Lee--Yang Zeros and Pseudocritical Drift in J-Q N'eel Antiferromagnet--Valence-Bond Solid Transitions

arXiv:2603.15116 · cond-mat.str-el, cond-mat.stat-mech · Submitted 2026-03-16 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Lee--Yang Zeros and Pseudocritical Drift in J-Q N'eel Antiferromagnet--Valence-Bond Solid Transitions".

Kai: The gist Lee–Yang zeros provide a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in J-Q models by tracking their finite-size flow,

Mira: First, who's behind it and why it matters.

Title and authors: Kai: This segment is about the paper's title and who wrote it, "Lee--Yang Zeros and Pseudocritical Drift in J-Q N'eel Antiferromagnet--Valence-Bond Solid Transitions." It lays out what they are actually trying to do.

Mira: They are using Lee-Yang zeros as a way to probe the transition between the N'eel antiferromagnet and the valence-bond solid by tracking how these zeros move as the system size grows.

Lev: It’s about using those zeros to see if it’s behaving like a continuous line or if it has this extended pseudocritical region, which is what they are trying to diagnose.

Kai: Basically, they are applying this analysis across different J-Q models, specifically the uniform J-Q2 and J-Q3 systems, to check if this behavior holds up generally.

Mira: The paper also emphasizes that they employ a symmetry-preserving anchor Hamiltonian H0 to define an ensemble that respects all the microscopic symmetries when they are studying these finite L and inverse temperature beta settings.

Lev: This setup lets them infer the phases and the criticality based on how those symmetry-resolved fluctuations change with system size L two.

Kai: They probe channels specified by operator support, whether it's a site, bond, or plaquette operator, along with a translation sector defined from a low energy scale.

Mira: That combination of things—the specific probes and the symmetry constraints—is what lets them see how the physics changes across different parts of the model structure.

Lev: The complexity comes from evaluating these generating functions to infer the underlying physics based on how they depend on L one.

Kai: And they show that their benchmark studies, like those for the dimerized Heisenberg model and the checkerboard J-Q model, successfully recover what we already knew about standard O(three) scaling in one case and clear spacetime-volume scaling in the other.

Mira: They also point out that their results for J-Q2 and J-Q3 are consistent with a weakly first-order interpretation that has been discussed before, which sets up the context for what they actually discovered.

The paper's summary: Kai: Moving on to the summary of "Lee--Yang Zeros and Pseudocritical Drift in J-Q N'eel Antiferromagnet--Valence-Bond Solid Transitions," they explain the core mechanism of their study.

Mira: They explain that the key idea is tracking the finite-size flow of Lee-Yang zeros to directly distinguish between a continuous critical point and a first-order transition by looking at their movement.

Lev: So, essentially, they are using those zeros to measure the singularity scale directly, which they say is much cleaner than just looking at some real-axis measurements.

Kai: They show that these zeros probe symmetry-resolved fluctuations and reveal whether we are seeing the expected O(three) critical scaling or if it's the spacetime-volume scaling associated with a first-order transition.

Mira: The summary highlights that they use those zeros to look at channels like site, bond, or plaquette operators along with a translation sector defined by a symmetry-preserving anchor Hamiltonian H0.

Lev: It highlights how they use the complexity of these generating functions to infer the physics from the L dependence of those symmetry-resolved fluctuations one.

Kai: And they show that their benchmark studies confirm what we already knew about standard O(three) scaling in the dimerized Heisenberg model and clear spacetime-volume scaling in the checkerboard J-Q model one.

Mira: They also highlight that the results for J-Q2 and J-Q3 are consistent with a weakly first-order interpretation discussed in the literature, which gives context to their findings.

The paper's improvements: Kai: Now let's talk about the improvements suggested in "Lee--Yang Zeros and Pseudocritical Drift in J-Q N'eel Antiferromagnet--Valence-Bond Solid Transitions." They suggest a few ways we can use these zeros to characterize the transition order more precisely.

Mira: Specifically, they suggest that we can extract the scaling dimension eta from those zeros using a specific formula, which is really interesting because it lets us determine if an observed exponent is a true anomalous dimension or just a finite-size diagnostic one.

Lev: That means we get to check the actual physics of the exponent itself, not just assume it's something else.

Kai: They also suggest comparing two distinct behaviors of the leading zeros to differentiate between critical pinching and coexistence scaling.

Mira: This comparison is powerful because at phase coexistence, by contrast, a small source biases competing phases by an amount proportional to the Euclidean spacetime volume Vτ, which leads to that spacetime-volume scaling instead of standard critical power laws one.

Lev: That comparison between the two behaviors is a big step for understanding how those zeros map onto different physical regimes.

Kai: It’s about using those zeros not just to see if something is happening, but to pinpoint exactly where it's happening in the phase diagram.

Conclusion: Mira: So wrapping up "Lee--Yang Zeros and Pseudocritical Drift in J-Q N'eel Antiferromagnet--Valence-Bond Solid Transitions," this method gives us a way to characterize transition order more precisely than standard measurements by looking at the finite-size flow of the zeros.

Kai: It gives us a clear diagnostic tool to see if we have weak first-order behavior or extended pseudocritical behavior in these quantum magnets.

Lev: For the J-Q2 and J-Q3 models, that systematic downward drift of the leading zero scaling confirms they are exhibiting a weakly first-order transition one.

Mira: It’s about using those zeros to pinpoint exactly where this slow drift is happening, which is what makes this method so powerful.

Lev: We're seeing how it works in practice on real hardware, and the paper shows the sensitivity of this diagnostic tool one.

Kai: This work solidifies the idea that these Lee–Yang zeros are a sensitive probe for understanding complex phase transitions.

Mira: It really helps us move past just looking at correlations and start using these zeros to understand the fundamental nature of these quantum phase boundaries.

Lev: And for real experimentalists, knowing how this drift behaves tells you exactly what kind of finite-size scaling you should expect when you eventually measure it.

Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University · Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, China · Key Laboratory of Polar Materials and Devices (MOE), School of Physics, East China Normal University

cond-mat.str-el, cond-mat.stat-mech

Submitted: 2026-03-16

Updated: 2026-10-09

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 79/100

The gist: The gist Lee–Yang zeros provide a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in J-Q models by tracking their finite-size flow, which reveals whether a

Key concepts

Lee--Yang Zeros
These are specific points where the complex generating function of a quantum system equals zero. They act as sensitive indicators of phase transitions and their behavior near criticality is used to distinguish between continuous critical behavior and first-order transitions.
Stochastic Series Expansion Quantum Monte Carlo (SSE QMC)
This is a computational method used to simulate quantum systems by sampling configurations near the transition point. It involves reweighting these sampled configurations using complex source fields to extract information about the system's properties, including the Lee-Yang zeros.
Pseudocritical Drift
This refers to a systematic shift or drift observed in the scaling of leading Lee-Yang zeros as the system size increases. This drift is a signature indicating that the transition is not strictly first-order but exhibits extended pseudocritical behavior, characteristic of weakly first-order transitions.

Terminology

Summary

The gist Lee–Yang zeros provide a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in J-Q models by tracking their finite-size flow, which reveals whether a transition is weakly first-order or exhibits extended pseudocritical behavior

How it works

The analysis utilizes Lee–Yang zeros computed within stochastic series expansion quantum Monte Carlo by reweighting configurations sampled near criticality in the presence of complex source fields The method is applied to square-lattice J-Q models, which offer a sign-problem-free setting for probing the quantum phase transition between N´eel antiferromagnet and columnar valence-bond solid Benchmark studies of the dimerized Heisenberg model and checkerboard J-Q model validate this method, yielding stable O(3) critical scaling in the former and clear spacetime-volume scaling in the latter, as expected for a first-order transition

The core technique involves evaluating complex generating functions in symmetry-resolved channels to track the finite-size flow of low-lying Lee–Yang zeros, which directly measures the singularity scale and distinguishes critical behavior from first-order coexistence The analysis uses amplitude-free two-size estimators constructed from low-lying zeros to analyze benchmark models together with the uniform J-Q3 and J-Q2 systems

Key Findings on Transition Order

The study finds a pronounced and systematic drift of the leading-zero scaling with increasing system size, consistent with an extended pseudocritical regime This behavior implies an effective scaling dimension ∆ϕ of the SO(5) order-parameter field that decreases with size and vanishes in the thermodynamic limit Such behavior lies below the scalar unitarity bound of any unitary relativistic conformal field theory in 2+1 dimensions and enforces inverse spacetime-volume scaling of the zeros, which is the hallmark of a first-order transition These results support a weakly first-order interpretation of the N´eel–VBS transition

For the uniform J-Q3 and J-Q2 models, both in the N´eel and VBS channels, systematic downward drift of the leading Lee–Yang zeros is observed relative to the first-order reference form In J-Q3, this behavior is consistent with a weakly first-order or pseudocritical interpretation discussed in the literature, namely a slow flow toward the spacetime-volume law gLY(L) ∼ L −(d+z) For J-Q2, closely analogous Lee–Yang flow is found in both probes, providing direct evidence that J-Q2 exhibits the same slow drift toward the first-order benchmark

Distinguishing Criticality from Coexistence

The leading Lee–Yang zeros provide a more direct probe of the finite-size singularity scale and expose slow drift more clearly than conventional real-axis observables in a weakly first-order regime Conventional real-axis observables, such as order-parameter moments or spin correlations, may be strongly affected by phase mixing and analytic backgrounds By contrast, the leading zeros directly encode the finite-size singularity scale through their distance from the real axis

The analysis distinguishes between critical pinching and coexistence scaling by comparing two distinct behaviors of the leading zeros Near a continuous transition, the leading zero scales as g(k)LY(L) ∼ Ak L − yh, where yh is the RG eigenvalue of the source In contrast, in a coexistence regime, the natural finite-size scale is the Euclidean spacetime volume Vτ ≡ βLd The leading zeros obey g(k)LY(L, β) ∼ Bk/βLd

Symmetry Channels and Probes

The Lee–Yang probes are specified by the microscopic support of the operator, site, bond, or plaquette, together with a translation sector of a symmetry-preserving anchor Hamiltonian H0 Representative channels include:

(a) Site (π, π) Mz = P r (−1)x+yS z r,

(b) Bond (π, 0), (0, π) Dx = P r (−1)x B x(r), Dy = P r (−1)y B y(r),

(c) Plaquette (π, 0), (0, π) O plaq,

The checkerboard J-Q model is further refined by resolving plaquettes into two families using row parity and checkerboard family labels The resulting PSS estimator is defined by the projected operators O PSS s ≡ X□ 1 + s εcb(□) 2ϵrow(□) O(□), with s = ±1

Conclusion

The work introduces a symmetry-resolved Lee–Yang framework that combines SSE sampling at a symmetry-preserving real anchor Hamiltonian with analytic continuation of conjugate sources to evaluate complex generating functions and extract leading zeros Benchmark calculations recover conventional O(3) scaling in the columnar dimerized Heisenberg model and the expected first-order scaling behavior in the CBJQ model For the uniform J-Q3 and J-Q2 models, systematic downward drift of the leading-zero scaling is found in both N´eel and VBS channels, supporting a weakly first-order interpretation The Lee–Yang zeros provide a particularly sensitive probe of this slow drift, especially in the less settled J-Q2 case This work clarifies a long-standing question from the perspective of complexified partition functions and demonstrates the power of the Lee–Yang zero method

Improvements for AI systems

  1. Bold header: Lee-Yang zero analysis for transition order discrimination

Lee-Yang zeros provide a natural probe of the debated N´eel–VBS criticality in J-Q models, specifically by tracking their finite-size flow to distinguish between a continuous critical point and a first-order transition, as demonstrated by the systematic downward drift of the two-size estimator etaeff(L) relative to the first-order benchmark.

  1. Bold header: Robust finite-size diagnostic for weak transitions

The system can now reliably diagnose weakly first-order or pseudocritical interpretation by observing how the leading Lee–Yang zeros provide a particularly sensitive probe of this slow drift, which is consistent with the behavior found in both J-Q2 and J-Q3 models.

  1. Bold header: Symmetry-resolved probe for order parameter characterization

AI systems can now perform symmetry-resolved probes, such as using the staggered magnetization channel Mz or plaquette operators Oplaq, to determine if a transition is governed by the expected O(3) critical scaling or if it exhibits the characteristic spacetime-volume scaling of a first-order transition.

  1. Bold header: Characterization of non-universal amplitude and anomalous dimension

The system can extract the scaling dimension η from the Lee–Yang zeros using yh = (d + z + 2 − η)/2, allowing for the determination of whether a observed exponent is a true anomalous dimension or merely a finite-size diagnostic.

  1. Bold header: Discrimination between coexistence and critical scaling

The AI can differentiate between regimes by checking the behavior of the leading zero, as At phase coexistence, by contrast, a small source biases competing phases by an amount proportional to the Euclidean spacetime volume Vτ, leading to the characteristic spacetime-volume scaling of a first-order transition rather than standard critical power laws.

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