Second order quantum renormalisation group of XXZ chain with next nearest neighbour interactions

TL;DR

This paper extends the quantum renormalisation group method to the XXZ chain with next-nearest neighbour interactions, revealing a complex phase diagram and the importance of second order corrections for accurate modeling.

Contribution

It introduces a second order quantum renormalisation group approach for the XXZ chain with next-nearest neighbour interactions, highlighting the impact on phase diagrams and effective Hamiltonians.

Findings

Identified three phases: spin-fluid, dimerised, and Ne'el.

The anisotropy significantly alters the phase diagram.

Second order corrections improve ground state energy estimates.

Abstract

We have extended the application of quantum renormalisation group (QRG) to the anisotropic Heisenberg model with next-nearest neighbour (n-n-n) interaction. The second order correction has to be taken into account to get a self similar renormalized Hamiltonian in the presence of n-n-n-interaction. We have obtained the phase diagram of this model which consists of three different phases, i.e, spin-fluid, dimerised and Ne'el types which merge at the tri-critical point. The anisotropy of the n-n-n-term changes the phase diagram significantly. It has a dominant role in the Ne'el-dimer phase boundary. The staggered magnetisation as an order parameter defines the border between fluid-Ne'el and Ne'el-dimer phases. The improvement of the second order RG corrections on the ground state energy of the Heisenberg model is presented. Moreover, the application of second order QRG on the spin lattice model has been discussed generally. Our scheme shows that higher order corrections lead to an effective Hamiltonian with infinite range of interactions.