Numerical renormalization group integrated Hamiltonian truncation: Toward generic deformation of integrable lattice models

TL;DR

This paper introduces a hybrid numerical method combining NRG with Hamiltonian truncation to efficiently study deformations of integrable lattice models, accurately capturing low-energy physics and excitations.

Contribution

The paper develops a novel hybrid NRG-based Hamiltonian truncation technique tailored for generic deformations of integrable lattice models, improving basis extension and error reduction.

Findings

Successfully applied to Ising chain in a magnetic field

Accurately captures E8 and D8^{(1)} excitations

Demonstrates computational efficiency and high performance

Abstract

We present a hybrid lattice Hamiltonian truncation method that integrates the numerical renormalization group (NRG) with a truncated lattice integrable spectrum. The technique is tailored for generic deformations of integrable lattice models, where the NRG enables a controlled incorporation of high-energy states. The method extends the basis set more effectively and efficiently than brute-force truncation, meanwhile significantly reducing errors. We show its capability on two paradigmatic models: an Ising chain in a magnetic field and a quantum Ising ladder. The resulting dynamical structure factors accurately capture the essential low-energy physics, including the $E_8$ and $\mathcal{D}_8^{(1)}$ excitations of the former and later models, respectively, demonstrating the approach's computational efficiency and high performance.