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Extracting average properties of disordered spin chains with translationally invariant tensor networks

by Kevin Vervoort, Wei Tang, Nick Bultinck

Submission summary

Authors (as registered SciPost users): Wei Tang · Kevin Vervoort
Submission information
Preprint Link: https://arxiv.org/abs/2504.21089v2  (pdf)
Date submitted: Feb. 3, 2026, 11:43 a.m.
Submitted by: Kevin Vervoort
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approach: Computational

Abstract

We develop a tensor network-based method for calculating disorder-averaged expectation values in random spin chains without having to explicitly sample over disorder configurations. The algorithm exploits statistical translation invariance and works directly in the thermodynamic limit. We benchmark our method on the infinite-randomness critical point of the random transverse field Ising model.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

Author comments upon resubmission

The manuscript has been revised and significantly expanded from our first submission, incorporating new data, additional simulations, and addressing all the referees’ comments and suggestions. Given these substantial improvements, we believe that the work is well suited for SciPost Physics. Our work clearly satisfies the acceptance criterion "Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work". As it opens up a new pathway for using tensor networks in the study of disordered spin chains, expanding upon the current tensor network methods for random spin chains in an orthogonal direction. We also argue it satisfies the acceptance criterion "Present a breakthrough on a previously-identified and long-standing research stumbling block". The need for sampling over many different disorder configurations in conventional algorithms poses a well-known bottleneck for the study of averaged quantities of random spin chains. Since our algorithm does not rely on any sampling of the different disorder configurations, it opens up a novel and more direct way of simulating random spin chains, that can be complementary to the conventional methods.

List of changes

Major Changes: Section 2 : - Added discussion of the numerical cost of the algorithm vs the cost of the standard TEBD-algorithm. Section 3 : - New data with both disorder in the magnetic fields as the nearest neighbour couplings. - Included data with respect to increasing the number of disorder values. - Rephrased and restructured the discussion of the data.

Added Section 4: - Discussion on how the final density matrix MPO can be sampled to get access to typical quantities. - Discussion on the distribution of the lyapunov exponents and correlation length.

Supplementary material: - Expanded the discussion of the accuracy of the MPO inversion, by including a more detailed discussion of the entanglement spectrum. - Included the new data in the additional results

Minor changes (see response to referees): - accommodated the responses of the referees making the presentation more clear and substantial.

Current status:
Refereeing in preparation

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