Quantum Renormalization Group for Ground-State Fidelity

TL;DR

This paper introduces a unified formalism combining ground-state fidelity and quantum renormalization group theory, enabling the calculation of fidelity without ground state approximation, thus improving analysis of quantum critical systems.

Contribution

It presents a novel method to compute ground-state fidelity directly through QRG, simplifying the study of quantum criticality and scaling behavior.

Findings

Validated in 1D Ising model in transverse field

Applied to anisotropic spin-1/2 Heisenberg model

Enhanced understanding of quantum phase transitions

Abstract

Ground-state fidelity (GSF) and quantum renormalization group theory (QRG) have proven useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method to calculate GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field and the anisotropic spin-1/2 Heisenberg model.