arXiv subjects

Yang Qi

Publications and source records attributed to Yang Qi.

At least 19 recordsLinked to original sources

arXiv2026

Nullspace-guided Adaptive Bootstrap of Quantum Many-body Systems

We introduce a nullspace-guided adaptive (NGA) bootstrap method that improves the energy lower bounds of quantum many-body ground states by refining the bootstrap basis in a dynamic and incremental way. At each iteration, the optimized moment matrix reveals a nullspace of saturated positivity directions, which is intuitively interpreted as annihilators of the approximate ground-state subspace. The NGA bootstrap then prunes operators with small nullspace leverage and grows the basis along descendants of these null directions. By applying the NGA bootstrap to the transverse-field Ising chain, we obtain nearly exact energy lower bounds because the algorithm automatically discovers the eigenoperator structure in terms of Jordan-Wigner fermions from a minimal local bootstrap basis. For the Hubbard chain, it improves upon state-of-the-art energy lower bounds by up to two orders of magnitude, reaching errors ranging from $10^{-3}$ down to $10^{-5}$ in the strongly correlated regimes. We further show that the NGA framework can be used to improve the certified two-sided bounds on general observables. In addition, the bootstrap error decreases approximately as a power law with increasing computational resources. These results suggest that our method provides a practical and scalable route toward accurate bootstrap of general quantum many-body systems.

cond-mat.str-el↗

arXiv2026

Algebra of free fermions: Classifying spaces, Hamiltonians, and computation

Research on topological phases of matter is a core field in modern condensed matter physics. Free fermion systems, such as topological insulators and superconductors, have been studied using the "Tenfold Way" and K-theory. Building on Kitaev's idea of $Ω$-spectrum and classifying space, as well as Freed-Moore's K-theory, this work demonstrates that free fermionic systems form a genuine $G$-$Ω$-spectrum and clarifies its connection to several distinct classification schemes appearing in the physical literature. By introducing the $\mathbb{Z}_2$-graded algebra $A_{\mathrm{sym}}^V$, the classification problem for systems with general symmetries, including antilinear symmetries, antisymmetries, projective representations, and point group symmetries, is turned into an extension problem in representation theory. To solve this, a computational method for the $\mathbb{Z}_2$-graded Wedderburn-Artin decomposition of $A_{\mathrm{sym}}^V$ is developed. This decomposition not only yields a classification but also enables the explicit construction of the corresponding Dirac Hamiltonian. Furthermore, a GAP programming package has been developed to automate these calculations.

cond-mat.mes-hall↗

arXiv2026

Quantum geometric localization length and localization criticality in an ideally flat Chern band

We propose that the localization length in an isolated, ideally flat Chern band is set by quantum geometry. We explore the corresponding localization transition and its critical scaling by applying transfer matrix calculations in the maximally localized hybrid Wannier basis, whose spatial spread is exactly characterized by a quantum geometric length. Remarkably, upon tuning the quantum metric of the Chern band, we observe a crossover from a universal regime controlled by the Dirac fixed point to a non-universal regime with continuously varying critical exponents. Within the universal regime, the localization length exhibits a pronounced linear dependence on the quantum geometric length, supporting its quantum geometric nature. These findings provide a novel quantum geometric perspective on the localization in quantum Hall systems such as twisted moiré superlattices, and shed new light on the long-standing controversy over the criticality of the integer quantum Hall transition.

cond-mat.str-el↗

arXiv2026

Emergent magnetic pseudogap from phase fluctuations and hierarchy of scales in two-dimensional superconductors

Preformed pairs and phase fluctuations are believed to play a vital role in predicting the charge pseudogap in the normal state of two-dimensional superconductors. In this work, we extend this idea and further identify the emergent magnetic pseudogap from pure phase fluctuations without invoking any competing order. We examine the NMR relaxation rate $1/T_1T$ by evaluating the bubble contribution and leading-order vertex correction within perturbation theory. It is found that the magnetic pseudogap, manifesting as a smooth suppression of $1/T_1T$ in the normal state, is characterized by a temperature scale $T_\text{mPG}$ distinct from the superconducting gap $Δ_\text{SC}$ and transition temperature $T_c$. The onset scales of both charge and magnetic pseudogap are dominated by the competition of BKT correlation length $ξ(T)$ and BCS coherence length $ξ_\text{BCS}$. Moreover, the vertex correction is shown to be irrelevant for $d$-wave pairing, while it becomes prominent in $s$-wave systems and drives a coherent enhancement of $1/T_1T$ at lower temperatures just above $T_c$. We attribute this normal-state enhancement of $1/T_1T$ to the diverging coherence peak at the $s$-wave superconducting gap edge, which shares the same spirit as the celebrated Hebel-Slichter peak in the BCS theory. Analogous to the coherent Hebel-Slichter peak, regularization by Fermi-liquid-like scatterings is important and is characterized by a scattering length $\ell$. The normal-state coherent enhancement of $1/T_1T$ is hence described by the competition of $ξ(T)$ and $\ell$, through which the coherence scale $T_\text{coh}$ is determined. As a result, the complete evolution of $1/T_1T$ is understood quantitatively in a unified picture as the interplay among hierarchy of scales $ξ(T)$, $ξ_\text{BCS}$ and $\ell$.

cond-mat.supr-con↗

arXiv2026

Structure-Preserving Spectral Dynamic Programming on Compact Lie Groups

We study spectral approximations of the dynamic programming semigroup for finite-horizon optimal control on a connected compact Lie group $G$, and of the associated first-order Hamilton-Jacobi-Bellman equation. The Bellman operator is monotone and non-expansive in the supremum norm, while the Peter-Weyl decomposition of $L^{2}(G)$, on which every Fourier method on $G$ rests, is orthogonal, and the mismatch is quantitative. The natural sup-norm error recursion of the Galerkin iteration is amplified at every step by the Lebesgue constant of the spectral projection, which grows logarithmically on $S^{1}$ and polynomially on compact Lie groups of rank one, including $\mathrm{SO}(3)$, and in computation the iteration violates elementary bounds within a few steps. We restore the dynamic programming structure at the discrete level by replacing the orthogonal projection with spectral filters of Markov type. An auxiliary heat-kernel/vanishing-viscosity scheme yields qualitative sup-norm convergence for Lipschitz data. The main result is a Fejér-type filter on $G$, finite-rank, positivity preserving and non-expansive, together with a convergence theorem at the rate $O(\sqrtδ+\sqrt{ε+1/(δN^2)})$ for Lipschitz data, where $δ$ is the time step, $N$ the spectral resolution and $ε$ the viscosity. The viscosity may be zero, and the coupling $δ=N^{-1}$ then gives the rate $N^{-1/2}$. The proof interprets the filter as a small random perturbation of the controlled dynamics, requires neither a priori regularity of the value function nor a consistency argument in the viscosity sense for the filtering step, and extends to a fully discrete realization based on positive cubature, with exact Wigner transport on $\mathrm{SO}(3)$. Numerical experiments confirm the predicted rates and filter bias and quantify the frame dependence of two chart-based baselines.

math.OC↗

arXiv2026

Phase diagram of a one-dimensional Ising model with an anomalous Z_2 symmetry

Anomalous global symmetries, which can be realized on the boundary of symmetry-protected topological phases, bring\wlx{s} new phases and phase transitions to condensed matter physics. In this work, we study a one-dimensional model with an anomalous $\mathbb Z_2$ symmetry, using the density-matrix renormalization group method. Besides a symmetry-breaking ferromagnetic phase, we find a gapless phase described by the Tomonaga-Luttinger Liquid theory with the central charge $c=1$. Our numerical finding is compatible of theoretical constraints on possible phases resulting from the symmetry anomaly.

cond-mat.str-el↗

arXiv2026

Tropical low-rank approximation and application to optimal control of N-body systems

We study the approximation of the value function of deterministic optimal control problems with fixed initial state, motivated by $N$-body systems. In this setting, the action functional consists of local kinetic and potential terms, along with an interaction potential. We exploit this structure to approximate the value function using a tropical tensor of small rank, i.e.\ a supremum of a small number of additively separable functions. We propose a trajectory-based tropical low-rank approximation method. Rather than propagating basis functions globally, as in usual tropical numerical methods, the approximation of the value function is improved only along a sequence of relevant trajectories. The resulting approximations form a monotone family of computable lower bounds for the exact value function, with the tropical tensor rank increasing at most linearly with the number of outer iterations. Under suitable regularity assumptions, we show that at the initial state, and also at the optimal trajectory starting from this state, the lower bounds converge to the exact value. In the $N$-body setting, the generated basis functions remain additively separable across subsystems, thereby yielding a structured tropical low-rank approximation. Numerical experiments on $N$-body systems with Coulomb-type repulsion illustrate the effectiveness of the approach up to state dimension $200$, within a half hour time budget.

math.OC↗

arXiv2026

Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the $t$-$t^\prime$ Hubbard Model

The Hubbard model and its extensions are canonical theoretical frameworks for understanding correlated electronic states, including those in high-$T_c$ cuprates. Here, we use state-of-the-art thermal tensor network method to map out the temperature-doping phase diagram of the $t$-$t^\prime$ Hubbard model. On the electron-doped side, we find a $d$-wave superconducting (dSC) regime, supporting the scenario of high-$T_c$ superconductivity. In contrast, on the hole-doped side, no robust dSC phase is detected. Instead, a finite-temperature regime dominated by strong pair-density-wave (PDW) fluctuations emerges, which may eventually give way to charge density wave order upon further cooling. The PDW state exhibits inter-arc pairing with net momentum near $(0, π)$, distinct from the zero-momentum pairing in conventional dSC. Furthermore, these fluctuating PDW states occupy the lower portion of the pseudogap regime on the hole-doped side. We provide a comprehensive finite-temperature perspective consistent with previous ground-state studies, shedding new light on pairing instabilities and exotic electronic states in high-$T_c$ superconductors.

cond-mat.str-el↗

arXiv2026

Multi-target density matrix renormalization group for 3D CFTs on the fuzzy sphere

The fuzzy sphere regularization provides a powerful framework for studying three-dimensional (3D) conformal field theories (CFTs) by mapping them onto numerically tractable lattice models on the spherical lowest Landau level. However, the system sizes accessible to this method have been limited by the exact diagonalization (ED). In this work, we transcend this limitation by combining the fuzzy sphere regularization with a sophisticated multi-target density matrix renormalization group (DMRG) algorithm. Focusing on the 3D Ising-type model on the spherical lowest Landau level, we calculate the 24 low-lying energies at a larger system size than previously feasible with ED. At criticality, we extract the scaling dimensions of six primary operators, and the results show significantly improved agreement with bootstrap benchmarks compared to previous ED results at smaller sizes. Our approach allows us to efficiently target multiple excited states in larger systems beyond the reach of exact diagonalization. This study establishes the fuzzy sphere regularization combined with advanced DMRG techniques as a powerful and general framework for precision physics in 3D CFTs.

cond-mat.str-el↗

arXiv2026

The interplay of phase fluctuations and nodal quasiparticles: ubiquitous Fermi arcs in two-dimensional d-wave superconductors

We propose that the pseudogap and Fermi arcs can universally emerge due to thermal (static) phase fluctuations in the normal state of 2D nodal superconductors. By considering a minimal phenomenological model with spatially fluctuating superconducting pairings, we theoretically investigate the role of superconducting phase fluctuations in generic 2D superconductors with disorder-average technique. It is shown for nodal d-wave superconductors that phase fluctuations mediate the scattering of d-wave quasiparticles, smearing out the nodal quasiparticle gap and further leading to pseudogap and Fermi arcs. Moreover, the evolution of Fermi arcs is quantitatively described by two emergent characteristic length scales of the system: one is the finite superconducting correlation length $ξ(T)$, and another the nodal BCS coherence length $ξ_\text{BCS}(k)$. To support our theoretical findings, we numerically report the observation of Fermi arcs in a Hubbard-like model, proposed originally by X. Y. Xu and T. Grover in Phys. Rev. Lett. $\textbf{126}$, 217002 (2021), with sign-problem-free determinant quantum Monte Carlo (DQMC) calculations. As far as we noticed, it is the first time in a correlated model that phase-fluctuating Fermi arcs are identified with unbiased simulations. The numerical results for the scattering rate $Γ_\text{pf}$ of Cooper pairs exhibit excellent agreements with our theoretical predictions, where $Γ_\text{pf}$ is expected to scale linearly with the inverse superconducting correlation length $ξ(T)^{-1}$. This convergence of theory and numerics thereby strongly validates the universal connection between phase fluctuations and Fermi arcs in 2D nodal superconductors.

cond-mat.supr-con↗

arXiv2025

Classification of Interacting Topological Crystalline Superconductors in Three Dimensions and Beyond

Although classification for free-fermion topological superconductors (TSC) is established, systematically understanding the classification of 3D interacting TSCs remains difficult, especially those protected by crystalline symmetries like the 230 space groups. We build up a general framework for systematically classifying 3D interacting TSCs protected by crystalline symmetries together with discrete internal symmetries. We first establish a complete classification for fermionic symmetry protected topological phases (FSPT) with purely discrete internal symmetries, which determines the crystalline case via the crystalline equivalence principle. Using domain wall decoration, we obtain classification data and formulas for generic FSPTs, what are suitable for systematic computation. The four layers of decoration data $(n_1, n_2, n_3, ν_4)$ characterize a 3D FSPT with symmetry $G_b\times_{ω_2}Z_2^f$, corresponding to $p+ip$, Kitaev chain, complex fermion, and bosonic SPT layers. Inspired by previous works, a crucial aspect is the $p+ip$ layer, where classification involves two possibilities: anti-unitary and infinite-order symmetries (e.g., translation). We show the former maps to some mirror FSPT classification with the mirror plane decorated by a $p+ip$ superconductor, while the latter is determined by the free part of $H^1(G_b, Z_T)$, corresponding to weak TSCs. Another key point is the Kitaev chain decoration for the anti-unitary symmetries, which differs essentially from unitary ones. We explicitly obtain formulas for all three layers of decoration $(n_2, n_3, ν_4)$, which are amenable to automatic computation. As an application, we classify the 230 space-group topological crystalline superconductors in interacting electronic systems.

cond-mat.str-el↗

arXiv2025

aiXiv: A Next-Generation Open Access Ecosystem for Scientific Discovery Generated by AI Scientists

Recent advances in large language models (LLMs) have enabled AI agents to autonomously generate scientific proposals, conduct experiments, author papers, and perform peer reviews. Yet this flood of AI-generated research content collides with a fragmented and largely closed publication ecosystem. Traditional journals and conferences rely on human peer review, making them difficult to scale and often reluctant to accept AI-generated research content; existing preprint servers (e.g. arXiv) lack rigorous quality-control mechanisms. Consequently, a significant amount of high-quality AI-generated research lacks appropriate venues for dissemination, hindering its potential to advance scientific progress. To address these challenges, we introduce aiXiv, a next-generation open-access platform for human and AI scientists. Its multi-agent architecture allows research proposals and papers to be submitted, reviewed, and iteratively refined by both human and AI scientists. It also provides API and MCP interfaces that enable seamless integration of heterogeneous human and AI scientists, creating a scalable and extensible ecosystem for autonomous scientific discovery. Through extensive experiments, we demonstrate that aiXiv is a reliable and robust platform that significantly enhances the quality of AI-generated research proposals and papers after iterative revising and reviewing on aiXiv. Our work lays the groundwork for a next-generation open-access ecosystem for AI scientists, accelerating the publication and dissemination of high-quality AI-generated research content. Code: https://github.com/aixiv-org aiXiv: https://aixiv.science

cs.AI↗

arXiv2025

Double Supersolid Phase in a Bosonic t-J-V Model with Rydberg Atoms

Recent advances in Rydberg tweezer arrays bring novel opportunities for programmable quantum simulations beyond previous capabilities. In this work, we investigate a bosonic t-J-V model currently realized with Rydberg atoms. Through large-scale quantum Monte Carlo simulations, we uncover an emergent double supersolid (DSS) phase with the coexistence of two superfluids and crystalline order. Tunable long-range tunneling and repulsive hole-hole interactions enable a rich phase diagram featuring a double superfluid phase, a DSS phase, and an antiferromagnetic insulator. Intriguingly, within the DSS regime we observe an unconventional thermal enhancement of crystalline order. Our results establish the bosonic t-J-V model as a promising and experimentally accessible platform for exploring exotic quantum phases in Rydberg atom arrays.

cond-mat.quant-gas↗

arXiv2025

Trification: A Comprehensive Tree-based Strategy Planner and Structural Verification for Fact-Checking

Technological advancement allows information to be shared in just a single click, which has enabled the rapid spread of false information. This makes automated fact-checking system necessary to ensure the safety and integrity of our online media ecosystem. Previous methods have demonstrated the effectiveness of decomposing the claim into simpler sub-tasks and utilizing LLM-based multi agent system to execute them. However, those models faces two limitations: they often fail to verify every component in the claim and lack of structured framework to logically connect the results of sub-tasks for a final prediction. In this work, we propose a novel automated fact-checking framework called Trification. Our framework begins by generating a comprehensive set of verification actions to ensure complete coverage of the claim. It then structured these actions into a dependency graph to model the logical interaction between actions. Furthermore, the graph can be dynamically modified, allowing the system to adapt its verification strategy. Experimental results on two challenging benchmarks demonstrate that our framework significantly enhances fact-checking accuracy, thereby advancing current state-of-the-art in automated fact-checking system.

cs.AI↗

arXiv2025

Stochastic Forward-Forward Learning through Representational Dimensionality Compression

The Forward-Forward (FF) learning algorithm provides a bottom-up alternative to backpropagation (BP) for training neural networks, relying on a layer-wise "goodness" function with well-designed negative samples for contrastive learning. Existing goodness functions are typically defined as the sum of squared postsynaptic activations, neglecting correlated variability between neurons. In this work, we propose a novel goodness function termed dimensionality compression that uses the effective dimensionality (ED) of fluctuating neural responses to incorporate second-order statistical structure. Our objective minimizes ED for noisy copies of individual inputs while maximizing it across the sample distribution, promoting structured representations without the need to prepare negative samples.We demonstrate that this formulation achieves competitive performance compared to other non-BP methods. Moreover, we show that noise plays a constructive role that can enhance generalization and improve inference when predictions are derived from the mean of squared output, which is equivalent to making predictions based on an energy term. Our findings contribute to the development of more biologically plausible learning algorithms and suggest a natural fit for neuromorphic computing, where stochasticity is a computational resource rather than a nuisance. The code is available at https://github.com/ZhichaoZhu/StochasticForwardForward

cs.LG↗

arXiv2025

On the minimal algebraic complexity of the rank-one approximation problem for general inner products

We study the algebraic complexity of Euclidean distance minimization from a generic tensor to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Veronese variety counts the number of complex critical points of this optimization problem. We regard this invariant as a function of inner products. We prove that Frobenius inner product is a local minimum of the ED degree, and conjecture that it is a global minimum. We prove our conjecture in the case of matrices and symmetric binary and $3\times 3\times 3$ tensors. We discuss the above optimization problem for other algebraic varieties, classifying all possible values of the ED degree. Our approach combines tools from Singularity Theory, Morse Theory, and Algebraic Geometry.

math.AG↗

arXiv2025

Universal Scaling Functions of the Gr{ü}neisen Ratio near Quantum Critical Points

The Grüneisen ratio, defined as $Γ_g \equiv (1/T) (\partial T/\partial g)_S$, serves as a highly sensitive probe for detecting quantum critical points (QCPs) driven by an external feild $g$ and for characterizing the magnetocaloric effect (MCE). Near a QCP, the Grüneisen ratio displays a universal divergence which is governed by a universality-class-dependent scaling function stemming from the scale invariance. In this work, we systematically investigate the universal scaling functions of Grüneisen ratio in both one-dimensional (1D) and two-dimensional (2D) quantum spin systems, including the transverse-field Ising model, the spin-1/2 Heisenberg model, the quantum $q$-state Potts model ($q=3,4$) and the $J_1$-$J_2$ columnar dimer model. Our approach employs the thermal tensor-network method for infinite-size 1D systems and the stochastic series expansion quantum Monte Carlo (SSE QMC) simulations for 2D systems, enabling precise calculations of the Grüneisen ratio near QCPs. Through data collapse analysis, we extract the corresponding scaling functions, which establish quantitative frameworks to interpret magnetocaloric experiments and guide the development of ultralow-temperature refrigeration.

cond-mat.str-el↗

arXiv2025

Integrating Diffusion-based Multi-task Learning with Online Reinforcement Learning for Robust Quadruped Robot Control

Recent research has highlighted the powerful capabilities of imitation learning in robotics. Leveraging generative models, particularly diffusion models, these approaches offer notable advantages such as strong multi-task generalization, effective language conditioning, and high sample efficiency. While their application has been successful in manipulation tasks, their use in legged locomotion remains relatively underexplored, mainly due to compounding errors that affect stability and difficulties in task transition under limited data. Online reinforcement learning (RL) has demonstrated promising results in legged robot control in the past years, providing valuable insights to address these challenges. In this work, we propose DMLoco, a diffusion-based framework for quadruped robots that integrates multi-task pretraining with online PPO finetuning to enable language-conditioned control and robust task transitions. Our approach first pretrains the policy on a diverse multi-task dataset using diffusion models, enabling language-guided execution of various skills. Then, it finetunes the policy in simulation to ensure robustness and stable task transition during real-world deployment. By utilizing Denoising Diffusion Implicit Models (DDIM) for efficient sampling and TensorRT for optimized deployment, our policy runs onboard at 50Hz, offering a scalable and efficient solution for adaptive, language-guided locomotion on resource-constrained robotic platforms.

cs.RO↗