arXiv subjects

Arpith Kumar

Publications and source records attributed to Arpith Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Isospin-Driven Splitting of Chemical Potentials in Isobar Collisions from Lattice QCD

Strong magnetic fields produced in relativistic heavy-ion collisions can modify fluctuations of conserved charges and, consequently, their associated chemical potentials. We present first-principles $(2+1)$-flavor lattice-QCD results for isospin-driven splittings of conserved-charge chemical potentials between the isobar systems $^{96}_{44}\mathrm{Ru}+^{96}_{44}\mathrm{Ru}$ and $^{96}_{40}\mathrm{Zr}+^{96}_{40}\mathrm{Zr}$ in the QCD crossover region, both at vanishing and nonzero magnetic fields along the pseudo-critical line $T_{pc}(eB)$. We outline a framework that, under strangeness neutrality and charge-to-baryon ratio $r\equiv n_{\rm Q}/n_{\rm B}$, maps the isospin difference between two nuclei, as encoded in $r_{\rm Zr}$ and $r_{\rm Ru}$, onto splitting ratios $\Delta\mu_{\rm Q}/\Delta\mu_{\rm B}$, $\Delta\mu_{\rm S}/\Delta\mu_{\rm B}$, and $\Delta\mu_{\rm S}/\Delta\mu_{\rm Q}$ as functions of $\mu_{\rm B}(r_{\rm Ru})/\Delta\mu_{\rm B}$. Using continuum-estimated lattice results for the leading-order coefficients $q_1\equiv(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ and $s_1\equiv(\mu_{\rm S}/\mu_{\rm B})_{\rm LO}$, we find that, at vanishing magnetic field, the splitting ratios are of similar magnitude to recent Bayesian extractions from STAR isobar data and yield $\Delta\mu_{\rm Q}<0$ and $\Delta\mu_{\rm S}>0$, with the electric-charge sector dominating. At nonzero magnetic fields, the splitting ratios show only moderate $eB$ dependence. We therefore further examine Ru--Zr differences in the normalized magnetic-field response of chemical-potential ratios, particularly those involving $\mu_{\rm Q}/\mu_{\rm B}$, which display a pronounced enhancement in lattice QCD. We also present hadron resonance gas (HRG) results and experimentally motivated proxy observables with kinematic cuts to facilitate contact with experiment.

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arXiv2026

QCD in strong magnetic fields: fluctuations of conserved charges and equation of state

We present continuum-estimated (2+1)-flavor lattice QCD results for second-order fluctuations of conserved charges and the leading-order equation of state in the presence of strong magnetic fields at nonzero baryon chemical potential, using the HISQ action at the physical pion mass. The baryon-electric charge correlation $\chi^{\rm BQ}_{11}$ exhibits striking sensitivity to the magnetic field: $R_{cp}$-like double ratios $\chi^{\rm BQ}_{11}/\chi^{\rm Q}_{2}$ and $\chi^{\rm BQ}_{11}/\chi^{\rm QS}_{11}$ reach enhancements of $\sim2$ and $\sim2.25$ at $eB \simeq 8M_\pi^2$ along the transition line, establishing $\chi^{\rm BQ}_{11}$ as a magnetometer of QCD. To bridge theoretical predictions and experimental observations, we construct HRG-based proxy observables and apply systematic kinematic cuts emulating STAR and ALICE detector acceptances, which retain $\sim80\%$ of the lattice QCD magnetic sensitivity. Extending to the QCD equation of state under strangeness neutrality and isospin asymmetry, we determine the chemical potential ratio $q_1\equiv(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ and the pressure coefficient $P_2$ for magnetic field strengths up to $eB \simeq 0.8~{\rm GeV}^2 \sim 45 M_{\pi}^2$. The results reveal temperature-band crossings, hierarchy reversals, and non-monotonic structures driven by the nontrivial interplay between thermal and magnetic effects.

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arXiv2026

Thermodynamic Consistency as a Reliability Test for Complex Langevin Simulations

The complex Langevin method (CLM) is a promising tool to address the sign problem in quantum field theories with complex actions. However, it can converge to incorrect results even when simulations appear stable, highlighting the need for robust diagnostics. Existing checks, such as monitoring drift distributions, are useful but indirect. We propose a complementary test based on the configurational temperature, constructed from the gradient and Hessian of the complex action. Unlike drift-based criteria, this estimator directly probes thermodynamic consistency and provides a physically interpretable cross-check of CLM dynamics. Using one-dimensional PT-symmetric models, we show that it reproduces the input temperature with high precision and sensitively detects algorithmic errors, step-size artifacts, and incomplete thermalization. While demonstrated in simple systems, the method extends naturally to higher-dimensional scalar and gauge theories. Since temperature is tied to the bare coupling in many lattice theories, configurational monitoring can also provide an independent check on coupling-dependent observables. Our results indicate that configurational temperature can enhance CLM reliability across a broad range of applications, including lattice QCD at finite density.

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arXiv2025

QCD in strong magnetic fields: fluctuations of conserved charges and EoS

Strong magnetic fields can profoundly affect the equilibrium properties, characterized by the equation of state and bulk thermodynamics of strongly interacting matter. Although such fields are expected in off-central heavy-ion collisions, directly measuring their experimental imprints remains extremely challenging. To address this, we propose the baryon-electric charge correlations $\chi^{\rm BQ}_{11}$ and the chemical potential ratio $\mu_{\rm Q}/\mu_{\rm B}$ as magnetic-field-sensitive probes, based on (2+1)-flavor QCD lattice simulations at physical pion masses. Along the transition line, $\chi^{\rm BQ}_{11}$ and $(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ in Pb-Pb collisions increase by factors of 2.1 and 2.4 at $eB \simeq 8M_\pi^2$, respectively. To bridge theoretical predictions and experimental observations, we construct HRG-based proxies and apply systematic kinematic cuts to emulate STAR and ALICE detector acceptances. Furthermore, we extend this investigation to the QCD equation of state, and examine the leading-order thermodynamic coefficients for strangeness-neutral scenarios up to $eB \simeq 0.8 {\rm GeV}^2 \sim 45 m_{\pi}^2$, revealing intriguing non-monotonic structures.

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arXiv2025

Configurational Temperature as a Diagnostic for Complex Langevin Dynamics in the 3D XY Model

We investigate the applicability of complex Langevin dynamics to the three-dimensional XY model at finite chemical potential. To assess correctness, we introduce a new diagnostic based on the configurational temperature (or configurational coupling) estimator, recently proposed as a thermodynamic consistency check. We compare this criterion with the established Nagata-Nishimura-Shimasaki drift-decay test across a range of couplings and chemical potentials. Our results show that complex Langevin dynamics yields reliable results in the ordered phase (large $\beta$), but fails in the disordered phase (small $\beta$), even when the sign problem is mild. The configurational estimator provides a clear and physics-driven reliability test that complements drift-based diagnostics. These findings establish the estimator as a practical tool for identifying incorrect convergence, and highlight its potential for broader applications in lattice field theories with complex actions.

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arXiv2025

Thermodynamic Diagnostics for Complex Langevin Simulations: The Role of Configurational Temperature

The complex Langevin method (CLM) offers a potential solution to the sign problem in quantum field theories with complex actions, but can converge to incorrect results even when simulations appear stable. Existing diagnostics monitor drift distributions or Langevin-time operators but do not explicitly test whether configurations are sampled with the correct Boltzmann statistical weight. We propose a complementary diagnostic based on configurational temperature, constructed from gradients and Hessians of the action. Testing in one-dimensional PT-symmetric models demonstrates 0.2-3\% accuracy in reproducing the expected value for the configurational temperature. Crucially, configurational temperature detects algorithmic errors -- including noise mis-scaling, step-size artifacts, and incomplete thermalization -- significantly more sensitively than existing drift-based or operator-based criteria. The method relies on the derivatives of the local action, making it applicable to general lattice theories, though computational cost requires consideration in higher dimensions. Our results suggest configurational temperature as a valuable addition to CLM diagnostics, complementing existing tools with potential applications from supersymmetric matrix models to lattice QCD at finite density.

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arXiv2025

Baryon Electric Charge Correlation as QCD Magnetometer

The detection of strong magnetic fields in peripheral heavy-ion collisions is crucial for observing effects such as the chiral magnetic effect but has proven exceptionally difficult. To address this, we propose the baryon electric charge correlation $\chi^{\rm BQ}_{11}$ and the chemical potential ratio $\mu_{\rm Q}/\mu_{\rm B}$ as sensitive probes of magnetic fields, based on (2+1)-flavor lattice QCD simulations at the physical pion mass. Along the transition line, $\chi^{\rm BQ}_{11}$ and $(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ in Pb-Pb collisions increase by factors of 2.1 and 2.4 at $eB \simeq 8M_\pi^2$, respectively. To bridge theoretical predictions with experimental observables, we implement systematic kinematic cuts that emulate detector acceptances of the STAR and ALICE experiments within the hadron resonance gas model. This allows us to construct experimentally relevant proxy observables. Furthermore, we demonstrate that $(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ is also sensitive to the collision system, showing a $1.5$-fold increase from Zr-Zr to Ru-Ru isobar collisions. Our findings offer new insights into thermo-magnetic effects and provide experimentally relevant guidance for the detection of magnetic fields in heavy-ion collisions.

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arXiv2025

Leading-Order QCD Equation of State in Strong Magnetic Fields at Nonzero Baryon Chemical Potential

We present continuum-estimated $(2+1)$-flavor lattice QCD results for the leading-order Taylor expansion coefficients of the equation of state in strong magnetic fields and at nonzero baryon chemical potential. Simulations employ the highly improved staggered quark (HISQ) action with physical pion masses on lattices of temporal extent $N_\tau = 8,\,12$, covering $145 \lesssim T \lesssim 165~\mathrm{MeV}$ and $eB \lesssim 0.8~\mathrm{GeV}^2$, imposing strangeness neutrality with baseline results at electric charge to baryon number ratio $r = 0.4$. We determine the $T$--$eB$ dependence of $q_1$ and $s_1$ (electric charge and strangeness chemical potential ratios), pressure coefficient $P_2$, baryon number density coefficient $N_1^{\rm B}$, and energy-like coefficients $\Theta_2$ (trace anomaly), $\epsilon_2$ (energy density), and $\sigma_2$ (entropy density). Magnetic fields induce temperature-band crossings for $q_1$ and $P_2$ and non-monotonic structures in the energy-like coefficients, with $\Theta_2$ at strong fields possibly vanishing or turning negative at higher $T$, indicating dominance of the pressure term over the energy contribution. We also examine the $r$-dependence, finding that $r=0$ (charge-neutral matter) shows the most muted magnetic-field enhancement of $P_2$ despite larger $|q_1|$, providing a useful reference for neutron-star-like conditions. Comparisons with the hadron resonance gas (HRG) model show qualitative agreement at low $T$ and weak $eB$, with clear deviations near the crossover and at strong fields. These results provide useful input for constraining models and effective theories of QCD matter in strong magnetic fields at finite baryon density.

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arXiv2025

Complex Langevin Simulations of Supersymmetric Theories

This review explores the Complex Langevin Method (CLM), a stochastic quantization technique designed to address the sign problem in quantum field theories with complex actions. Beginning with foundational principles, the review examines the applications of CLM across a range of models, including zero- and two-dimensional systems, supersymmetric quantum mechanics, and the IKKT matrix model, a candidate for non-perturbative string theory. Key advancements, such as stabilization techniques and mass deformations, are highlighted as solutions to challenges like numerical instability and singular drift terms. The review emphasizes the capacity of CLM to simulate complex systems and reveal non-perturbative phenomena, positioning it as a powerful tool for exploring quantum field theory and string theory. Future directions, including higher-dimensional applications and benchmarking against quantum simulations, underscore the potential of CLM to advance both theoretical understanding and computational methodologies.

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arXiv2025

Second order fluctuations of conserved charges in external magnetic fields

We present a first-principles lattice QCD investigation of second-order fluctuations of and correlations among conserved charges -- baryon number (B), electric charge (Q), and strangeness (S) -- in the presence of external magnetic fields. Our study employs lattice simulations of (2+1)-flavor QCD with physical pion masses using highly improved staggered fermions (HISQ) on $48^3 \times 12$ and $32^3 \times 8$ lattices, covering a wide range of magnetic field strengths up to $eB \simeq 0.8$ GeV$ ^2$. We identify clear signals of magnetic field-induced modifications to these fluctuations and correlations, with the baryon-electric charge correlation, $\chi^{\rm BQ}_{11}$, exhibiting particularly strong sensitivity to the magnetic field. To bridge theoretical predictions with experimental observables, we implement systematic kinematic cuts that emulate detector acceptances of the STAR and ALICE experiments within the hadron resonance gas (HRG) model and construct proxy observables for fluctuations measurable in heavy-ion collision experiments. Our findings highlight $\chi^{\rm BQ}_{11}$ as a promising ``magnetometer" for probing the presence of magnetic fields in QCD matter. Furthermore, we explore experimentally relevant ratios involving $\chi^{\rm BQ}_{11}$, demonstrating their potential in mitigating volume effects and enhancing sensitivity to magnetic fields in collision environments. Additionally, we assess the limitations of the HRG model at strong magnetic fields, revealing deviations that indicate nontrivial modifications to hadronic degrees of freedom. These results offer new insights into the interplay between thermal and magnetic effects in the QCD phase diagram and provide experimentally relevant guidance for the detection of magnetic fields in heavy-ion collisions.

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arXiv2025

Baryon-Electric Charge Correlations and Chemical Potentials as Probes of Magnetized QCD

We present the first lattice QCD results of quadratic fluctuations and correlations of conserved charges in (2+1)-flavor lattice QCD in the presence of a background magnetic field. The simulations were performed using the Highly Improved Staggered Quarks with physical pion mass $m_\pi$ = 135 MeV on $N_\tau=8$ and 12 lattices. We find that the correlation between net baryon number and electric charge, denoted as $\chi^{\rm BQ}_{11} $, can serve as a magnetometer of QCD. At pseudocritical temperatures ($T_{pc}$) the $\chi^{\rm BQ}_{11}$ starts to increase rapidly with magnetic field strength $eB \gtrsim 2M^2_{\pi}$ and by a factor 2 at $eB\simeq 8 M^2_{\pi}$. By comparing with the hadron resonance gas model, we find that the $eB$ dependence of $\chi^{\rm BQ}_{11}$ is mainly due to the doubly charged $\Delta$(1232) baryon. Although the doubly charged $\Delta$(1232) could not be detected experimentally, its decay products, protons and pions, retain the $eB$ dependence of $\Delta$(1232)'s contribution to $\chi^{\rm BQ}_{11}$. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, $\mu_{\rm Q}/\mu_{\rm B}$, shows significant dependence on the magnetic field strength and varies with the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results provide baselines for effective theory and model studies, and both $\chi^{\rm BQ}_{11}$ and $\mu_{\rm Q}/\mu_{\rm B}$ could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model.

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arXiv2025

QCD Equation of State with Strong Magnetic Fields and Nonzero Baryon Density

In this work, we have carried out lattice simulations of $(2+1)$-flavor QCD using highly improved staggered quarks at the physical pion mass on $32^3 \times 8$ and $48^3 \times 12$ lattices, with magnetic field strengths ranging up to 0.8 GeV$^2$ and nonzero baryon chemical potentials employing the Taylor expansion framework. We present lattice QCD continuum estimate results, along with the magnetized hadron resonance and ideal gas comparisons, for the leading-order Taylor expansion coefficients for bulk thermodynamic quantities such as pressure, number density, energy density, and entropy density, focusing on the significant impact of strong magnetic fields.

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arXiv2024

Nuclear correlation functions using first-principle calculations of lattice quantum chromodynamics

Exploring nuclear physics through the fundamental constituents of the strong force -- quarks and gluons -- is a formidable challenge. While numerical calculations using lattice quantum chromodynamics offer the most promising approach for this pursuit, practical implementation is arduous, especially due to the uncontrollable growth of quark-combinatorics, the so-called Wick-contraction problem of nuclei. We present here two novel methods providing a state-of-the-art solution to this problem. In the first, we exploit randomized algorithms inspired from computational number theory to detect and eliminate redundancies that arise in Wick contraction computations. Our second method explores facilities for automation of tensor computations -- in terms of efficient utilization of specialized hardware, algorithmic optimizations, as well as ease of programming and the potential for automatic code generation -- that are offered by new programming models inspired by applications in machine learning (e.g., TensorFlow). We demonstrate the efficacy of our methods by computing two-point correlation functions for Deuteron, Helium-3, Helium-4 and Lithium-7, achieving at least an order of magnitude improvement over existing algorithms with efficient implementation on GPU-accelerators. Additionally, we discover an intriguing characteristic shared by all the nuclei we study: specific spin-color combinations dominate the correlation functions, hinting at a potential connection to an as-yet-unidentified symmetry in nuclei. Moreover finding them beforehand can reduce the computing time further and substantially. Our results, with the efficiency that we achieved, suggest the possibility of extending the applicability of our methods for calculating properties of light nuclei, potentially up to A ~12 and beyond.

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arXiv2023

Baryon electric charge correlation as a magnetometer of QCD

The correlation between net baryon number and electric charge, $\chi_{11}^{\rm BQ}$, can serve as a magnetometer of QCD. This is demonstrated by lattice QCD computations using the highly improved staggered quarks with physical pion mass of $M_\pi=135~$MeV on $N_\tau=8$ and 12 lattices. We find that $\chi_{11}^{\rm BQ}$ along the transition line starts to increase rapidly with magnetic field strength $eB\gtrsim 2M_\pi^2$ and by a factor 2 at $eB\simeq 8M_\pi^2$. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, $\mu_{\rm Q}/\mu_{\rm B}$, shows significant dependence on the magnetic field strength and varies from the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results can provide baselines for effective theory and model studies, and both $\chi_{11}^{\rm BQ}$ and $\mu_{\rm Q}/\mu_{\rm B}$ could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model.

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arXiv2023

Non-Perturbative Simulations of Quantum Field Theories using Complex Langevin Dynamics

Non-perturbative formulations of field theories are essential to capture intriguing physical phenomena, including confinement in QCD, spontaneous supersymmetry breaking, and dynamical compactification in superstrings. Lattice regularization provides a robust framework to study these non-perturbative features through Euclidean path integrals. Conventionally, path integrals are numerically evaluated using Monte Carlo methods, where the Boltzmann factor is interpreted as a probability weight. However, complex actions in various physical systems render the Boltzmann factor complex, leading to the sign problem. The complex Langevin method overcomes the sign problem and can be used to evaluate complex integrals. This thesis employs the complex Langevin method to investigate various non-perturbative aspects of field-theoretic systems with complex actions. We probe the possibility of spontaneous supersymmetry breaking in the simplest realizations of supersymmetric field theories. These systems generally have complex actions arising from a complex determinant of the fermion operator. We studied various interesting classes of complex potentials, including those exhibiting PT-symmetry. Another exciting aspect explored is the dynamical compactification of extra dimensions in superstring theory. The IKKT matrix model, in the large-N limit, is a conjectured formulation for the 10D type IIB string theory. We employ the complex Langevin method to investigate the Euclidean version of this matrix model, which has an inherent complex Pfaffian, to probe the spontaneous breaking of SO(10) symmetry. The investigations performed in this thesis suggest that the complex Langevin method can successfully simulate non-perturbative aspects of quantum field theories by taming the associated sign problem.

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arXiv2023

Investigating Spontaneous SO(10) Symmetry Breaking in Type IIB Matrix Model

Non-perturbative formulations are essential to understand the dynamical compactification of extra dimensions in superstring theories. The type IIB (IKKT) matrix model in the large-$N$ limit is one such conjectured formulation for a ten-dimensional type IIB superstring. In this model, a smooth spacetime manifold is expected to emerge from the eigenvalues of the ten bosonic matrices. When this happens, the SO(10) symmetry in the Euclidean signature must be spontaneously broken. The Euclidean version has a severe sign problem since the Pfaffian obtained after integrating out the fermions is inherently complex. In recent years, the complex Langevin method (CLM) has successfully tackled the sign problem. We apply the CLM method to study the Euclidean version of the type IIB matrix model and investigate the possibility of spontaneous SO(10) symmetry breaking. In doing so, we encounter a singular-drift problem. To counter this, we introduce supersymmetry-preserving deformations with a Myers term. We study the spontaneous symmetry breaking in the original model at the vanishing deformation parameter limit. Our analysis indicates that the phase of the Pfaffian induces the spontaneous SO(10) symmetry breaking in the Euclidean type IIB model.

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arXiv2022

Complex Langevin study of spontaneous symmetry breaking in IKKT matrix model

The IKKT matrix model, in the large-$N$ limit, is conjectured to be a non-perturbative definition of the ten-dimensional type IIB superstring theory. In this work, we investigate the possibility of spontaneous breaking of the ten-dimensional rotational symmetry in the Euclidean IKKT model. Since the effective action, after integrating out the fermions, is inherently complex, we use the complex Langevin dynamics to study the model. In order to evade the singular-drift problem in the model, we add supersymmetry preserving deformations and then take the vanishing limit of the deformations. Our analysis suggests that the phase of the Pfaffian indeed induces the spontaneous SO(10) symmetry breaking in the Euclidean IKKT model.

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arXiv2022

Complex Langevin simulations for $PT$-symmetric models

Self-interacting scalar quantum field theories possessing $PT$-symmetry are physically admissible since their energy spectrum is real and bounded below. However, models with $PT$-invariant potentials can have complex actions in general and a non-perturbative study of such systems using methods based on traditional Monte Carlo is hindered due to numerical sign problem. In this work we employ complex Langevin based on stochastic quantization to study two-dimensional scalar field theories, including the ones exhibiting $PT$-symmetry. We also study the simplest supersymmetric version of these systems and address the question on dynamical supersymmetry breaking.

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