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

TL;DR

This study uses the density matrix renormalization group method to analyze the low energy properties of $S=1/2$ antiferromagnetic Heisenberg chains with quasiperiodic exchange modulation, revealing a different universality class from the XY chain.

Contribution

It demonstrates that quasiperiodic exchange modulation leads to a distinct universality class in the ground state of the Heisenberg chain, contrasting previous marginality assumptions.

Findings

Ground state belongs to a different universality class from the XY chain.

Energy gap distribution scaling supports the new universality class.

Results align with recent bosonization analysis.

Abstract

The low energy behavior of the $S=1/2$ antiferromagnetic Heisenberg chains with precious mean quasiperiodic exchange modulation is studied by the density matrix renormalization group method. Based on the scaling behavior of the energy gap distribution, it is found that the ground state of this model belongs to the universality class different from that of the XY chain for which the precious mean exchange modulation is marginal. This result is consistent with the recent bosonization analysis of Vidal et al.