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Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings.

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Author(s):
Helder Luciani Casa Grande
Total Authors: 1
Document type: Doctoral Thesis
Press: São Paulo.
Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
Defense date:
Examining board members:
Andre de Pinho Vieira; Angsula Ghosh; José Abel Hoyos Neto; Mario Jose de Oliveira; Silvio Roberto de Azevedo Salinas
Advisor: Andre de Pinho Vieira
Abstract

We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We utilize different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to that found for the aperiodic spin-1/2 XXZ chain. We show that approaches providing the same qualitative behaviour in the random spin-1 chain may lead to qualitatively incompatible predictions in aperiodic chain. (AU)

FAPESP's process: 09/08171-3 - Thermodynamic properties of dimer models and aperiodic quantum spin chains
Grantee:Helder Luciani Casa Grande
Support type: Scholarships in Brazil - Doctorate