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Strong-Disorder Renormalization Group (SDRG), despite being a relativelysimple real-space renormalization procedure, provides in principle exactresults on the critical properties at the infinite-randomness fixed point ofrandom quantum spin chains. Numerically, SDRG can be efficiently implemented asa renormalization of Matrix Product Operators (MPO-RG). By considering largerblocks than SDRG, MPO-RG was recently used to compute non-critical quantitiesof finite chains that are inaccessible to SDRG. In this work, the accuracy ofthis approach is studied and two simple and fast improvements are proposed. Theaccuracy on the ground state energy is improved by a factor at least equal to 4for the random Ising chain in a transverse field. Finally, the proposedalgorithms are shown to yield Binder cumulants of the 3-color randomAshkin-Teller chain that are compatible with a second-order phase transitionwhile a first-order one is predicted by the original MPO-RG algorithm.

Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain