Density Matrix Renormalization Group approach to non-Hermitian quantum many-body systems.

• Grant number: 25/02103-9
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: April 01, 2025
• End date: March 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Luis Gregório Godoy de Vasconcellos Dias da Silva
• Grantee: Luan de Souza Silva
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 22/15453-0 - Correlated quantum materials, AP.TEM

Abstract

The exploration of non-Hermitian Hamiltonians in the context of open quantum systems has gained significant interest in recent years. This direct doctorate research project aims to introduce the student to a research program in these fascinating topics. Concretely, the project goals are two-fold: (i) to establish a generic platform to study non-Hermitian quantum many-body systems; and (ii) The study of open quantum systems using the Lindblad master equation. In both cases, our focus is to apply renormalization group-based numerical methods such as the density matrix renormalization group (DMRG) and Wilson's numerical renormalization group (NRG) methods. One of the challenges of this doctoral project is to adapt these methods to handle non-Hermitian systems. In part (i), we start with a prototypical quantum many-body phenomena: the Kondo effect in a PT-symmetric quantum dot (QD) system. Inspired by previous studies, we will focus on a 1D model that describes a QD coupled to leads and a dissipative environment. By analyzing the PT-symmetric non-Hermitian Anderson model, we will explore the interplay between the Kondo effect and the breaking of PT symmetry. Now, in part (ii), we will consider open quantum systems described by the Lindblad master equation and look for steady-state solutions. While the dissipative nature of the problem naturally connects to the non-hermiticity of the time-evolution operator, we will explore ways to calculate such time evolution numerically, using modified versions of DMRG in order to achieve this goal. We expect that the student will gain insights into the intriguing properties of non-Hermitian quantum impurity models and open quantum systems, as well as a further familiarity with the DMRG method.