arXiv subjects

Weicheng Ye

Publications and source records attributed to Weicheng Ye.

At least 19 recordsLinked to original sources

arXiv2026

AgonAlpha: Autonomous Alpha Discovery via Prompt Economy and Scalable Agentic Search

Language models can propose many plausible trading factors, but an autonomous research system must also allocate its evaluation budget, verify its own evidence, and preserve how each candidate was produced. We present AgonAlpha, an architecture that searches over frozen research artifacts---hypotheses, executable expressions, platform evidence, rationales, and review status---rather than formulas alone. To our knowledge, AgonAlpha is the first alpha-mining system to combine verified artifact search, a fresh-context adversarial reviewer with re-execution and veto authority, and pending-aware parallel budget allocation, together with a complete public evidence trail. Independent deployments on WorldQuant BRAIN produced SPECTACULAR-grade alphas across five users and six model backends, with Fitness reaching 9.50 and Sharpe reaching 3.48, while retaining prompt-to-expression provenance for every submission.

cs.AI↗

arXiv2026

Topologically shadowed quantum criticality: A non-compact conformal manifold

We put forward a proposal for topological quantum critical points (tQCPs) separating non-invertible chiral topological orders in $(2+1)$ dimensions. We conjecture that these tQCPs can be captured by a family of scale-invariant field theories forming a non-compact scale-invariant manifold. A central feature of our proposal is topological shadowing: the underlying critical theory is rigorously constrained by the global topological data of the two adjacent gapped phases. These theories can be further projected into quantum field theories with universal non-local structures. Specifically, we show that the quantum dynamics of the $U(1)$ symmetric critical point uniquely characterized by a topological angle $Θ_{\text{cft}}$ -- which is defined by a commutator between two Wilson loop operators on a torus -- is determined by the braiding angles $Θ_{1,2}$ of the adjacent gapped phases via the relation $Θ_{\text{cft}}^{-1} =\frac{1}{2}[Θ_1^{-1} + Θ_2^{-1}]$. Despite the non-locality, our renormalization group calculations (up to two-loop order) strongly suggest that the theory shall maintain exact scale invariance. This establishes, without supersymmetry, a continuous manifold of fixed points that naturally becomes a conformal manifold when the local structure is further enforced.

cond-mat.str-el↗

arXiv2026

How to Build Anomalous (3+1)d Topological Quantum Field Theories

We develop a systematic framework for constructing (3+1)-dimensional topological orders or topological quantum field theories (TQFTs) that realize specified anomalies of finite symmetries, as encountered in gauge theories with fermions or in fermionic lattice systems. Our approach generalizes the symmetry-extension construction to the fermionic setting, and is grounded in recent advances in the categorical classification of anomalous TQFTs in (3+1)d. In this framework, symmetry-extension data of a supercohomology theory are translated into a fusion 2-category, on which the anomalous TQFT is built. Building on this machinery, we demonstrate explicit calculations for various symmetry groups and their associated anomalies, with the help of a hastened Adams spectral sequence for computing supercohomology groups which we will detail in a planned sequel. Finally, we prove that all supercohomology anomalies can be realized by fermionic topological orders, whereas beyond-supercohomology anomalies cannot, resolving a question of Córdova--Ohmori for fermionic (3+1)d systems with finite symmetries.

math-ph↗

arXiv2026

Symmetric Gapped States and Symmetry-Enforced Gaplessness in 3-dimension

We establish a comprehensive framework for characterizing the infrared (IR) phases of a fermionic quantum theory in three spatial dimensions, based on its quantum anomalies associated with a finite symmetry. We uncover a fundamental dichotomy among these anomalies: the first class of anomalies can always be realized by symmetric gapped states, while the second class can never be realized by gapped states without breaking the given symmetry, establishing the phenomenon of symmetry-enforced gaplessness in these settings. Moreover, using the construction of symmetry extension, we construct the candidate gapped states that theories with the first class of anomalies can flow to in the IR. As an application, we provide concrete predictions of the candidate IR phases of (3+1)-dimensional gauge theories based on our results. Our results also suggest that systems with discrete chiral anomalies cannot be gapped out by adding arbitrary bosonic degrees of freedom.

hep-th↗

arXiv2025

Universal quantum phase classification on quantum computers from machine learning

The classification of quantum phases of matter remains a fundamental challenge in condensed matter physics. We present a novel framework that combines shadow tomography with modern time-series machine learning models to enable efficient and practical quantum phase classification. Our approach leverages the definition of quantum phases based on connectivity through finite-depth local unitary circuits, generating abundant training data by applying Haar random evolution to representative quantum states for a given phase. In this way, the training data can be efficiently obtained from a quantum simulator. Additionally, we demonstrate that advanced time-series models can be used to process the training data and achieve universal quantum phase classification that does not rely on local order parameters. To validate the universality and versatility of our method, we test the model against one-dimensional quantum spin chains such as the Ising model and the axial next-nearest-neighbor Ising (ANNNI) model, showing excellent agreement with known phase boundaries.

quant-ph↗

arXiv2025

Higher obstructions to conformal boundary conditions and lattice realizations

Although it is long believed that vanishing of chiral central charges of a 2d conformal field theory (CFT) implies the existence of conformal boundary conditions, there are yet higher obstructions. In this paper, we focus on 2d rational CFTs, for which we identify a series of obstructions, known as higher central charges. We also discuss its implication for lattice realizations and the generalization with global symmetries.

hep-th↗

arXiv2025

Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders

We provide a mathematical proposal for the anomaly indicators of symmetries of (2+1)-d fermionic topological orders, and work out the consequences of our proposal in several nontrivial examples. Our proposal is an invariant of a super modular tensor category with a fermionic group action, which gives a (3+1)-d topological field theory (TFT) that we conjecture to be invertible; the anomaly indicators are partition functions of this TFT on $4$-manifolds generating the corresponding twisted spin bordism group. Our construction relies on a bosonization construction due to Gaiotto-Kapustin and Tata-Kobayashi-Bulmash-Barkeshli, together with a ``bosonization conjecture'' which we explain in detail. In the second half of the paper, we discuss several examples of our invariants relevant to condensed-matter physics. The most important example we consider is $\mathbb{Z}/4^T\times \mathbb{Z}/2^f$ time-reversal symmetry with symmetry algebra $\mathcal T^2 = (-1)^FC$, which many fermionic topological orders enjoy, including the $\mathrm{U}(1)_5$ spin Chern-Simons theory. Using newly developed tools involving the Smith long exact sequence, we calculate the cobordism group that classifies its anomaly, present the generating manifold, and calculate the partition function on the generating manifold which serves as our anomaly indicator. Our approach allows us to reproduce anomaly indicators known in the literature with simpler proofs, including $\mathbb{Z}/4^{Tf}$ time-reversal symmetry with symmetry algebra $\mathcal T^2 = (-1)^F$, and other symmetry groups in the 10-fold way involving Lie group symmetries.

math-ph↗

arXiv2025

Global Structure in the Presence of a Topological Defect

We investigate the global structure of topological defects which wrap a submanifold $F\subset M$ in a quantum field theory defined on a closed manifold $M$. The Pontryagin-Thom construction oversees the interplay between the global structure of $F$ and the global structure of $M$. We will employ this construction to two distinct mathematical frameworks with physical applications. The first framework is the concept of a characteristic structure, consisting of the data of pairs of manifolds $(M,F)$ where $F$ is Poincar\'e dual to some characteristic class. This concept is discussed in the mathematics literature, and shown here to have meaningful physical interpretations related to defects. In our examples we will mainly focus on the case where $M$ is 4-dimensional and $F$ has codimension 2. The second framework uses obstruction theory and the fact that spontaneously broken finite symmetries leave behind domain walls, to determine the conditions on which dimensions a higher-form finite symmetry can spontaneously break. We explicitly study the cases of higher-form $\mathbb Z/2$ symmetry, but the method can be generalized to other groups.

math-ph↗

arXiv2024

Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints

We present a computational study of the mod-2 cohomology of three-dimensional (3D) space groups, with an eye toward their applications in Lieb--Schultz--Mattis constraints. We prove finite-generation results for the cohomology of crystallographic groups and give ring presentations for $H^*(G,\mathbb Z_2)$ for \emph{all} 230 3D space groups, together with explicit inhomogeneous representatives for the degree-$\leq 3$ cocycles used in the lattice applications. The all-degree interpretation of the ring presentations is organized through finite LHS-spectral-sequence and Hilbert-series verification checks. We then associate distinguished classes in $H^3(G,\mathbb{Z}_2)$ to irreducible Wyckoff positions and use these classes as cohomological representatives of Lieb--Schultz--Mattis anomaly candidates when the on-site projective representations are classified by powers of $\mathbb{Z}_2$. Finally, we apply the resulting anomaly data to $\mathrm U(1)$ quantum spin liquids on the 3D pyrochlore lattice and compare the symmetry-fractionalization constraints with projective-symmetry-group calculations.

cond-mat.str-el↗

arXiv2024

Classification of symmetry-enriched topological quantum spin liquids

We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian, chiral or non-chiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain anti-unitary symmetry, and may permute anyons. The framework applies to all types of lattices, and can systematically distinguish different lattice systems with the same symmetry group using their Lieb-Schultz-Mattis anomalies. We apply this framework to classify $U(1)_{2N}$ chiral states and non-Abelian Ising$^{(ν)}$ states enriched by a $p6\times SO(3)$ or $p4\times SO(3)$ symmetry, and $\mathbb{Z}_N$ topological orders and $U(1)_{2N}\times U(1)_{-2N}$ topological orders enriched by a $p6m\times SO(3)\times\mathbb{Z}_2^T$, $p4m\times SO(3)\times\mathbb{Z}_2^T$, $p6m\times\mathbb{Z}_2^T$ or $p4m\times\mathbb{Z}_2^T$ symmetry, where $p6$, $p4$, $p6m$ and $p4m$ are lattice symmetries, while $SO(3)$ and $\mathbb{Z}_2^T$ are spin rotation and time reversal symmetries, respectively. In particular, we identify symmetry-enriched topological quantum spin liquids that are not easily captured by the usual parton-mean-field approach, including examples with the familiar $\mathbb{Z}_2$ topological order.

cond-mat.str-el↗

arXiv2024

Complexity and order in approximate quantum error-correcting codes

We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems, covering systems with both all-to-all connectivity and geometric scenarios like lattice systems in finite spatial dimensions. To this end, we introduce a type of code parameter that we call subsystem variance, which is closely related to the optimal AQEC precision. Our key finding is that, for a code encoding $k$ logical qubits in $n$ physical qubits, if the subsystem variance is below an $O(k/n)$ threshold, then any state in the code subspace must obey certain circuit complexity lower bounds, which identify nontrivial "phases" of codes. Based on our results, we propose $O(k/n)$ as a boundary between subspaces that should and should not count as AQEC codes. This theory of AQEC provides a versatile framework for understanding quantum complexity and order in many-body quantum systems, generating new insights for wide-ranging physical scenarios, in particular topological order and critical quantum systems which are of outstanding importance in many-body and high energy physics. We observe from various different perspectives that roughly $O(1/n)$ represents a common, physically significant "scaling threshold" of subsystem variance for features associated with nontrivial quantum order.

quant-ph↗

arXiv2024

Why Groups Matter: Necessity of Group Structures in Attributions

Explainable machine learning methods have been accompanied by substantial development. Despite their success, the existing approaches focus more on the general framework with no prior domain expertise. High-stakes financial sectors have extensive domain knowledge of the features. Hence, it is expected that explanations of models will be consistent with domain knowledge to ensure conceptual soundness. In this work, we study the group structures of features that are naturally formed in the financial dataset. Our study shows the importance of considering group structures that conform to the regulations. When group structures are present, direct applications of explainable machine learning methods, such as Shapley values and Integrated Gradients, may not provide consistent explanations; alternatively, group versions of the Shapley value can provide consistent explanations. We contain detailed examples to concentrate on the practical perspective of our framework.

q-fin.CP↗

arXiv2024

Generalized Groves of Neural Additive Models: Pursuing transparent and accurate machine learning models in finance

While machine learning methods have significantly improved model performance over traditional methods, their black-box structure makes it difficult for researchers to interpret results. For highly regulated financial industries, model transparency is equally important to accuracy. Without understanding how models work, even highly accurate machine learning methods are unlikely to be accepted. We address this issue by introducing a novel class of transparent machine learning models known as generalized groves of neural additive models. The generalized groves of neural additive models separate features into three categories: linear features, individual nonlinear features, and interacted nonlinear features. Additionally, interactions in the last category are only local. A stepwise selection algorithm distinguishes the linear and nonlinear components, and interacted groups are carefully verified by applying additive separation criteria. Through some empirical examples in finance, we demonstrate that generalized grove of neural additive models exhibit high accuracy and transparency with predominantly linear terms and only sparse nonlinear ones.

cs.LG↗

arXiv2024

Topological holography for fermions

Topological holography is a conjectured correspondence between the symmetry charges and defects of a $D$-dimensional system with the anyons in a $(D+1)$-dimensional topological order: the symmetry topological field theory (SymTFT). Topological holography is conjectured to capture the topological aspects of symmetry in gapped and gapless systems, with different phases corresponding to different gapped boundaries (anyon condensations) of the SymTFT. This correspondence was previously considered primarily for bosonic systems, excluding many phases of condensed matter systems involving fermionic electrons. In this work, we extend the SymTFT framework to establish a topological holography correspondence for fermionic systems. We demonstrate that this fermionic SymTFT framework captures the known properties of $1+1D$ fermion gapped phases and critical points, including the classification, edge-modes, and stacking rules of fermionic symmetry-protected topological phases (SPTs), and computation of partition functions of fermionic conformal field theories (CFTs). Beyond merely reproducing known properties, we show that the SymTFT approach can additionally serve as a practical tool for discovering new physics, and use this framework to construct a new example of a fermionic intrinsically gapless SPT phase characterized by an emergent fermionic anomaly.

cond-mat.str-el↗

arXiv2023

How to address monotonicity for model risk management?

In this paper, we study the problem of establishing the accountability and fairness of transparent machine learning models through monotonicity. Although there have been numerous studies on individual monotonicity, pairwise monotonicity is often overlooked in the existing literature. This paper studies transparent neural networks in the presence of three types of monotonicity: individual monotonicity, weak pairwise monotonicity, and strong pairwise monotonicity. As a means of achieving monotonicity while maintaining transparency, we propose the monotonic groves of neural additive models. As a result of empirical examples, we demonstrate that monotonicity is often violated in practice and that monotonic groves of neural additive models are transparent, accountable, and fair.

cs.LG↗

arXiv2023

Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory

Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)$D$ on-site symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory to calculate the anomaly indicators of a (2+1)$D$ topological order with a general symmetry group $G$, which may be discrete or continuous, Abelian or non-Abelian, contain anti-unitary elements or not, and permute anyons or not. These anomaly indicators are partition functions of the (3+1)$D$ topological quantum field theory on a specific manifold equipped with some $G$-bundle, and they are expressed using the data characterizing the topological order and the symmetry actions. Our framework is applied to derive the anomaly indicators for various symmetry groups, including $\mathbb{Z}_2\times\mathbb{Z}_2$, $\mathbb{Z}_2^T\times\mathbb{Z}_2^T$, $SO(N)$, $O(N)^T$, $SO(N)\times \mathbb{Z}_2^T$, etc, where $\mathbb{Z}_2$ and $\mathbb{Z}_2^T$ denote a unitary and anti-unitary order-2 group, respectively, and $O(N)^T$ denotes a symmetry group $O(N)$ such that elements in $O(N)$ with determinant $-1$ are anti-unitary. In particular, we demonstrate that some anomaly of $O(N)^T$ and $SO(N)\times \mathbb{Z}_2^T$ exhibit symmetry-enforced gaplessness, i.e., they cannot be realized by any symmetry-enriched topological order. As a byproduct, for $SO(N)$ symmetric topological orders, we derive their $SO(N)$ Hall conductance.

cond-mat.str-el↗

arXiv2023

Probing sign structure using measurement-induced entanglement

The sign structure of quantum states is closely connected to quantum phases of matter, yet detecting such fine-grained properties of amplitudes is subtle. Here we employ as a diagnostic measurement-induced entanglement (MIE): the average entanglement generated between two parties after measuring the rest of the system. We propose that for a sign-free state, the MIE upon measuring in the sign-free basis decays no slower than correlations in the state before measurement. Concretely, we prove that MIE is upper bounded by mutual information for sign-free stabilizer states (essentially CSS codes), which establishes a bound between scaling dimensions of conformal field theories describing measurement-induced critical points in stabilizer systems. We also show that for sign-free qubit wavefunctions, MIE between two qubits is upper bounded by a simple two-point correlation function, and we verify our proposal in several critical ground states of one-dimensional systems, including the transverse field and tri-critical Ising models. In contrast, for states with sign structure, such bounds can be violated, as we illustrate in critical hybrid circuits involving both Haar or Clifford random unitaries and measurements, and gapless symmetry-protected topological states.

quant-ph↗

arXiv2022

Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system. We derive the topological partition functions that characterize the LSM constraints in spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group in one or two spatial dimensions, and $G_{int}$ is any internal symmetry whose projective representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then apply these results to study the emergibility of a class of exotic quantum critical states, including the well-known deconfined quantum critical point (DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the competition between a magnetic state and a non-magnetic state. We identify all possible realizations of these states on systems with $SO(3)\times \mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ lattice symmetry. Many interesting examples are discovered, including a DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb lattices, and a class of quantum critical spin-quadrupolar liquids of which the most relevant spinful fluctuations carry spin-$2$. In particular, there is a realization of spin-quadrupolar DSL that is beyond the usual parton construction. We further use our formalism to analyze the stability of these states under symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete example, we find that a DSL can be stable in a recently proposed candidate material, NaYbO$_2$.

cond-mat.str-el↗