Quantum Ising model in a transverse random field: A density-matrix renormalization group analysis

TL;DR

This paper investigates the quantum Ising chain with a transverse random magnetic field using density-matrix renormalization group, analyzing phase transition, magnetization, and correlation functions.

Contribution

It provides a detailed numerical analysis of the phase transition and critical behavior in the disordered quantum Ising model using DMRG.

Findings

Identifies the transition from ordered to paramagnetic phase with increasing disorder.

Determines magnetization dependence on uniform and random fields.

Studies spin-spin correlation functions at and above criticality.

Abstract

The spin-1/2 quantum Ising chain in a transverse random magnetic field is studied by means of the density-matrix renormalization group. The system evolves from an ordered to a paramagnetic state as the amplitude of the random field is increased. The dependence of the magnetization on a uniform magnetic field in the z direction and the spontaneous magnetization as a function of the amplitude of the transverse random magnetic field are determined. The behavior of the spin-spin correlation function both above and at criticality is studied. The scaling laws for magnetization and correlation functions are tested against previous numerical and renormalization-group results.