arXiv subjects

Andrei Alexandru

Publications and source records attributed to Andrei Alexandru.

At least 19 recordsLinked to original sources

arXiv2026

Negative-Power Density of States in Chiral-Orthogonal Disordered Systems and the IR Phase of QCD

The recently discovered IR phase of QCD is characterized by an infrared (IR) sector of Dirac modes that separates and dynamically decouples from the bulk of the spectrum, becoming scale invariant in the process [1]. Among key features of this IR sector is the negative power-law behavior of Dirac spectral density near zero with power $p$ close to $-1$. Here we start investigating to what extent can this behavior be mimicked by chiral Anderson models. In particular, we study 3-D chiral-orthogonal systems with logarithmic off-diagonal disorder where negative-power ``spikes'' have been observed [2]. We find that at finite disorder strength $W$ of moderate strength, these models in fact do not have a power-singular density of states (DOS) at zero energy in the thermodynamic limit. Rather, this power $p_1$ vanishes and the spectrum features a very accurate power behavior with $p<0$ on an interval around $E = 1$ spreading increasingly closer to $E=0$ and $E = \infty$ with increasing $W$. We connect this to the fact that random hoppings $t$ in these quantum systems are drawn from a scale-invariant $1/t$ distribution regularized via $t \in [e^{-W/2}, e^{W/2}]$, and DOS with negative power can naturally arise inside that range. We show that $\lim_{W \to \infty} p(W, E)=-1$ for all energies accessible by our data. This indicates that, upon removing the cutoff $W$, quantum mechanics transforms the scale-invariant $1/t$ noise into a scale-invariant $1/E$ distribution of eigenstates, which mimics the interpretation of scale-invariant Dirac spectral densities in the IR phase as being due to scale-invariant glue backgrounds [1]. Our results imply that, to model the IR sector of the IR phase, the IR cutoff in chiral Anderson systems needs to be viewed as descending from the randomness strength $W$ rather than the lattice size $L$.

hep-lat↗

arXiv2026

Pion vector form factor from LapH-smeared currents in lattice QCD

We explore a method to extract pion vector form factor from three-point functions using currents constructed from LapH-smeared quark fields. LapH employs the low eigenmodes of the Laplacian Heaviside operator on the lattice to smear out the quark fields in spatial directions. The LapH-smeared quark propagator retains all symmetry properties of the original one and can be re-used to construct correlation functions at a reduced cost, with equal treatment of connected and disconnected diagrams. The calculations are performed on a two-flavor dynamical nHYP-smeared ensemble on the $24^3\times 48$ lattice at a spacing of 0.12 fm and pion mass of 315 MeV. We show that an extrapolation in the number of low eigenmodes in the LapH subspace can reproduce the same form factor computed from the conventional SST method with point source, sink, and current. The study opens up the possibility of applying LapH-smeared currents to extract hadron form factors and polarizabilities including disconnected diagrams.

hep-lat↗

arXiv2026

Coupled-channel approach to isotensor $πππ$ scattering from lattice QCD

The quest to understand three-body dynamics from first-principle QCD includes the study of non-resonant and resonant systems. The isospin $I=2$ system is of particular interest having no three-body resonance but featuring a resonance in a sub-channel, while also being a coupled-channel problem. In this study, we calculate the finite-volume spectrum from lattice QCD at two different pion masses, map the amplitude to the infinite volume through a generalized Finite-Volume Unitarity (FVU) three-body quantization condition, investigate the limit of a narrow $ρ$, and compare with an effective Lagrangian prediction at leading order. Chiral extrapolations between different pion masses are performed.

hep-lat↗

arXiv2026

Higher order quantization conditions for two-body scattering with spin

We examine the Lüscher quantization condition to high order for the scattering of a spinless particle and a spin-1/2 particle in a periodic box. First, we derive the quantization conditions in a non-relativistic framework up to total angular momentum $J=11/2$ in both cubic and elongated geometries, and for both rest and moving frames. Then, we introduce a method to transparently cross-check their convergence, using both quantized energy levels in the box and infinite-volume phase shifts for the same potential. We clarify how to incorporate spin-orbit coupling into the formalism and show in detail how the quantization conditions converge order by order in the various irreducible representations. In all, we validated 19 quantization conditions (12 in cubic box, 7 in elongated box). This is a necessary step in applying the method in precision studies of systems in finite volume with half-integer spin, such as meson-baryon scattering.

hep-lat↗

arXiv2026

Electric Polarizability of Charged Pions from nHYP Four-Point Functions

Understanding a hadron's electric and magnetic polarizabilities allows one to access internal structural information. Traditionally, the external field two-point function method has been used to calculate polarizabilities. However, recent work has demonstrated the effectiveness of using four-point functions for computing polarizabilities of charged and neutral hadrons. Our previous study on the electric polarizability of the charged pion used a quenched Wilson action on a lattice with pion mass from 1100 MeV to 370 MeV. In this work, we employ a number of improvements, including a dynamical action (nHYP), smaller pion masses (220 MeV and 315 MeV), and a variable lattice size in order to extrapolate to infinite volume. Preliminary results are presented.

hep-lat↗

arXiv2025

Toward extracting scattering phase shift from integrated correlation functions V: complex $ϕ^4$ field model in $3+1$ dimensions

In Ref.~\cite{Guo:2024zal} and associated studies, a relativistic finite-volume formalism in $1+1$ dimensions is proposed to extract infinite-volume scattering phaseshift. It is based on the difference of integrated correlation functions (ICF) rather than energy spectrum in the finite volume, and can be regarded as complementary to the well-known L\"{uscher} formalism. In the present work, the formalism is further extended into $3+1$ dimensional spacetime. The aim is to explore and demonstrate the challenges in applying the formalism to more practical settings. Specifically, Monte Carlo simulations of a complex $ϕ^4$ relativistic field model are carried out in both 2+1 and 3+1 dimensions on lattices of varying sizes, and phaseshifts for the contact interaction are extracted from the formalism using modest computing resources.

hep-lat↗

arXiv2025

Atla Selene Mini: A General Purpose Evaluation Model

We introduce Atla Selene Mini, a state-of-the-art small language model-as-a-judge (SLMJ). Selene Mini is a general-purpose evaluator that outperforms the best SLMJs and GPT-4o-mini on overall performance across 11 out-of-distribution benchmarks, spanning absolute scoring, classification, and pairwise preference tasks. It is the highest-scoring 8B generative model on RewardBench, surpassing strong baselines like GPT-4o and specialized judges. To achieve this, we develop a principled data curation strategy that augments public datasets with synthetically generated critiques and ensures high quality through filtering and dataset ablations. We train our model on a combined direct preference optimization (DPO) and supervised fine-tuning (SFT) loss, and produce a highly promptable evaluator that excels in real-world scenarios. Selene Mini shows dramatically improved zero-shot agreement with human expert evaluations on financial and medical industry datasets. It is also robust to variations in prompt format. Preliminary results indicate that Selene Mini is the top-ranking evaluator in a live, community-driven Judge Arena. We release the model weights on HuggingFace (https://hf.co/AtlaAI/Selene-1-Mini-Llama-3.1-8B) and Ollama to encourage widespread community adoption.

cs.CL↗

arXiv2024

Separation of Infrared and Bulk in Thermal QCD

A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N$_f$=0) and ``real-world" (N$_f$=2+1 at physical quark masses) QCD. In this {\it IR phase}, elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QCD, such non-analyticities have been shown to arise via Anderson-like mobility edges in Dirac spectra ($λ_{\rm IR} \!=\! 0$, $\pm λ_\text{A} \!\neq\! 0$), as manifested in the dimension function $d_{\rm IR} (λ)$. Here, we present the first evidence, based on lattice QCD calculation at $a$=0.105 fm, that this mechanism is also at work in real-world QCD, thus supporting the existence of the proposed IR regime in nature. An important aspect of our results is that, while at $T\!=\!234\,$MeV we find a dimensional jump between zero modes and lowest near-zero modes very close to unity ($d_{\rm IR} \!=\!3$ to $d_{\rm IR} \!\simeq\! 2$), similar to the IR phase of pure-glue QCD, at $T\!=\!187\,$MeV we observe a continuous $λ$-dependence. This suggests that thermal states just {\it above} the chiral crossover are non-analytically (in $T$) connected to thermal state at $T\!=\!234\,$MeV, supporting the key original proposition that the transition into the IR regime occurs at a temperature strictly above the chiral crossover.

hep-lat↗

arXiv2024

Detecting the flavor content of the vacuum using the Dirac operator spectrum

We compute the overlap Dirac spectrum on three gauge ensembles generated using $2+1$-flavor domain wall fermions. The three ensembles have different lattice spacings and two of them have quark masses tuned to the physical point. The spectral density is determined up to $λ\sim$100 MeV with subpercentage statistical uncertainty. We find that the density is close to a constant below $λ\sim$ 20 MeV as predicted by chiral perturbative theory ($χ$PT), and then increases linearly due to the strange quark mass. By fitting to the next-to-leading order $χ$PT form and using the non-perturbative RI/MOM renormalization, the $\rm SU(2)$ (keeping the strange quark mass at the physical point) and $\rm SU(3)$ chiral condensates at $\overline{\textrm{MS}}$ 2 GeV are determined to be $Σ=(265.4(0.5)(4.2)\ \textrm{MeV})^3$ and $Σ_0=(234.3(0.5)(25.8)\ \textrm{MeV})^3$, respectively. The pion decay constants are also determined to be $F=84.1(1.9)(8.0)$ and $F_0=58.6(0.5)(10.0)$ MeV. The systematic errors are carefully estimated including the effects of fitting ranges and the uncertainty of low-energy constant $L_6$. We also show that one can resolve the sea flavor content of the sea quarks and constrain their masses with {$\sim10\%-20\%$} statistical uncertainties using the Dirac spectral density.

hep-lat↗

arXiv2024

Dirac Spectral Density in N$_f$=2+1 QCD at T=230 MeV

We compute the renormalized Dirac spectral density in $N_f = 2+1$ QCD at physical quark masses, temperature $T = 230$ MeV and system size $L_s = 3.4$ fm. To that end, we perform a point-wise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a non-trivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently-proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical; (ii) improve the upper bound for IR-phase transition temperature $T_{\mathrm{IR}}$ so that the new window is $200 < T_{\mathrm{IR}} < 230\,$MeV; (iii) are consistent with non-restoration of anomalous U$_{\mathrm A}$(1) symmetry (chiral limit) below $T = 230$ MeV.

hep-lat↗

arXiv2024

Neutral pion polarizabilities from four-point functions in lattice QCD

We report a proof-of-principle lattice QCD simulation of the electric and magnetic polarizabilities for a neutral pion in the four-point function method. The results are based on the same quenched Wilson ensembles on a $24^3\times 48$ lattice at $β=6.0$ with pion mass from 1100 to 370 MeV previously used for a charged pion. For electric polarizability, the results are largely consistent with those from the background field method and ChPT. In contrast, there are significant differences for magnetic polarizability among the four-point function method, the background field method, and ChPT. The situation points to the potentially important role of disconnected diagrams for a neutral pion. We elucidate a transparent quark decomposition in the four-point function method that can be used to shed light on the issue.

hep-lat↗

arXiv2024

Fuzzy gauge theory for quantum computers

Continuous gauge theories, because of their bosonic degrees of freedom, have an infinite-dimensional local Hilbert space. Encoding these degrees of freedom on qubit-based hardware demands some sort of ``qubitization'' scheme, where one approximates the behavior of a theory while using only finitely many degrees of freedom. We propose a novel qubitization strategy for gauge theories, called ``fuzzy gauge theory,'' building on the success of the fuzzy $σ$-model in earlier work. We provide arguments that the fuzzy gauge theory lies in the same universality class as regular gauge theory, in which case its use would obviate the need of any further limit besides the usual spatial continuum limit. Furthermore, we demonstrate that these models are relatively resource-efficient for quantum simulations.

hep-lat↗

arXiv2024

Complex path simulations of geometrically frustrated ladders

Quantum systems with geometrical frustration remain an outstanding challenge for numerical simulations due to the infamous numerical sign problem. Here, we overcome this obstruction via complex path integration in a geometrically frustrated ladder of interacting bosons at finite density. This enables studies of the many-body ground state properties, otherwise inaccessible with standard quantum Monte Carlo methods. Specifically, we study a chemical potential tuned quantum phase transition, along which we track the emergence of quasi-long-range order and critical softening of the single particle gap. We chart future methodological improvements and applications in generalized geometrically frustrated lattice models.

cond-mat.str-el↗

arXiv2024

Localized Modes in the IR Phase of QCD

Infrared (IR) dimension function $d_\text{IR}(λ)$ characterizes the space effectively utilized by QCD quarks at Dirac scale $λ$, and indirectly the space occupied by glue fields. It was proposed that its non-analytic behavior in thermal infrared phase reflects the separation of QCD system into an IR component and an independent bulk. Here we study the ``plateau modes" in IR component, whose dimensional properties were puzzling. Indeeed, in the recent metal-to-critical scenario of transition to IR phase, this low-dimensional plateau connects the Anderson-like mobility edge $λ_\text{IR}=0$ in Dirac spectrum with mobility edges $\pm λ_\text{A}$. For this structure to be truly Anderson-like, plateau modes have to be exponentially localized, implying that both the effective distances $L_\text{eff} \propto L^γ$ and the effective volumes $V_\text{eff} \propto L^{d_\text{IR}}$ in these modes grow slower than any positive power of IR cutoff $L$. Although $γ=0$ was confirmed in the plateau, it was found that $d_\text{IR}\approx 1$. Here we apply the recently proposed multidimension technique to the problem. We conclude that a plateau mode of pure-glue QCD at UV cutoff $a \!=\! 0.085\,$fm occupies a subvolume of IR dimension zero with probability at least 0.9999, substantiating this aspect of metal-to-critical scenario to a respective degree.

hep-lat↗

arXiv2023

A solution for infinite variance problem of fermionic observables

Fermionic Monte Carlo calculations with continuous auxiliary fields often encounter infinite variance problem from fermionic observables. This issue renders the estimation of observables unreliable, even with an infinite number of samples. In this work, we show that the infinite variance problem stems from the fermionic determinant. Also, we propose an approach to address this problem by employing a reweighting method that utilizes the distribution from an extra time-slice. Two strategies to compute the reweighting factor are explored: one involves truncating and analytically calculating the reweighting factor, while the other employs a secondary Monte Carlo estimation. With Hubbard model as a testbed, we demonstrate that utilizing the sub-Monte Carlo estimation, coupled with an unbiased estimator, offers a solution that effectively mitigates the infinite variance problem at a minimal additional cost.

hep-lat↗

arXiv2023

Magnetic polarizability of a charged pion from four-point functions in lattice QCD

Electromagnetic dipole polarizabilities are fundamental properties of a hadron that represent its resistance to deformation under external fields. For a charged hadron, the presence of acceleration and Landau levels complicates the isolation of its deformation energy in the conventional background field method. In this work, we explore a general method based on four-point functions in lattice QCD that takes into account all photon, quark and gluon interactions. The electric polarizability ($α_E$) has been determined from the method in a previous proof-of-principle simulation. Here we focus on the magnetic polarizability ($β_M$) using the same quenched Wilson action on a $24^3\times 48$ lattice at $β=6.0$ with pion mass from 1100 to 370 MeV. The results from the connected diagrams show a large cancellation between the elastic and inelastic contributions, leading to a relatively small and negative value for $β_M$ consistent with chiral perturbation theory. We also discuss the mechanism for $α_E+β_M$ from combining the two studies.

hep-lat↗

arXiv2023

On the Infinite Variance Problem in Fermion Models

Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance. If a system has the infinite variance problem, one cannot estimate observables reliably even with an infinite number of samples. In this paper, we explore a method to deal with this problem based on sampling according to the distribution of a system with an extra time-slice. The necessary reweighting factor is computed both perturbatively and through a secondary Monte Carlo. We show that the Monte Carlo reweigthing coupled to the use of a non-biased estimator of the reweigthing factor leads to a method that eliminates the infinite variance problem at a very small extra cost. We compute the double occupancy in the Hubbard model at half-filling to demonstrate the method and compare the results to well established results obtained by other methods.

hep-lat↗

arXiv2023

Charged pion electric polarizability from four-point functions in lattice QCD

Polarizabilities reveal valuable information on the internal structure of hadrons in terms of charge and current distributions. For neutral hadrons, the standard approach is the background field method. But for a charged hadron, its acceleration under the applied field complicates the isolation of the polarization energy. In this work, we explore an alternative method based on four-point functions in lattice QCD. The approach offers a transparent picture on how polarizabilities arise from photon, quark, and gluon interactions. We carry out a proof-of-concept simulation on the electric polarizability of a charged pion, using quenched Wilson action on a $24^3\times 48$ lattice at $β=6.0$ with pion mass from 1100 to 370 MeV. We show in detail the evaluation and analysis of the four-point correlation functions and report results on charge radius and electric polarizability. Our results from connected diagrams suggest that charged pion $α_E$ is due to a cancellation between elastic and inelastic contributions. It would be interesting to see how the cancellation plays out at smaller pion masses in future simulations.

hep-lat↗