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

Abstract

We use a tensor network strong-disorder renormalization group (tSDRG) method to study spin-1 random Heisenberg antiferromagnetic chains. The ground state of the clean spin-1 Heisenberg chain with uniform nearest-neighbor couplings is a gapped phase known as the Haldane phase. Here we consider disordered chains with random couplings, in which the Haldane gap closes in the strong disorder regime. As the randomness strength is increased further and exceeds a certain threshold, the random chain undergoes a phase transition to a critical random-singlet phase. The strong-disorder renormalization group method formulated in terms of a tree tensor network provides an efficient tool for exploring ground-state properties of disordered quantum many-body systems. Using this method we detect the quantum critical point between the gapless Haldane phase and the randomsinglet phase via the disorder-averaged string order parameter. We determine the critical exponents related to the average string order parameter, the average end-to-end correlation function and the average bulk spin-spin correlation function, both at the critical point and in the random-singlet phase. Furthermore, we study energy-length scaling properties through the distribution of energy gaps for a finite chain. Our results are in closer agreement with the theoretical predictions than what was found in previous numerical studies. As a benchmark, a comparison between tSDRG results for the average spin correlations of the spin-1/2 random Heisenberg chain with those obtained by using unbiased zero-temperature QMC method is also provided.

Tensor network models of AdS/qCFT

“…From their construction on regular tilings, these models necessarily inherit the discretely broken conformal symmetries we discussed, thus falling into the rubric of our proposed AdS/qCFT correspondence. The HaPPY pentagon code, studied here in its Majorana dimer form, shows that qCFTs are closely related to strongly disordered critical models, which have been extensively studied in the condensed matter literature [37,[43][44][45][46][47]. As the HaPPY code is a model of quantum error correction, we find that AdS/qCFT includes exact holographic codes, rather than the approximate codes found in AdS/MERA models [48].…”

Entanglement-based tensor-network strong-disorder renormalization group

“…Then, a promising numerical approach is the tensor-network strong-disorder renormalization group (tSDRG) method [24,25]. The tSDRG was introduced as an extension of the perturbative strong-disorder renormalization group (SDRG) method [26,27] and has proven to be efficient for realizing accurate numerical calculations of 1D random quantum spin systems [24,25,28,29]. In the context of tensor network, the tSDRG is based on the tree-tensor network (TTN), as dipicted in Fig.…”

Studying dynamics in two-dimensional quantum lattices using tree tensor network states

“…For this purpose, in this work we propose to employ Tree Tensor Network States (TTNS), which encompass all loop-free tensor network states. While similarly to MPS, hierarchical, tree-like TTNS can only efficiently encode states with area-law entanglement in one dimensional systems they offer a more robust description of ground states of critical one dimensional systems [26,27], and therefore might provide more flexibility in encoding complex entanglement structures in two and higher dimensional systems. TTNS are used in the context of interacting lattice systems [28][29][30][31][32][33][34][35][36], but they feature more prominently in applications like electronic structure methods [37][38][39] or molecular quantum dynamics in the chemical physics literature.…”