Physical review. B, Condensed matter

Strongly disordered antiferromagnetic spin-1 chains with random anisotropy

A. Saguia, B. Boechat, M. A. Contínentino

Published Jul 1, 1998• 22 citations

Abstract

The zero-temperature phase diagram of the anisotropic, strongly disordered antiferromagnetic quantum spin-1 chain is investigated, within the framework of a real-space renormalization-group approach. In the presence of uniform anisotropy there occurs a phase transition from a random singlet phase to an Ising antiferromagnetic phase controlled by a fixed point that does not have Heisenberg symmetry. We find evidence of a fixed point due to randomness in the anisotropy similar to that which occurs for quantum Heisenberg spin-$\frac{1}{2}$ chains.

DOI: 10.1103/physrevb.58.58

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Physical review. B, Condensed matter

Strongly disordered antiferromagnetic spin-1 chains with random anisotropy

A. Saguia, B. Boechat, M. A. Contínentino

Published Jul 1, 1998• 22 citations

Publisher

Abstract

\frac{1}{2}

chains.

DOI: 10.1103/physrevb.58.58

Related papers

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Daniel S. Fisher

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Péter Lajkó, Jean-Christian Anglès d’Auriac, Heiko Rieger +1 more

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arXiv:1912.06035Physical review. B./Physical review. BJan 30, 20209 citations

\frac{1}{2}

chains.

{J}_{i}>~0

are independent random variables obeying a probability distribution

P(J)

, and $0<~\ensuremath{\gamma}<~\ensuremath{\infty}$. The approach used is a numerical implementation of a real-space renormalization-group (RG) method previously introduced. The isotropic Heisenberg case ($\ensuremath{\gamma}=1$), the

\mathrm{XY}

case ($\ensuremath{\gamma}=0$). and the Ising case ($\ensuremath{\gamma}=\ensuremath{\infty}$) are fixed points of the RG transformation. It is found that in the

\mathrm{XY}

region $\ensuremath{\gamma}<~1$, including the Heisenberg point, the system exhibits singular behavior in the thermodynamic properties for arbitrary probability distributions for the couplings. For the

\mathrm{XY}

limit ($\ensuremath{\gamma}=0$) this is in agreement with known exact results. The functional form for the low-temperature susceptibility is found to be $\ensuremath{\chi}\ensuremath{\sim}\frac{1}{(T{\mathrm{ln}}^{m}(\frac{T}{{T}_{0}}))}$ in the entire region $0<~\ensuremath{\gamma}<~1$ for arbitrary probability distributions. In the Ising region ($\ensuremath{\gamma}>1$) the susceptibility shows an approximate power-law divergence for small anisotropy but goes eventually to zero as $T\ensuremath{\rightarrow}0$. Possible relevance of these results to recent experiments on Qn

{(\mathrm{TCNQ})}_{2}

is discussed.

h

. Using different numerical techniques (density-matrix renormalization group, combinatorial optimization, and strong disorder renormalization group methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line $(h=0,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=1)$ there is an infinite disorder quantum fixed point, while at the other end $(h=2,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=0)$ there is a classical random first-order transition point. Close to this fixed point, for

h>2

and ${\mathrm{\ensuremath{\Gamma}}}_{0}>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.