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QCD Crossover at Low Temperatures from Lee-Yang Edge Singularity
D. A. Clarke, H. -T. Ding, J. -B. Gu, S. -T. Li, Swagato Mukherjee, P. Petreczky, C. Schmidt, H. -T. Shu, K. -F. Ye
arXiv·2026
We provide the first lattice-QCD estimate of the crossover line down to $T\simeq108$~MeV. We introduce a new method that combines the Lee-Yang edge in the complex plane of baryon chemical potential $μ_B$ with universal chiral scaling to determine the $μ_B$ dependence of the QCD chiral critical and pseudo-critical temperatures. By performing $(2\!+\!1)$-flavor lattice QCD simulations at $T\simeq108$~MeV and purely imaginary $μ_B$ with a single lattice spacing and two volumes, we compute $μ_B$-dependent baryon-number susceptibilities and extract the location of the Lee-Yang edge. Together with universal scaling near the QCD chiral transition, it constrains the mapping function between $\{T,μ_B\}$ and the scaling variable (\textit{i.e.}\ the argument of the universal scaling functions). This mapping function then yields the $μ_B$ dependence of the critical and pseudo-critical temperatures for $T\gtrsim108$~MeV. While our calculation is performed only at a single value of low temperature without explicit input from small-$μ_B$ expansion, the resulting $μ_B$ dependence of the pseudo-critical temperature is consistent with established lattice-QCD determinations at small $μ_B$ and compatible with chemical freeze-out parameters of heavy-ion collisions down to low temperatures, demonstrating the validity and robustness of the method. Application of this method can be systematically extended to additional temperatures and finer discretizations, opening a pathway to charting the QCD phase diagram in the low-$T$, high-$μ_B$ regime.
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View paper →Direct and Indirect Loop Equations in Lattice Yang-Mills Theory
Xizhe Liu, Gang Yang
arXiv·2026
The dynamics of Wilson loops is governed by an infinite set of Schwinger-Dyson equations and trace relations. In the context of the lattice positivity bootstrap, a central challenge is determining a dynamically independent basis of these operators within a truncated space. We present a systematic framework to solve this problem, utilizing a geometric plaquette-cut and subloop-cut strategy to efficiently generate all (local) direct equations. Furthermore, we identify and analyze ``indirect equations", which arise from the elimination of higher-length intermediate loops. We elucidate the origin of these subtle relations and propose a vertex-filtering strategy to construct them. Applying the above framework to SU(2) lattice Yang-Mills theory, we provide explicit counting of independent canonical loops and equations in 2, 3, and 4 dimensions, along with a statistical analysis of their asymptotic growth.
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View paper →The Squirrel Parser: A Linear-Time PEG Packrat Parser Capable of Left Recursion and Optimal Error Recovery
Luke A. D. Hutchison
arXiv·2026
We present the squirrel parser, a PEG packrat parser that directly handles all forms of left recursion with optimal error recovery, while maintaining linear time complexity in the length of the input even in the presence of an arbitrary number of errors. Traditional approaches to handling left recursion in a recursive descent parser require grammar rewriting or complex algorithmic extensions. We derive a minimal algorithm from first principles: cycle detection via per-position state tracking and $O(1)$-per-LR-cycle communication from descendant to ancestor recursion frames, and fixed-point search via iterative expansion. For error recovery, we derived a set of four axioms and twelve constraints that must be imposed upon an optimal error recovery design to ensure completeness, correctness, optimality of performance, and intuitiveness of behavior. We utilized a constraint satisfaction mechanism to search the space of all possibilities, arriving at a provably optimal and robust error recovery strategy that maintains perfect performance linearity.
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