Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

Abstract

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S = 1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution, at weak disorder the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, z, and z = 1 signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-toend correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.

Tensor network renormalization group study of spin-1 random Heisenberg chains

“…4 we show the average string order parameters as functions of L for various disorder parameters δ near the transition point. From the decay behavior of the curves in the log-log plot and a comparison of the exponent η st with the theoretical conjecture (η st ≈ 0.5093), it seems reasonable to fix δ c = 1 for our results, which is also consistent with previous numerical results obtained by the density matrix renormalization group (DMRG) [26,29]. At δ c = 1 we obtain η st ≈ 0.52, slightly larger than the theoretical value.…”

“…Our tSDRG results alongside the results from previous DMRG studies in Ref. [26] and Ref. [29] are listed in Table I.…”

Self-assembling tensor networks and holography in disordered spin chains

“…An example is the string order parameter [48] that is used to find a hidden topological order in the ground state [49]. If the entanglement entropy can be found, so too can the entanglement spectrum, which has become a popular means of characterizing many-body wave functions [50][51][52][53][54][55][56], for better or for worse [57].…”

Estudo de cadeias quânticas de Heisenberg desordenadas com acoplamentos aperiódicos

“…Por outro lado, para as cadeias de spin 1, investigações baseadas em extensões do SDRG [19,20,21,22,23,24], assim como estudos numéricos [25,26,27,28,29,30], mostraram que a fase de Haldaneé estável frente a desordem fraca 1 . Porém para desordem suficientemente forte, uma transição para uma fase de singleto aleatórioé observada.…”

“…Para desordem intermediária foi observado uma fase de Haldane com gap nulo, embora o parâmetro de ordem de corda seja não nulo [26]. Essa fase intermediária está associada a…”