String Theory Journal Club

In this talk, I will introduce Density Matrix Renormalization Group(DMRG) method in its original and Matrix Product State (Tensor train) versions using examples of 1D spin systems. DMRG, introduced by S. White in 1992, is a variational numerical method that was found to be particularly efficient for low-dimensional fermionic and spin systems. This method lets us look beyond Landau's theory into frustrated magnetic systems, quantum spin liquids and other exotic phases and phenomena of quantum matter. Since the conception of DMRG, many other methods have been created that fit into a family of Tensor Network(TN) methods. I would like to show how TN serves as a practical and elegant language to describe systems where topological and boundary effects play a crucial role via entanglement. I will provide a short overview of the current and emerging methods in this field.