Tensor-network strong-disorder renormalization groups for random quantum spin systems in two dimensions

TL;DR

This paper extends the tensor-network strong-disorder renormalization group method to two-dimensional quantum spin systems, improving its accuracy for disordered ground states in 2D lattices.

Contribution

It proposes an improved algorithm for tSDRG tailored for 2D systems and demonstrates enhanced accuracy over previous methods.

Findings

Improved tSDRG algorithm shows higher accuracy in 2D systems.

Validation against exact results up to 36 sites confirms effectiveness.

Algorithm performs well in the strong-randomness regime.

Abstract

Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches is the tensor-network strong-disorder renormalization group (tSDRG), which was basically established for one-dimensional (1D) systems. In this paper, we propose a possible improvement of its algorithm toward 2D random spin systems, focusing on a generating process of the tree network structure of tensors, and precisely examine their performances for the random antiferromagnetic Heisenberg model not only on the 1D chain but also on the square- and triangular-lattices. On the basis of comparison with the exact numerical results up to 36 site systems, we demonstrate that accuracy of the optimal tSDRG algorithm is significantly improved even for the 2D systems in the strong-randomness regime.