Azad, F;
Mcroberts, Adam J;
Hooley, Chris;
Green, AG;
(2025)
Generalized Haldane map from the matrix product state path integral to the
critical theory of the J1-J2 chain.
Physical Review Research
, 7
(1)
, Article L012037. 10.1103/PhysRevResearch.7.L012037.
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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.
| Type: | Article |
|---|---|
| Title: | Generalized Haldane map from the matrix product state path integral to the critical theory of the J1-J2 chain |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1103/PhysRevResearch.7.L012037 |
| Publisher version: | https://doi.org/10.1103/physrevresearch.7.l012037 |
| Language: | English |
| Additional information: | Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10206358 |
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