P R O J E C T   C R I P O N T
CTIPONT VEGA 2/0123/19

Title: Critical properties of non-standard tensor networks
Duration: 01/01/2019 - 31/12/2021
Principal Investigator: Dr. Roman Krčmár

Project Goals: The essence of this project is to research quantum and classical systems on non-standard, i.e., fractal and hyperbolic lattices. These systems can be represented by tensor networks. Our goal is to represent strongly-correlated critical systems. The reason for studying the quantum systems on the fractal lattices is to improve existing methods and development of new algorithms for describing two-dimensional quantum systems. We intend to achieve this goal by a gradual change of the dimension between one- and two-dimensional lattice systems. In case of the hyperbolic lattices, the reasoning of the study lies in understanding the connection of the quantum systems of the dimension D with the corresponding gravitational systems of the dimension D+1. We aim to study Majorana's bound states observed in presence of strong interactions. The reason of this study is an insufficient theoretical analysis of these states with the interaction turned on, especially, its potential connection to quantum-information processing.

Researchers: Andrej Gendiar, Roman Krčmár, Peter Rapčan