Exact NMR simulation of protein-size spin systems using tensor train formalism

D. V. Savostyanov, S. V. Dolgov, J. M. Werner, Ilya Kuprov

Research output: Contribution to journalArticlepeer-review

25 Citations (SciVal)


We introduce a new method, based on alternating optimization, for compact representation of spin Hamiltonians and solution of linear systems of algebraic equations in the tensor train format. We demonstrate the method's utility by simulating, without approximations, a N15 NMR spectrum of ubiquitin - a protein containing several hundred interacting nuclear spins. Existing simulation algorithms for the spin system and the NMR experiment in question either require significant approximations or scale exponentially with the spin system size. We compare the proposed method to the Spinach package that uses heuristic restricted state space techniques to achieve polynomial complexity scaling. When the spin system topology is close to a linear chain (e.g., for the backbone of a protein), the tensor train representation is more compact and can be computed faster than the sparse representation using restricted state spaces.

Original languageEnglish
Article number085139
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number8
Publication statusPublished - 25 Aug 2014

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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