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Journal of the Physical Society of Japan

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

Kazuo Hida

Published May 1, 2000• 5 citations
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The S = 1/2 antiferromagnetic XXZ chains with precious mean quasiperiodic exchange modulation is studied by the density matrix renormalization group method. It is found that the energy gap ΔE scales as exp (-cNω) with the system size N if the Ising component of the exchange coupling is antiferromagnetic. This is in contrast to the XY case in which ΔE ∼N-z. Our results are not only consistent with the bosonization analysis of Vidal, Mouhanna and Giamarchi but also clarify the nature of the strong coupling ground state which is unreachable within the weak coupling calculation of Ref. 9).
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⁡(−cNω)\exp (-cN^ω)exp(−cNω) with nonuniversal exponent ωωω 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−zN^{-z}N−z. On the contrary, it is also verified that the energy gap scales as N−1N^{-1}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.
Low energy behavior of the S = 1/2 antiferromagnetic XXZ chains with Fibonacci exchange/field modulation is studied by the density matrix renormalization group method. For both types of modulation, the energy gap of the chain with length N scales as exp(-cNω ) with nonuniversal exponent ω if the z-component of the exchange coupling is antiferromagnetic. For the field modulation case, the possibility of fully localized ground state is suggested. This is in contrast to the XY chains for which the gap scales as N−z .