Density Matrix Renormalization Group Study of the S=1/2 Anisotropic Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation

TL;DR

This study investigates the low-energy properties of S=1/2 antiferromagnetic XY-like XXZ chains with quasiperiodic exchange modulation, revealing different scaling behaviors of the energy gap depending on the Ising coupling's nature.

Contribution

It provides a detailed analysis of how quasiperiodic exchange modulation affects the energy gap scaling in quantum spin chains, extending understanding beyond previous bosonization results.

Findings

Energy gap scales as exp(-cN^ω) for antiferromagnetic Ising coupling.

Energy gap scales as N^{-1} for ferromagnetic Ising coupling.

Results align with and clarify the limitations of bosonization analysis.

Abstract

The low energy behavior of the S=1/2 antiferromagnetic XY-like XXZ chains with precious mean quasiperiodic exchange modulation is studied by the density matrix renormalization group method. It is found that the energy gap of the chain with length N scales as $\exp (-cN^{\omega})$ with nonuniversal exponent $\omega$ if the Ising component of the exhange coupling is antiferromagnetic. This behavior is expected to be the characteristic feature of the quantum spin chains with relevant aperiodicity. This is in contrast to the XY chain for which the precious mean exchange modulation is marginal and the gap scales as $N^{-z}$. On the contrary, it is also verified that the energy gap scales as $N^{-1}$ if the Ising component of the exhange coupling is ferromagnetic. Our results are not only consistent with the recent bosonization analysis of Vidal, Mouhanna and Giamarchi but also clarify the nature of the strong coupling regime which is inaccesssible by the bosonization approach.