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Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition

Denise Cocchiarella1,2, Mingru Yang1,2, Yueshui Zhang3, Mari Carmen Bañuls1,2, Hong-Hao Tu3, and Yuhan Liu1,2,*

  • *Contact author: yuhan.liu@mpq.mpg.de
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Phys. Rev. B 113, 205145 – Published 26 May, 2026

DOI: https://doi.org/10.1103/prgj-ndfm

Abstract

Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from the ground state obtained by variational matrix product state (MPS) optimization. Despite its numerical success, the theoretical mechanism underlying this method has remained largely unexplored. In this work, we provide a conformal field theory (CFT) perspective that helps elucidate this connection. The key insight is that this construction effectively uses a truncated basis of ground-state Schmidt vectors to represent excited states, where the contribution of each Schmidt vector can be expressed as a CFT correlation function and shown to decay with increasing Schmidt index. The CFT analysis further predicts an entanglement-spectrum transition of excited states as the ratio of the subsystem size to the total system size is varied. Our numerical results support this picture and demonstrate a reorganization of the entanglement spectrum into distinct conformal towers as this ratio changes.

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Phys. Rev. B 113, 205145– Published 26 May, 2026
  • Received 8 January 2026
  • Revised 27 March 2026
  • Accepted 27 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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