Field Theory of the Gutzwiller Projection
Abstract
The Gutzwiller projection produces a well-known ansatz for spin-liquid and quantum Hall ground-state wavefunctions that is amenable to numerical simulation, with the Laughlin wavefunction being the most celebrated example. A long-standing issue is the precise relation between the Gutzwiller projection and the closely related parton gauge theory. Here, we clarify this issue by providing a field-theoretic description of the Gutzwiller projection. In a path integral description, the universal physics of the projected state is described in terms of a gauge field supported on a temporal slab of vanishing width ε→ 0 coupled to the bulk matter fields. We analytically derive the universal physics of various Gutzwiller projected states. Our construction is also applicable to discrete symmetries, and we use it to analyze various projected SPT states. Among our results, we show that the Gutzwiller projection is not a good ansatz for the long-distance properties of U(1) Dirac spin liquids, spinon Fermi surface spin liquids or composite Fermi liquids, and that the Gutzwiller projection of a quantum spin Hall state has only quasi-long range order. In contrast, in examples where the gauge field is gapped, including Laughlin states, ℤ2 spin liquids and Luttinger liquids, we show that the slab gauge theory from Gutzwiller projection reproduces the correct universal physics of the full parton gauge theory. We also present a generalization of our field theory that describes G-intertwining defects, with application to self-duality defects of recent theoretical interest.
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BibTeX
@misc{sarma2026field,
title = {{Field Theory of the Gutzwiller Projection}},
author = {Abhijat Sarma and Cenke Xu and Chong Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27050},
eprint = {2610.27050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27050},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Field Theory of the Gutzwiller Projection
AU - Abhijat Sarma
AU - Cenke Xu
AU - Chong Wang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27050
UR - https://arxiv.org/abs/2610.27050
AB - The Gutzwiller projection produces a well-known ansatz for spin-liquid and quantum Hall ground-state wavefunctions that is amenable to numerical simulation, with the Laughlin wavefunction being the most celebrated example. A long-standing issue is the precise relation between the Gutzwiller projection and the closely related parton gauge theory. Here, we clarify this issue by providing a field-theoretic description of the Gutzwiller projection. In a path integral description, the universal physics of the projected state is described in terms of a gauge field supported on a temporal slab of vanishing width ε→ 0 coupled to the bulk matter fields. We analytically derive the universal physics of various Gutzwiller projected states. Our construction is also applicable to discrete symmetries, and we use it to analyze various projected SPT states. Among our results, we show that the Gutzwiller projection is not a good ansatz for the long-distance properties of U(1) Dirac spin liquids, spinon Fermi surface spin liquids or composite Fermi liquids, and that the Gutzwiller projection of a quantum spin Hall state has only quasi-long range order. In contrast, in examples where the gauge field is gapped, including Laughlin states, ℤ_2 spin liquids and Luttinger liquids, we show that the slab gauge theory from Gutzwiller projection reproduces the correct universal physics of the full parton gauge theory. We also present a generalization of our field theory that describes G-intertwining defects, with application to self-duality defects of recent theoretical interest.
ER -