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  • Letter
  • Open Access

Generalized Haldane map from the matrix product state path integral to the critical theory of the J1−J2 chain

F. Azad1,2,*, Adam J. McRoberts3,4,*, Chris Hooley4, and A. G. Green2

  • *These authors contributed equally to this work.
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Phys. Rev. Research 7, L012037 – Published 19 February, 2025Erratum Phys. Rev. Research 7, 049001 (2025)

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012037

Abstract

We study the J1−J2 spin-1/2 chain using a path integral constructed over matrix product states (MPS). By virtue of its nontrivial entanglement structure, the MPS ansatz captures the key phases of the model even at a semiclassical, saddle-point level, and, as a variational state, is in good agreement with the field theory obtained by Abelian bosonization. Going beyond the semiclassical level, we show that the MPS ansatz facilitates a physically motivated derivation of the field theory of the critical phase: By carefully taking the continuum limit—a generalization of the Haldane map—we recover from the MPS path integral a field theory with the correct topological term and emergent SO(4) symmetry, constructively linking the microscopic states and topological field-theoretic structures. Moreover, the dimerization transition is particularly clear in the MPS formulation—an explicit dimerization potential becomes relevant, gapping out the magnetic fluctuations.

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Erratum

Erratum: Generalized Haldane map from the matrix product state path integral to the critical theory of the J1−J2 chain [Phys. Rev. Research 7, L012037 (2025)]

F. Azad, Adam J. McRoberts, Chris Hooley, and A. G. Green
Phys. Rev. Research 7, 049001 (2025)

Article Text

Supplemental Material

References (45)

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Phys. Rev. Research 7, L012037– Published 19 February, 2025
  • Received 29 April 2024
  • Revised 2 December 2024
  • Accepted 17 January 2025
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