model's ground state is too expensive for large systems,
we turn to DMRG, a numerical method that approximates the ground state using
states with a short entanglement length. The Hall conductivity is calculated
using the method of charge pumping, where magnetic flux is adiabatically added
passing through the hole of a 2D cylindrical system and causes a shift in the
charge distribution. This shift in charge is known to be related to the Hall
conductivity. Though our calculation shows large fluctuations in the sign of
the Hall conductivity at large electron fillings, we argue that the change in
this sign is correlated with the binding of electron pairs, which could help to
understand this phenomenon.