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arxiv: 2606.19732 · v1 · pith:RDDYNKEKnew · submitted 2026-06-18 · ✦ hep-th · cond-mat.stat-mech· cond-mat.str-el· quant-ph

Quantum models with the Yang-Lee phase transition

Erick Arguello Cruz , Grigory Tarnopolsky This is my paper

Pith reviewed 2026-06-26 16:41 UTC · model grok-4.3

classification ✦ hep-th cond-mat.stat-mechcond-mat.str-elquant-ph
keywords Yang-Lee transitionPT symmetry1+1D quantum modelsIsing chainSchwinger modelbosonizationcriticality
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0 comments X

The pith

Four 1+1D quantum models tuned by PT-symmetric deformations realize the Yang-Lee phase transition described by a massless boson with iφ³ interaction.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs four lattice and field-theoretic models in one plus one dimensions that can be deformed while preserving PT symmetry to reach the Yang-Lee critical point. These include the antiferromagnetic Ising chain, the massive Schwinger model, the Blume-Capel model, and the three-state quantum clock model. Using state-operator correspondence, the authors compute scaling dimensions that match known results for the Yang-Lee theory in two dimensions. Bosonization and related mappings show that the critical theory is a massless scalar with an imaginary cubic term, and numerical checks confirm the expected growth of the phi two-point function.

Core claim

We present four different 1+1D quantum models that realize the Yang-Lee phase transition under a deformation that preserves PT symmetry. These are the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields, the massive Schwinger model, the Blume-Capel model, and the three-state quantum clock model. Using the state-operator correspondence, we identify the YL critical point, compute the scaling dimensions of the lowest operators in each model, and find perfect agreement with the exact results for the YL criticality in two dimensions. Using bosonization for the Schwinger model and the Polyakov-Hubbard transformation for the other models, we show that in all of these q

What carries the argument

PT-symmetric deformations that tune the four models to the Yang-Lee fixed point, realized through state-operator correspondence and bosonization mappings to the massless bosonic field with i φ³ interaction.

If this is right

  • Scaling dimensions of the lowest operators match exact Yang-Lee results in two dimensions.
  • The two-point function of the field phi grows with distance at the critical point.
  • In the quantum clock model the massless field couples to a massive bosonic field whose states appear in the Hamiltonian spectrum.
  • All four microscopically distinct models flow to the same Yang-Lee universality class.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These lattice realizations may enable sign-problem-free numerical studies of the non-unitary Yang-Lee theory.
  • Similar PT-symmetric deformations could be applied to other 1+1D models to reach additional non-Hermitian critical points.
  • The consistency across spin chains, gauge theories, and clock models indicates that the i φ³ description is insensitive to microscopic details.
  • Experimental systems with engineered PT symmetry could test signatures of the growing phi correlator.

Load-bearing premise

The chosen PT-symmetric deformations tune the models precisely to the Yang-Lee fixed point without additional relevant operators or lattice artifacts that would alter the universality class.

What would settle it

Numerical extraction of the scaling dimension of the lowest-lying operator in any of the four models that deviates from the known Yang-Lee value would falsify the claim that the models reach that critical point.

read the original abstract

In this article, we present four different $1+1$D quantum models that realize the Yang-Lee (YL) phase transition under a deformation that preserves $PT$ symmetry. These are the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields, the massive Schwinger model, the Blume-Capel model, and the three-state quantum clock model. Using the state-operator correspondence, we identify the YL critical point, compute the scaling dimensions of the lowest operators in each model, and find perfect agreement with the exact results for the YL criticality in two dimensions. Using bosonization for the Schwinger model and the Polyakov-Hubbard transformation for the other models, we show that in all of these quantum models the YL critical point is described, as expected, by a massless bosonic field with an $i \phi^3$ interaction. In the quantum clock model, this critical field interacts with a massive bosonic field, and we identify the massless and massive states in the Hamiltonian spectrum. In addition, we numerically compute the two-point function of $\phi$ at the Yang-Lee critical point and show that it grows with distance, in agreement with theoretical expectations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper constructs four 1+1D quantum models (antiferromagnetic Ising chain in transverse and longitudinal fields, massive Schwinger model, Blume-Capel model, and three-state quantum clock model) that realize the Yang-Lee edge singularity under PT-symmetric deformations. It identifies the critical points via state-operator correspondence, reports exact matching of the lowest scaling dimensions to the non-unitary YL CFT (c = -22/5), maps each critical theory to a massless boson with iφ³ interaction (via bosonization for the Schwinger model and Polyakov-Hubbard for the others), and numerically verifies that the two-point function of φ grows with distance.

Significance. If the central identifications hold, the work supplies concrete, numerically accessible lattice realizations of the non-unitary Yang-Lee CFT inside standard quantum spin and gauge models. The use of four independent models, the combination of state-operator correspondence with explicit field-theory mappings, and the direct numerical check of the growing correlator constitute clear strengths. These constructions open routes for studying non-unitary fixed points in condensed-matter and lattice-gauge settings without invoking complex couplings by hand.

minor comments (3)
  1. [Abstract] Abstract: the phrase 'perfect agreement' is stated without reference to a table or figure that lists the computed dimensions versus the exact YL values; adding such a compact comparison (even if already present in §4 or §5) would improve readability.
  2. The Polyakov-Hubbard mapping for the clock and Blume-Capel models is invoked without an explicit statement of the auxiliary-field decoupling or the resulting interaction terms; a short appendix deriving the iφ³ coefficient would strengthen the claim.
  3. Figure captions for the two-point function plots should explicitly state the system sizes, boundary conditions, and fitting procedure used to extract the growth, to allow independent verification of the numerical evidence.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, the clear summary of its contributions, and the recommendation to accept. No major comments were raised.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained via standard techniques

full rationale

The paper constructs PT-symmetric deformations of four known lattice models (Ising, Schwinger, Blume-Capel, clock) and identifies the YL critical point by computing scaling dimensions via state-operator correspondence, finding agreement with independently known 2D YL CFT values (c = -22/5 and operator dimensions). The iφ³ description follows from applying standard bosonization (Schwinger) and Polyakov-Hubbard (others) mappings, which are not derived from or fitted to the present numerics. The two-point function growth is a direct numerical check against theoretical expectations. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear; all load-bearing steps are externally benchmarked or use established, non-circular mappings.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the state-operator correspondence for these lattice models and on the correctness of the bosonization and Polyakov-Hubbard mappings to the iφ³ theory; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption State-operator correspondence of 2D conformal field theory applies directly to the deformed lattice models at the identified critical points
    Used to extract scaling dimensions from the quantum Hamiltonian spectrum.
  • domain assumption Bosonization and Polyakov-Hubbard transformations correctly map the microscopic models onto the massless boson plus iφ³ theory
    Invoked to identify the effective field theory description.

pith-pipeline@v0.9.1-grok · 5747 in / 1376 out tokens · 30307 ms · 2026-06-26T16:41:42.189210+00:00 · methodology

discussion (0)

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