arXiv subjects

P. V. Buividovich

Publications and source records attributed to P. V. Buividovich.

At least 19 recordsLinked to original sources

arXiv2026

Chiral Magnetic Effect and Negative Magnetoresistance across the phase diagram of finite-density SU(2) gauge theory

We study the signatures of the Chiral Magnetic Effect (CME) in $SU(2)$ gauge theory with $N_f = 2$ flavours of dynamical fermions at finite temperature $T$, quark chemical potential $μ$ and a weak external magnetic field $e B$. We consider both the correlator of the axial density and the vector current, which gives direct access to the out-of-equilibrium CME, and the correlator of two vector currents, which probes the CME indirectly via the enhancement of the longitudinal electric conductivity (Negative Magnetoresistance, NMR). We find that the CME response extracted from the vector-axial correlator exhibits a rather weak dependence on temperature and density in the quark-gluon plasma regime, and is very close to the universal value for free massless quarks. The CME appears to be mildly suppressed at low temperatures in the hadronic phase. In contrast, the NMR behaves in a qualitatively different way across the phase diagram, and is strongly suppressed at either large densities or temperatures. The magnitude of the NMR response appears to be considerably smaller than the prediction based on the lowest Landau level calculation for free quarks. Our findings suggest that for relatively small magnetic field strengths $e B \lesssim m_π^2$ the relation between the CME and NMR might not be as direct as expected. We also do not find statistically significant indications for an enhancement of the CME or NMR strength in the vicinity of the crossover or second-order phase transition lines in the $(μ, T)$ phase diagram.

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arXiv2026

Hamiltonian-based dimensional reduction and spectral reconstruction with Wilson-Dirac fermions

Motivated by the process of reconstructing real-time spectral functions from Euclidean correlators in lattice QCD, we derive explicit expressions for the fermionic determinant and the propagator of the four-dimensional clover-improved Wilson-Dirac fermions on anisotropic lattices in terms of the three-dimensional Wilson-Dirac Hamiltonian operator. We derive an effective Hamiltonian that governs Euclidean time evolution at finite temporal lattice spacing, and demonstrate its hermiticity and particle-anti-particle symmetry. Our results allow to quantify lattice artifacts of the numerical spectral reconstruction based on Euclidean fermionic correlators at finite temporal lattice spacing.

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arXiv2025

Spectral reconstruction based on dimensional reduction in high-temperature gauge theories

We propose a numerical spectral reconstruction workflow for high-temperature gauge theories that incorporates elements of semi-classical real-time evolution directly into standard lattice QCD simulations via high-temperature dimensional reduction, thus counteracting the deterioration of Euclidean-time correlators at high temperatures. With a moderate numerical cost, our method allows to estimate spectral functions with parametrically better frequency resolution as compared with spectral reconstruction methods based on Euclidean-time correlators alone. The method is tested on a simple (1+1)-dimensional Abelian gauge theory with fermions, where our method precisely reproduces the full quantum spectral functions calculated using exact numerical diagonalization in the high-temperature, weak-coupling regime. We also demonstrate the feasibility of our approach by applying it to light-quark meson correlators in lattice QCD deep in the deconfinement regime.

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arXiv2024

Out-of-equilibrium Chiral Magnetic Effect from simulations on Euclidean lattices

The status of the Chiral Magnetic Effect (CME) response in full Quantum Chromodynamics (QCD) has been controversial so far, with previous lattice QCD studies indicating either its strong suppression or vanishing in thermal equilibrium state. We introduce the Euclidean-time correlator of axial charge and electric current as an observable that can be used to study the finite out-of-equilibrium CME response in first-principle lattice QCD simulations with background magnetic field. This observable directly reflects the fact that in the background magnetic field, a state with nonzero axial charge features nonzero electric current. For free fermions, the axial-vector correlator only receives contributions from the Lowest Landau Level, and exhibits a linear dependence on both magnetic field and temperature with a universal coefficient. With an appropriate regularization, non-vanishing axial-vector correlator is compatible with the vanishing of the CME current in thermal equilibrium state with nonzero chiral chemical potential $μ_5$. We demonstrate that the real-time counterpart of the Euclidean-time axial-vector correlator is intimately related to the real-time form of the axial anomaly equation, which strongly limits possible corrections in full QCD. We present numerical results for the Euclidean-time axial-vector correlator in $SU(2)$ lattice gauge theory with $N_f = 2$ light quark flavours, demonstrating reasonable agreement with free fermion result on both sides of the chiral crossover. The proposed methodology should help to answer the question whether the QCD corrections might be responsible for non-observation of CME in heavy-ion collision experiments such as the RHIC isobar run.

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arXiv2022

Quantum chaos in supersymmetric quantum mechanics: an exact diagonalization study

We use exact diagonalization to study energy level statistics and out-of-time-order correlators (OTOCs) for the simplest supersymmetric extension $\hat{H}_S = \hat{H}_B \otimes I + \hat{x}_1 \otimes σ_1 + \hat{x}_2 \otimes σ_3$ of the bosonic Hamiltonian $\hat{H}_B = \hat{p}_1^2 + \hat{p}_2^2 + \hat{x}_1^2 \, \hat{x}_2^2$. For a long time, this bosonic Hamiltonian was considered one of the simplest systems which exhibit dynamical chaos both classically and quantum-mechanically. Its structure closely resembles that of spatially compactified pure Yang-Mills theory. Correspondingly, the structure of our supersymmetric Hamiltonian is similar to that of spatially compactified supersymmetric Yang-Mills theory, also known as the BFSS model. We present numerical evidence that a continuous energy spectrum of the supersymmetric model leads to monotonous growth of OTOCs down to the lowest temperatures, which is also expected for the BFSS model from holographic duality. This growth is saturated by low-energy eigenstates with effectively one-dimensional wave functions and a completely non-chaotic energy level distribution. We observe a sharp boundary separating these low-energy states from the bulk of chaotic high-energy states. Our data suggests, although with a limited confidence, that at low temperatures the OTOC growth might be exponential over a finite range of time, with the corresponding Lyapunov exponent scaling linearly with temperature. In contrast, the gapped low-energy spectrum of the bosonic Hamiltonian leads to oscillating OTOCs at low temperatures without any signatures of exponential growth. We also find that the OTOCs for the bosonic Hamiltonian are never sufficiently close to the classical Lyapunov distance. On the other hand, the OTOCs for the supersymmetric system agree with the classical limit reasonably well over a finite range of temperatures and evolution times.

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arXiv2021

Static magnetic susceptibility in finite-density SU(2) lattice gauge theory

We study static magnetic susceptibility $χ(T, μ)$ in $SU(2)$ lattice gauge theory with $N_f = 2$ light flavours of dynamical fermions at finite chemical potential $μ$. Using linear response theory we find that $SU(2)$ gauge theory exhibits paramagnetic behavior in both the high-temperature deconfined regime and the low-temperature confining regime. Paramagnetic response becomes stronger at higher temperatures and larger values of the chemical potential. For our range of temperatures $0.727 \leq T/T_c \leq 2.67$, the first coefficient of the expansion of $χ(T, μ)$ in even powers of $μ/T$ around $μ=0$ is close to that of free quarks and lies in the range $(2 \ldots 5) \cdot 10^{-3}$. The strongest paramagnetic response is found in the diquark condensation phase at $μ> m_π/2$.

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arXiv2021

Numerical Study of the Chiral Separation Effect in Two-Color QCD at Finite Density

We study the Chiral Separation Effect (CSE) in finite-density SU(2) lattice gauge theory with dynamical quarks. We find that the CSE is well described by the free quark result in the high-temperature quark-gluon plasma phase. As one enters the confinement regime with broken chiral symmetry at chemical potential smaller than half of the pion mass, the CSE response is gradually suppressed towards low temperatures in comparison to the free quark result. This suppression can be approximately described by assuming that the CSE current is proportional to the charge density, rather than the chemical potential, as suggested in the literature (ArXiv:1712.01256, Phys.Rev.D97(2018)085020). We also provide an upper bound on the contribution of disconnected fermionic diagrams to the CSE, which is consistent with zero within our statistical errors and small compared to that of the connected diagrams. Our results are obtained mainly in the QCD-like regime of SU(2) gauge theory at low densities, and hence should be at least qualitatively applicable to QCD as well.

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arXiv2020

Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions

We study the dependence of the electric conductivity on chemical potential in finite-density $SU(2)$ gauge theory with $N_f = 2$ flavours of rooted staggered sea quarks, in combination with Wilson-Dirac and Domain Wall valence quarks. The pion mass is reasonably small with $m_π/m_ρ \approx 0.4$. We concentrate in particular on the vicinity of the chiral crossover, where we find the low-frequency electric conductivity to be most sensitive to small changes in fermion density. Working in the low-density QCD-like regime with spontaneously broken chiral symmetry, we obtain an estimate of the first nontrivial coefficient $c(T)$ of the expansion of conductivity $σ(T,μ) = σ(T,0) \left(1 + c(T) (μ/T)^2 + O(μ^4)\right)$ in powers of $μ$, which has rather weak temperature dependence and takes its maximal value $c(T) \approx 0.10 \pm 0.07$ around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows towards the diquark condensation phase, and also becomes closer to the free quark result. As a by-product of our study we confirm the conclusions of previous studies with heavier pion that for $SU(2)$ gauge theory the ratio of crossover temperature to pion mass $T_c/m_π \approx 0.4$ at $μ=0$ is significantly smaller than in real QCD.

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arXiv2018

Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model

We study numerically the onset of chaos and thermalization in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model with and without fermions, considering Lyapunov exponents, entanglement generation, and quasinormal ringing. We approximate the real-time dynamics in terms of the most general Gaussian density matrices with parameters which obey self-consistent equations of motion, thus extending the applicability of real-time simulations beyond the classical limit. Initial values of these Gaussian density matrices are optimized to be as close as possible to the thermal equilibrium state of the system. Thus attempting to bridge between the low-energy regime with a calculable holographic description and the classical regime at high energies, we find that quantum corrections to classical dynamics tend to decrease the Lyapunov exponents, which is essential for consistency with the Maldacena-Shenker-Stanford (MSS) bound at low temperatures. The entanglement entropy is found to exhibit an expected "scrambling" behavior - rapid initial growth followed by saturation. At least at high temperatures the entanglement saturation time appears to be governed by classical Lyapunov exponents. Decay of quasinormal modes is found to be characterized by the shortest time scale of all. We also find that while the bosonic matrix model becomes non-chaotic in the low-temperature regime, for the full BFSS model with fermions the leading Lyapunov exponent, entanglement saturation time, and decay rate of quasinormal modes all remain finite and non-zero down to the lowest temperatures.

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arXiv2017

The Chiral Separation Effect in quenched finite-density QCD

We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coefficient for the CSE in the confining and de-confining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coefficient within small statistical errors. Our results suggest that the CSE can be used to determine the renormalisation factor of the axial current.

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arXiv2017

Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model

We develop numerical tools for Diagrammatic Monte-Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First we note that the path integral measure of such theories contributes a bare mass term in the effective action which is proportional to the bare coupling constant. This mass term renders the perturbative expansion infrared-finite and allows to study it directly in the large-N and infinite-volume limits using the Diagrammatic Monte-Carlo approach. On the exactly solvable example of a large-N O(N) sigma model in D=2 dimensions we show that this infrared-finite weak-coupling expansion contains, in addition to powers of bare coupling, also powers of its logarithm, reminiscent of re-summed perturbation theory in thermal field theory and resurgent trans-series without exponential terms. We numerically demonstrate the convergence of these double series to the manifestly non-perturbative dynamical mass gap. We then develop a Diagrammatic Monte-Carlo algorithm for sampling planar diagrams in the large-N matrix field theory, and apply it to study this infrared-finite weak-coupling expansion for large-N U(N)xU(N) nonlinear sigma model (principal chiral model) in D=2. We sample up to 12 leading orders of the weak-coupling expansion, which is the practical limit set by the increasingly strong sign problem at high orders. Comparing Diagrammatic Monte-Carlo with conventional Monte-Carlo simulations extrapolated to infinite N, we find a good agreement for the energy density as well as for the critical temperature of the "deconfinement" transition. Finally, we comment on the applicability of our approach to planar QCD at zero and finite density.

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arXiv2017

Lattice study of continuity and finite-temperature transition in two-dimensional SU(N) x SU(N) Principal Chiral Model

We present first-principle lattice study of the two-dimensional SU(N) x SU(N) Principal Chiral Model (PCM) on the cylinder R x S1 with variable compactification length L0 of S1 and with both periodic and ZN-symmetric twisted boundary conditions. For both boundary conditions our numerical results can be interpreted as signatures of a weak crossover or phase transition between the regimes of small and large L0. In particular, at small L0 thermodynamic quantities exhibit nontrivial dependence on L0, and the static correlation length exhibits a weak enhancement at some "critical" value of L0. We also observe important differences between the two boundary conditions, which indicate that the transition scenario is more likely in the periodic case than in the twisted one. In particular, the enhancement of correlation length for periodic boundary conditions becomes more pronounced at large N, and practically does not depend on N for twisted boundary conditions. Using Gradient Flow we study non-perturbative content of the theory and find that the peaks in the correlation length appear when the length L0 becomes comparable with the typical size of unitons, unstable saddle points of PCM. With twisted boundary conditions these saddle points become effectively stable and one-dimensional in the regime of small N L0, whereas at large N L0 they are very similar to the two-dimensional unitons with periodic boundary conditions. In the context of adiabatic continuity conjecture for PCM with twisted boundary conditions, our results suggest that while the effect of the compactification is clearly different for different boundary conditions, one still cannot exclude the possibility of a weak crossover separating the strong-coupling regime at large N L0 and the Dunne-Unsal regime at small N L0 with twisted boundary conditions.

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arXiv2017

A numerical study of non-perturbative corrections to the Chiral Separation Effect in quenched finite-density QCD

We demonstrate the non-renormalization of the Chiral Separation Effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian fields inside instanton cores.

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arXiv2016

First experience with classical-statistical real-time simulations of anomalous transport with overlap fermions

We present first results of classical-statistical real-time simulations of anomalous transport phenomena with overlap fermions. We find that even on small lattices overlap fermions reproduce the real-time anomaly equation with much better precision than Wilson-Dirac fermions on an order of magnitude larger lattices. The difference becomes much more pronounced for quickly changing electromagnetic fields, especially if one takes into account the back-reaction of fermions on electromagnetism. As test cases, we consider chirality pumping in parallel electric and magnetic fields and mixing between the plasmon and the Chiral Magnetic Wave.

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arXiv2016

A method to compute derivatives of functions of large complex matrices

A recently developed numerical method for the calculation of derivatives of functions of general complex matrices, which can also be combined with implicit matrix function approximations such as Krylov-Ritz type algorithms, is presented. An important use case for the method in the context of lattice gauge theory is the overlap Dirac operator at finite quark chemical potential. Derivatives of the lattice Dirac operator are necessary for the computation of conserved lattice currents or the fermionic force in Hybrid Monte-Carlo and Langevin simulations. To calculate the overlap Dirac operator at finite chemical potential the product of the sign function of a non-Hermitian matrix with a vector has to be computed. For non-Hermitian matrices it is not possible to efficiently approximate the sign function with polynomials or rational functions. Implicit approximation algorithms, like Krylov-Ritz methods, that depend on the source vector have to be used instead. Our method can also provide derivatives of such implicit approximations. We show how a generalised deflation prescription can be used to improve the performance of the method, if some eigenvalues and eigenvectors of the matrix being differentiated are known. To show that the method is efficient and well suited for practical calculations we provide test results for the two-sided Lanczos approximation of the finite-density overlap Dirac operator on SU(3) gauge field configurations on lattices with sizes up to $14 \times 14^3$.

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arXiv2016

Metropolis updates for Diagrammatic Monte-Carlo algorithms from Schwinger-Dyson equations

We describe a general recipe for constructing Metropolis updates for Diagrammatic Monte-Carlo (DiagMC) algorithms, based on the Schwinger-Dyson equations in quantum field theory. This approach bypasses explicit duality transformations, enumeration or classification of diagrams and can be used for lattice quantum field theories with unknown or complicated dual representations (such as non-Abelian lattice gauge theories). DiagMC algorithms constructed in this way can still be plagued by the sign problem, which is, however, completely different from the sign problem in conventional Monte-Carlo simulations and has its origin in cancellations between diagrams with positive and negative weights. To test the presented approach, we apply DiagMC to calculate the first 7 orders of 1/N expansion in the quartic matrix model and find good agreement with analytic results, with the exception of the close vicinity of the critical coupling where the critical slowing down sets in.

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arXiv2016

A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential

We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular with implicit Krylov-Ritz-type approximations. An important use case for the method is the evaluation of the overlap Dirac operator in lattice Quantum Chromodynamics (QCD) at finite chemical potential, which requires the application of the sign function of a non-Hermitian matrix to some source vector. While the sign function of non-Hermitian matrices in practice cannot be efficiently approximated with source-independent polynomials or rational functions, sufficiently good approximating polynomials can still be constructed for each particular source vector. Our method allows for an efficient calculation of the derivatives of such implicit approximations with respect to the gauge field or other external parameters, which is necessary for the calculation of conserved lattice currents or the fermionic force in Hybrid Monte-Carlo or Langevin simulations. We also give an explicit deflation prescription for the case when one knows several eigenvalues and eigenvectors of the matrix being the argument of the differentiated function. We test the method for the two-sided Lanczos approximation of the finite-density overlap Dirac operator on realistic $SU(3)$ gauge field configurations on lattices with sizes as large as $14\times14^3$ and $6\times18^3$.

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arXiv2016

Numerical study of chiral plasma instability within the classical statistical field theory approach

We report on a numerical study of real-time dynamics of electromagnetically interacting chirally imbalanced lattice Dirac fermions within the classical statistical field theory approach. Namely, we perform exact simulations of the real-time quantum evolution of fermionic fields coupled to classical electromagnetic fields, which are in turn coupled to the vacuum expectation value of the fermionic electric current. We use Wilson-Dirac Hamiltonian for fermions, and non-compact action for the gauge field. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to transform to helicity of electromagnetic field. By performing simulations on large lattices we show that in most cases this decay process is accompanied by the inverse cascade phenomenon which transfers energy from short-wavelength to long-wavelength electromagnetic fields. In some simulations, however, we observe a very clear signature of inverse cascade for the helical magnetic fields which is not accompanied by the axial charge decay. This suggests that the relation between inverse cascade and axial charge decay is not as straightforward as predicted by the simplest form of anomalous Maxwell equations.

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