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  • Letter
  • Open Access

Dispersion relations in two- and three-dimensional quantum systems

Valeriia Bilokon1,2,*, Elvira Bilokon1,2,†, Illya Lukin2,3,‡, Andrii Sotnikov2,4,§, and Denys I. Bondar1,∥

  • 1Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
  • 2Akhiezer Institute for Theoretical Physics, NSC KIPT, Akademichna 1, 61108 Kharkiv, Ukraine
  • 3Haiqu, Inc., 95 Third Street, San Francisco, California 94103, USA
  • 4Karazin Kharkiv National University, Svobody Square 4, 61022 Kharkiv, Ukraine

  • *Contact author: vbilokon@tulane.edu
  • †Contact author: ebilokon@tulane.edu
  • ‡Contact author: illya.lukin11@gmail.com
  • §Contact author: a_sotnikov@kipt.kharkov.ua
  • ∥Contact author: dbondar@tulane.edu
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Phys. Rev. Research 8, L012063 – Published 13 March, 2026

DOI: https://doi.org/10.1103/rnr1-bbjw

Abstract

Extracting momentum-resolved excitation spectra in strongly correlated quantum systems remains a major challenge, especially beyond one spatial dimension. We present an efficient tensor-network approach to compute dispersion relations via imaginary-time evolution within the infinite projected entangled-pair states framework. Benchmarking on the transverse-field Ising model, the method successfully captures dispersion relations in both paramagnetic and ferromagnetic phases for two- and three-dimensional lattices, achieving strong agreement with series-expansion methods, where these are applicable. Crucially, this work presents the first demonstration of dispersion relation calculations for three-dimensional quantum lattice models—a long-standing computational challenge that opens previously inaccessible research frontiers. The method demonstrates remarkable efficiency, requiring only modest computational resources while maintaining high accuracy across wide parameter ranges. Its broad applicability makes it a powerful tool for quantum simulation, photonic material design, and quantum information platforms requiring precise momentum-resolved spectra.

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Phys. Rev. Research 8, L012063– Published 13 March, 2026
  • Received 26 September 2025
  • Accepted 17 February 2026
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