arXiv subjects

Zhijie Fan

Publications and source records attributed to Zhijie Fan.

At least 19 recordsLinked to original sources

arXiv2026

Two-dimensional percolation with algebraically decaying interactions II: Critical exponents in the long-range regime

We present a comprehensive Monte Carlo study of two-dimensional bond percolation with algebraically decaying connection probabilities $p(r)\propto 1/r^{2+\sigma}$, establishing the universality diagram in the long-range (LR) regime for $\sigma\le2$. Using the event-based ensemble method, we simulate systems with linear sizes up to $L=16384$ and investigate three universality regimes: LR Wilson--Fisher (WF) A ($1<\sigma\le2$), LR Wilson--Fisher B ($2/3<\sigma\le1$), and LR mean-field (MF) ($0<\sigma\le2/3$). In the LR-WF-B regime, the anomalous dimension is consistent with $\eta=2-\sigma$, in agreement with mathematical results for $2/3<\sigma<1$, while the correlation-length exponent $\nu(\sigma)$ exhibits nontrivial, non-Gaussian variation. In the LR-WF-A regime, although $\eta$ remains close to $2-\sigma$ for smaller $\sigma$, statistically resolvable deviations $\delta\eta(\sigma)=\eta-(2-\sigma)>0$ start to appear near $\sigma\simeq3/2$ and grow toward the short-range crossover at $\sigma=2$. Finally, by complementing the event-based simulations with conventional ensemble simulations, we reveal the coexistence of complete-graph asymptotics and LR Gaussian-fixed-point scaling in the LR-MF regime. These results further clarify the critical properties in long-range percolation and provide crucial benchmarks for long-range statistical systems.

cond-mat.stat-mech↗

arXiv2026

The $6-\epsilon$ Expansion for Long-Range Lee--Yang and Percolation Criticality

The crossover from long-range (LR) to short-range (SR) criticality in percolation has remained unsettled because previous renormalization-group (RG) analysis within the $\epsilon'=3\sigma-d$ expansion fixes the anomalous dimension at $\eta=2-\sigma$, whereas SR percolation has $\eta_{\rm SR}<0$ near $d=6$. Sak's matching condition then places the crossover above $\sigma=2$, outside the regime in which the LR interaction dominates. In spatial dimension $d=6-\epsilon$, we formulate a perturbative expansion for the LR $\phi^3$ field theory and perform a one-loop RG analysis throughout the perturbatively accessible nonclassical regime $0<\delta<\epsilon/3$, where $\delta = 2-\sigma$. We derive the one-loop corrections to the critical exponents $\eta$ and $\nu$, which acquire nontrivial dependence on $\epsilon$ and $\delta$. They reduce to their mean-field values at the LR upper critical line and continuously recover the SR $6-\epsilon$ results as $\sigma\to2$. These results support a crossover threshold $\sigma_*=2$ and remove the apparent discontinuity of $\eta$ between the LR and SR values within this framework. The same approach also yields the anomalous and edge exponents of the LR Lee--Yang universality class and $q$-state Potts universality classes with $q<2$.

cond-mat.stat-mech↗

arXiv2026

Perturbative Renormalization and Universality Diagram for Long-Range Quantum Criticality

Experimental progress in quantum simulators highlights the role of long-range (LR) interactions in reshaping quantum criticality and stabilizing exotic phases beyond the short-range (SR) paradigm. We study ferromagnetic long-range quantum $O(n)$ models with interactions decaying as $1/r^{d+\sigma}$ and develop a perturbative renormalization-group expansion around the LR--SR boundary by setting $d=3-\epsilon$ and $\sigma=2-\delta$. In this parametrization, the full interacting LR window $2d/3<\sigma<2$ becomes $0<\delta<2\epsilon/3$, and is therefore perturbatively controlled. A two-loop calculation yields explicit expressions, in terms of $\epsilon$, $\delta$, and $n$, for the correlation-length exponent $\nu$ and for the frequency and momentum anomalous dimensions $\eta_\omega$ and $\eta_k$. The resulting exponents reduce to long-range Gaussian scaling at $\sigma=2d/3$ and to SR quantum Wilson-Fisher scaling in the $\sigma \to 2$ limit, thereby identifying $\sigma_*=2$ as the LR--SR boundary within the controlled $3-\epsilon$ expansion. Combining the RG results with scaling boundaries and classical LR analogies, we propose a $(d,\sigma)$ universality diagram for ferromagnetic long-range quantum $O(n)$ criticality and use it as an organizing framework for the phase diagram of long-range quantum spin chains.

cond-mat.stat-mech↗

arXiv2026

Transformer refined quantum sampling for strongly correlated electronic structure

Although quantum computing offers a promising solution for strongly correlated system simulation, existing algorithms face significant bottlenecks on current noisy intermediate-scale quantum (NISQ) devices. Here, we introduce QiankunNet-QSCI, a hybrid quantum-classical framework that addresses this challenge by combining efficient quantum-sampling with a transformer neural network. An efficient unitary selected configuration Interaction (USCI) ansatz especially designed for quantum sampling is proposed to identify the most chemically significant electronic configurations on the Zuchongzhi 3.1 quantum processor. Subsequently, the transformer model QiankunNet learns from these sparse yet critical quantum data to infer and reconstruct the complete electronic wavefunction with high fidelity. Simulation of the challenging 40-qubit [2Fe-2S] ferredoxin active center achieves chemical accuracy. Simulation of the nitrogenase P-cluster in a 114-electron 73-orbital active space also reaches 12 milli-Hartree-level agreement with the best density matrix renormalization group (DMRG) result. QiankunNet-QSCI thus offers a practical route to accurate quantum-assisted electronic structure calculations on current devices.

quant-ph↗

arXiv2026

Scaling of Long-Range Loop-Erased Random Walks

We study the scaling properties of long-range loop-erased random walks (LR-LERW), where the underlying random walker performs L\'evy-flight-like jumps with a power-law step-length distribution $P(\mathbf{r})\sim |\mathbf{r}|^{-(d+\sigma)}$. Using extensive Monte Carlo simulations, we measure the scaling relation $N \sim R^{d_N}$ between the loop-erased step number $N$ and the spatial extent $R$, and determine the geometric exponent $d_N$ for various values of $\sigma$ in spatial dimensions $d = 1, 2,$ and $3$, as well as at the marginal point $\sigma = 2$ in $d=4$ and $5$. We observe a continuous crossover from long-range (LR) to short-range (SR) behavior as $\sigma$ increases. Below the upper critical dimension $d<d_c=4$, for $\sigma < d/2$, loop erasure is asymptotically irrelevant and $d_N=\sigma$, consistent with L\'evy-flight scaling. For $d/2 < \sigma < 2$, loop erasure becomes relevant and $d_N$ varies continuously toward the SR-LERW value. At the marginal points with $\sigma=d/2$ or $\sigma=2$, clear logarithmic corrections are observed. At and above the upper critical dimension, $d \geq 4$, the scaling at $\sigma=2$ is found to be $N \sim R^2/\ln R$, consistent with that of the corresponding L\'evy flight. Our results provide a systematic numerical determination of $d_N(\sigma)$ for the LR-LERW across dimensions, and are consistent with $\sigma_* = 2$ as the boundary between LR and SR critical behaviors recently established in a broad variety of statistical models.

cond-mat.stat-mech↗

arXiv2025

On Sak's criterion for statistical models with long-range interaction

Determining the threshold value $\sigma_*$ that separates the short-range (SR) and long-range (LR) universality classes in phase transitions remains a controversial issue. While Sak's criterion, $\sigma_* = 2 - \eta_{\mathrm{SR}}$, has been widely accepted, recent studies of two-dimensional (2D) models with long-range interactions have challenged it. In this work, we focus on the crossover between LR and SR criticality in several classical 2D statistical models, including the XY, Heisenberg, percolation, and Ising models, whose interactions decay as $1/r^{2+\sigma}$. Our previous simulations for the XY, Heisenberg, and percolation models consistently indicate a universal boundary at $\sigma_* = 2$. Here, we complete the picture by performing large-scale Monte Carlo simulations of the 2D LR-Ising model, reaching lattice sizes up to $L = 8192$. By analyzing the Fortuin-Kasteleyn critical polynomial $R_p$, the Binder ratio $Q_m$, and the anomalous dimension $\eta$, we obtain convergent and self-consistent evidence that the universality class already changes sharply at $\sigma = 2$. Taken together, these results establish a unified scenario for LR interacting systems: across all studied models, the crossover from LR to SR universality occurs at $\sigma_* = 2$.

cond-mat.stat-mech↗

arXiv2025

Universality Diagram of Phase Transitions in Long-range Statistical Systems

The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group theory. However, the universality of the transitions in these models remains elusive when algebraically decaying long-range interactions $\sim 1/r^{d+\sigma}$ are introduced, where $d$ is the dimensionality and $\sigma$ is the decay exponent. Building upon insights from L\'evy flight, i.e., long-range simple random walk, we propose three universality diagrams in the $(d,\sigma)$ plane for the percolation model, the O($n$) model, and the Fortuin-Kasteleyn Ising model, respectively. The conjectured universality diagrams are consistent with recent high-precision numerical studies and rigorous mathematical results, offering a unified perspective on critical phenomena in systems with long-range interactions.

cond-mat.stat-mech↗

arXiv2025

Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model

Algebraically decaying interactions $\sim 1/r^{d+\sigma}$ can lead to nontrivial universality beyond short-range (SR) theories and spontaneous symmetry breaking in low-dimensional systems. We perform large-scale Monte Carlo simulations for the classical long-range (LR) Heisenberg model in two dimensions (2D) up to linear size $L=8192$. We show that the system enters a long-range-ordered phase through a single continuous phase transition for all $\sigma \leq 2$, including the marginal case $\sigma=2$. In contrast, for $\sigma > 2$ it recovers the SR asymptotically free behavior with no finite-temperature transition. This places the LR--SR crossover threshold at $\sigma_* = 2$. To characterize the ordered phase, we introduce an LR simple random walk with a fixed total length $\mathcal{L} \sim\mathcal{O}(L^d)$. This fixed-$\mathcal L$ walk reproduces the finite-size scaling of the Goldstone-mode fluctuations in the LR Heisenberg model in both two and three dimensions, including the logarithmic scaling at $\sigma = 2$. These results further motivate a general criterion for the existence of finite-temperature long-range order in LR systems with continuous symmetry in any spatial dimension.

cond-mat.stat-mech↗

arXiv2025

Absolute summability from diagonal operators to Carleson embeddings and Hankel operators

The present paper consists of three parts, each building on the preceding one. In Part I, we characterize the scalar sequences $\mathbf b=\{b_k\}$ for which the diagonal operator $\mathscr{M}_{\mathbf b}\bigl(\{a_k\}\bigr):=\{b_ka_k\}$ is $r$-summing from $\ell^p$ to $\ell^q$ for $1\le p,q\le \infty$ and $1\le r<\infty$. This resolves a problem left open in Garling's 1974 classification of $r$-summing diagonal operators. In particular, in the previously unresolved exceptional range $\{(p,q,r):1 \max\{p',q\}\},$ we identify a new intermediate exponent $\kappa\in(\max\{p',q\},r)$ and prove that $\mathscr M_{\mathbf b}$ is $r$-summing if and only if $\mathbf b\in\ell^\kappa$. In Part II, by developing two general transference principles for $r$-summability and building on the characterization from Part I, we characterize the positive Borel measures $\mu$ for which the Carleson embedding operator $J_\mu$ is $r$-summing from the weighted Bergman space $A_\alpha^p(\mathbb B_n)$ to $L^q(\mathbb B_n,d\mu)$ for $ 1\leq p,q<\infty$ , $1\leq r<\infty$, and $\alpha>-1$, thereby extending the existing theory to the full off-diagonal range. In Part III, building on the characterization from Part II, we characterize the symbols $f$ and $g$ for which the big and little Hankel operators $H_f^\beta$ and $h_{\bar g}^\beta$, respectively, are $r$-summing from $A_\alpha^p(\mathbb B_n)$ to $L^q(\mathbb B_n,dv_\beta)$, where $1\leq p<\infty$, $1 -1$, and $dv_\beta(z):=c_\beta(1-|z|^2)^\beta\,dv(z)$. These characterizations appear to be new even in the diagonal case $p=q$ and $\alpha=\beta$.

math.FA↗

arXiv2025

Two-dimensional percolation model with long-range interaction

We perform large-scale simulations of the two-dimensional long-range bond percolation model with algebraically decaying percolation probabilities $\sim 1/r^{2+σ}$, using both conventional ensemble and event-based ensemble methods for system sizes up to $L=16384$. We accurately determine the critical points, the universal values of several dimensionless quantities, and the corresponding critical exponents. Our results provide compelling evidence that the system undergoes a crossover from short-range to long-range universality at $σ= 2$, in contradiction to Sak's criterion. Notably, we observe a pronounced jump in the universal values and critical exponents at $σ= 2$, a feature absent from previous studies.

cond-mat.stat-mech↗

arXiv2025

Quantum Path-integral Method for Fictitious Particle Hubbard Model

We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a continuous parameter $ξ$ in the partition function that interpolates between bosonic ($ξ= 1$) and fermionic ($ξ= -1$) statistics. We generalize this approach to discrete lattice models and apply it to the two-dimensional Hubbard model of fictitious particles, including the Bose- and Fermi-Hubbard models as special cases. By combining reweighting and $ξ$-extrapolation techniques, we access both half-filled and doped regimes. In particular, we demonstrate that the method remains effective even in strongly correlated, doped systems where the fermion sign problem hinders conventional quantum Monte Carlo approaches. Our results validate the applicability of the fictitious particle framework on lattice models and establish it as a promising tool for sign-problem mitigation in strongly interacting fermionic systems.

cond-mat.str-el↗

arXiv2025

SWE-Perf: Can Language Models Optimize Code Performance on Real-World Repositories?

Code performance optimization is paramount in real-world software engineering and critical for production-level systems. While Large Language Models (LLMs) have demonstrated impressive capabilities in code generation and bug fixing, their proficiency in enhancing code performance at the repository level remains largely unexplored. To address this gap, we introduce SWE-Perf, the first benchmark specifically designed to systematically evaluate LLMs on code performance optimization tasks within authentic repository contexts. SWE-Perf comprises 140 carefully curated instances, each derived from performance-improving pull requests from popular GitHub repositories. Each benchmark instance includes the relevant codebase, target functions, performance-related tests, expert-authored patches, and executable environments. Through a comprehensive evaluation of representative methods that span file-level and repo-level approaches (e.g., Agentless and OpenHands), we reveal a substantial capability gap between existing LLMs and expert-level optimization performance, highlighting critical research opportunities in this emerging field.

cs.SE↗

arXiv2025

The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study

The two-dimensional (2D) XY model plays a crucial role in statistical and condensed matter physics. With the introduction of long-range interactions, the system exhibits a richer set of physical phenomena and a crossover between non-classical and short-range universality classes.In this work, we investigate the 2D XY model with algebraically decaying interactions $\sim 1/r^{2+σ}$, and provide a comprehensive numerical analysis of its thermodynamic properties. We demonstrate that for $σ\leq 2$, the system undergoes a second-order phase transition into a ferromagnetic phase characterized by the emergence of long-range order. In the low-temperature phase, due to the presence of the Goldstone mode, the correlation function saturates to a non-zero constant in the form of a power law for $σ< 2$, with decaying exponent $2-σ$, and in the form of the inverse logarithm of distance for $σ=2$. Moreover, the critical points and exponents are also determined for various $σ$. We provide compelling evidence that the crossover between non-classical and short-range regimes occurs at $σ=2$. This work presents a detailed account of the simulation methodology, extensive numerical data, and new insights into the physics of long-range interacting systems.

cond-mat.stat-mech↗

arXiv2025

Asymptotic Freedom and Finite-size Scaling of Two-dimensional Classical Heisenberg Model

The classical Heisenberg model is one of the most fundamental models in statistical and condensed matter physics. Extensive theoretical and numerical studies suggest that, in two dimensions, this model does not exhibit a finite-temperature phase transition but instead manifests asymptotic freedom. However, some research has also proposed the possibility of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition over the years. In this study, we revisit the classical two-dimensional (2D) Heisenberg model through large-scale simulations with linear system sizes up to $L=16384$. Our Monte-Carlo data, without any extrapolation, clearly reveal an exponential divergence of the correlation length $ξ$ as a function of inverse temperature $β$, a hallmark of asymptotic freedom. Moreover, extrapolating $ξ$ to the thermodynamic limit in the low-temperature regime achieves close agreement with the three-loop perturbative calculations. We further propose a finite-size scaling (FSS) ansatz for $ξ$, demonstrating that the pseudo-critical point $β_L$ diverges logarithmically with $L$. The thermodynamic and finite-size scaling behaviors of the magnetic susceptibility $χ$ are also investigated and corroborate the prediction of asymptotic freedom. Our work provides solid evidence for asymptotic freedom in the 2D Heisenberg model and advances understanding of finite-size scaling in such systems.

cond-mat.stat-mech↗

arXiv2024

Spectral asymptotic formula of Bessel--Riesz commutator

Let $R_{λ,j}$ be the $j$-th Bessel--Riesz transform, where $n\geq 1$, $λ>0$, and $j=1,\ldots,n+1$. In this article, we establish a Weyl type asymptotic for $[M_f,R_{λ,j}]$, the commutator of $R_{λ,j}$ with multiplication operator $M_f$, based on building a preliminary result that the endpoint weak Schatten norm of $[M_f,R_{λ,j}]$ can be characterised via homogeneous Sobolev norm $\dot{W}^{1,n+1}(\mathbb{R}_+^{n+1})$ of the symbol $f$. Specifically, the asymptotic coefficient is equivalent to $\|f\|_{\dot{W}^{1,n+1}(\mathbb{R}_+^{n+1})}.$ Our main strategy is to relate Bessel--Riesz commutator to classical Riesz commutator via Schur multipliers, and then to establish the boundedness of Schur multipliers.

math.FA↗

arXiv2024

Codebook Configuration for RIS-aided Systems via Implicit Neural Representations

Reconfigurable Intelligent Surface (RIS) is envisioned to be an enabling technique in 6G wireless communications. By configuring the reflection beamforming codebook, RIS focuses signals on target receivers to enhance signal strength. In this paper, we investigate the codebook configuration for RIS-aided communication systems. We formulate an implicit relationship between user's coordinates information and the codebook from the perspective of signal radiation mechanisms, and introduce a novel learning-based method, implicit neural representations (INRs), to solve this implicit coordinates-to-codebook mapping problem. Our approach requires only user's coordinates, avoiding reliance on channel models. Additionally, given the significant practical applications of the 1-bit RIS, we formulate the 1-bit codebook configuration as a multi-label classification problem, and propose an encoding strategy for 1-bit RIS to reduce the codebook dimension, thereby improving learning efficiency. Experimental results from simulations and measured data demonstrate significant advantages of our method.

cs.IT↗

arXiv2024

IDA function and asymptotic behavior of singular values of Hankel operators on weighted Bergman spaces

In this paper, we use the non-increasing rearrangement of ${\rm IDA}$ function with respect to a suitable measure to characterize the asymptotic behavior of the singular values sequence $\{s_n(H_f)\}_n$ of Hankel operators $H_f$ acting on a large class of weighted Bergman spaces, including standard Bergman spaces on the unit disc, standard Fock spaces and weighted Fock spaces. As a corollary, we show that the simultaneous asymptotic behavior of $\{s_n(H_f)\}$ and $\{s_n(H_{\bar{f}})\}$ can be characterized in terms of the asymptotic behavior of non-increasing rearrangement of mean oscillation function. Moreover, in the context of weighted Fock spaces, we demonstrate the Berger-Coburn phenomenon concerning the membership of Hankel operators in the weak Schatten $p$-class.

math.CV↗

arXiv2024

Dipolar bosons in a twisted bilayer geometry

In recent years, twisted bilayer systems such as bilayer graphene have attracted a great deal of attention as the twist angle introduces a degree of freedom which can be used to non-trivially modify system properties. This idea has been picked up in the cold atom community, first with a theoretical proposal to simulate twisted bilayers in state-dependent optical lattices, and, more recently, with an experimental realization of twisted bilayers with bosonic atoms in two different spin states. In this manuscript, we theoretically investigate dipolar bosons in a twisted bilayer geometry. The interplay between dipolar interaction and the twist between the layers results in the emergence of quantum states not observed in the absence of twist. We study how system properties vary as we change the twist angle at fixed distance between the layers and fixed dipolar interaction. We find that at a twist angle $θ=0.1^{\circ}$, the observed quantum phases are consistent with those seen in the absence of twist angle, i.e. paired superfluid, paired supersolid, and paired solid phases. However, a slight increase in the twist angle to $θ=0.2^{\circ}$ disrupts these paired phases in favor of a phase separation between checkerboard solid and superfluid regions. Notably, at a twist angle of $θ=5.21^{\circ}$, the local occupation number follows the moiré pattern of the underlying moiré bilayers so that a periodic structure of insulating islands is formed. These insulating islands are surrounded by a superfluid.

cond-mat.quant-gas↗