A non-perturbative real-space renormalization group scheme for the spin-1/2 XXX Heisenberg model

TL;DR

This paper introduces a non-perturbative real-space renormalization group method based on density matrix concepts to analyze the spin-1/2 XXX Heisenberg model at finite temperatures, providing insights into its phase behavior.

Contribution

It develops a rigorous, non-perturbative renormalization group scheme for the Heisenberg model using a novel analytical approach linked to the density matrix renormalization group.

Findings

Calculated ferromagnetic fixed point and compared with other methods

Analyzed temperature-dependent RG flow behavior

Applied scheme to both ferromagnetic and antiferromagnetic regimes

Abstract

In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct non-perturbative renormalization group transformations for the spin-1/2 XXX Heisenberg model in the finite temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behaviour in the temperature dependent coupling constant. The constructed renormalization group transformations are applied within the ferromagnetic and the anti-ferromagnetic regime of the Heisenberg chain. The ferromagnetic fixed point is computed and compared to results derived by other techniques.