Manual for the Flexible DM-NRG code

TL;DR

This paper introduces the Flexible DM-NRG code, a versatile tool for simulating quantum impurity models using advanced density matrix NRG techniques with dynamic non-Abelian symmetries.

Contribution

It presents a new flexible implementation of the DM-NRG method capable of handling user-defined symmetries and various density of states for quantum impurity models.

Findings

Supports multiple non-Abelian symmetries dynamically

Calculates spectral functions and local operator expectation values

Handles user-defined impurity models and density of states

Abstract

Quantum impurity models describe interactions between some local degrees of freedom and a continuum of non-interacting fermionic or bosonic states. The investigation of quantum impurity models is a starting point towards the understanding of more complex strongly correlated systems, but quantum impurity models also provide the description of various correlated mesoscopic structures, biological and chemical processes, atomic physics and describe phenomena such as dissipation or dephasing. Prototypes of these models are the Anderson impurity model, or the single- and multi-channel Kondo models. The numerical renormalization group method (NRG) proposed by Wilson in mid 70's has been used in its original form for a longtime as one of the most accurate and powerful methods to deal with quatum impurity problems. Recently, a number of new developments took place: First, a spectral sum-conserving density matrix NRG approach (DM-NRG) has been developed, which has also been generalized for non-Abelian symmetries. In this manual we introduce some of the basic concepts of the NRG method and present recently developed Flexible DM-NRG code. This code uses user-defined non-Abelian symmetries dynamically, computes spectral functions, expectation values of local operators for user-defined impurity models. The code can also use a uniform density of states as well as a user-defined density of states. The current version of the code assumes fermionic bath's and it uses any number of U(1), SU(2) charge SU(2) or Z(2) symmetries. The Flexible DM-NRG code can be downloaded from http://www.phy.bme.hu/~dmnrg