Spin reduction transition in spin-32random Heisenberg chains

Abstract

Random spin-3 2 antiferromagnetic Heisenberg chains are investigated using an asymptotically exact renormalization group. Randomness is found to induce a quantum phase transition between two random-singlet phases. In the strong randomness phase the effective spins at low energies are S e f f ϭ 3 2 , while in the weak randomness phase the effective spins are S e f f ϭ 1 2 . Separating them is a quantum critical point near which there is a nontrivial mixture of spin-1 2 , spin-1, and spin-3 2 effective spins at low temperatures. Some of the most dramatic effects of randomness in solids appear in the low-temperature behavior of quantum systems. A ͑deceptively͒ simple class of such systems are random quantum spin chains, in particular, Heisenberg antiferromagnetic chains with the HamiltonianFrom a real-space renormalization-group ͑RG͒ analysis, 1 it has been shown that the spin-1 2 random antiferromagnetic ͑AFM͒ chain is strongly dominated by randomness at low temperatures even when the disorder is weak. 2 Its ground state is a random-singlet ͑RS͒ phase in which pairs of spins-mostly close together but occasionally arbitrarily far apart-form singlets. As the temperature is lowered, some of these singlets form at temperatures of order of the typical exchange and become inactive. But their neighboring spins will interact weakly across them via virtual triplet excitations. At lower temperatures, such further neighbors can form singlets and the process repeats. Concomitantly, the distribution of effective coupling strengths broadens rapidly. Eventually, singlets form on all length scales and the ground state is controlled by an RG fixed point with extremely strong disorder: an infinite randomness fixed point.This low-temperature behavior is in striking contrast to that of the pure spin-1 2 AFM chain, in which spin-spin correlations decay as x Ϫ1 because of long-wavelength lowenergy spin-wave ͑or spinon͒ modes. In the random-singlet phase, the average correlations decay as a power of distance -as x Ϫ2 -but for a very different reason: A typical pair of widely spaced spins will have only exponentially ͑in the square root of their separation͒ small correlations. But a small fraction, those that form a singlet pair, will have correlations of order unity independent of their separation; these rare pairs completely dominate the average correlations as well as the other low-temperature properties of the random system.Infinite randomness fixed points are ubiquitous in random quantum systems. They probably control phase discretesymmetry-breaking transitions in all random quantum systems -in any dimension 12 -and, in addition to the spin-1 2 AFM chain, also control the low-temperature properties of a range of random quantum phases. 15 Because of their ubiquity, further investigation of what types of random quantum phases and transitions can occur should shed light more generally on the combined roles of randomness and quantum fluctuations. The simplest cases to analyze are one dimensional because asymptotically exact RG's can be ...

c-theorem violation for effective central charge of infinite-randomness fixed points

“…21, which has a random-singlet ground state. A similar situation prevails in the case of the spin-3/2 Heisenberg model: 28 the decimation rules for the spin model are almost exactly the same as the fusion rules for SU͑2͒ 3 ͑except for the Heisenberg model not allowing the fusion 1 1=1, which could be corrected by allowing biquadratic coupling͒.…”

Permutation-symmetric critical phases in disordered non-Abelian anyonic chains

“…These fixed points were dubbed the S n permutation symmetric points, with n =2S + 1 the number of competing domains. [7][8][9][10] Because of the unique structure of their Hilbert spaces, disordered anyonic chains are particularly amenable to treatment via strong randomness renormalization-group ͑RG͒ methods and indeed have been shown to exhibit infiniterandomness fixed points. 11,12 They are thus an especially fertile ground for trying to discover and classify new universality classes of strongly random behavior.…”

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

“…Hence, we have concluded that the mean-field type calculation, in spite of its simplicity and limitations such as the correlation of spin fluctuations have not been considered, is still an adequate starting point, in which within this theoretical framework it is easy to determine the complete phase diagrams. It also predicts the existence of multicritical points in simple, such as spin-1 2 Ising model [18] …”

“…Finally, we should also mention that recently many researches have investigated the antiferromagnetic spin- Moreover, random spin-3 2 antiferromagnetic Heisenberg chains [18] and the random quantum antiferromagnetic spin-3 2 chain [19] have been studied using the RG calculations.…”