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arXiv:1912.03529 · The European Physical Journal B

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

Zheng-Lin Tsai, Pochung Chen, Yu-Cheng Lin

Published Apr 1, 2020• 9 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2020-100585-8

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In this thesis, we use a tree tensor network strong disorder renormalization group method to study spin-1 random Heisenberg chains. The ground state of the clean spin-1 Heisenberg chain with uniform nearest-neighbor couplings is a gapped phase as 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 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 random singlet 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 closer agreement with the theoretical predictions than what was found in previous numerical studies.
We propose an entanglement-based algorithm of the tensor-network strong-disorder renormalization group (tSDRG) method for quantum spin systems with quenched randomness. In contrast to the previous tSDRG algorithm based on the energy spectrum of renormalized block Hamiltonians, we directly utilize the entanglement structure associated with the blocks to be renormalized. We examine accuracy of the algorithm for the random antiferromagnetic Heisenberg models on one-dimensional, triangular, and square lattices. We then find that the entanglement-based tSDRG achieves better accuracy than the previous one for the square-lattice model with weak randomness, while it is less efficient for the one-dimensional and triangular-lattice models particularly in the strong-randomness region. The theoretical background and possible improvements of the algorithm are also discussed.