arXiv subjects

Pavel Buividovich

Publications and source records attributed to Pavel Buividovich.

At least 19 recordsLinked to original sources

arXiv2025

Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration

The hybrid Monte Carlo (HMC) algorithm is a ubiquitous method in computational physics with applications ranging from condensed matter to lattice QCD and beyond. However, HMC simulations often suffer from long autocorrelation times, severely reducing their efficiency. In this work two of the main sources of autocorrelations are identified and eliminated. The first source is the sampling of the canonical momenta from a sub-optimal normal distribution, the second is a badly chosen trajectory length. Analytic solutions to both problems are presented and implemented in the exact Fourier acceleration (EFA) method. It completely removes autocorrelations for near-harmonic potentials and consistently yields (close-to-) optimal results for numerical simulations of the Su-Schrieffer-Heeger and the Ising models as well as in lattice gauge theory, in some cases reducing the autocorrelation by multiple orders of magnitude. EFA is advantageous for and easily applicable to any HMC simulation of an action that includes a quadratic part.

hep-lat↗

arXiv2024

Strongly interacting matter in extreme magnetic fields

Magnetic fields are ubiquitous across different physical systems of current interest; from the early Universe, compact astrophysical objects and heavy-ion collisions to condensed matter systems. A proper treatment of the effects produced by magnetic fields during the dynamical evolution of these systems, can help to understand observables that otherwise show a puzzling behavior. Furthermore, when these fields are comparable to or stronger than Λ_QCD, they serve as excellent probes to help elucidate the physics of strongly interacting matter under extreme conditions of temperature and density. In this work we provide a comprehensive review of recent developments on the description of QED and QCD systems where magnetic field driven effects are important. These include the modification of meson static properties such as masses and form factors, the chiral magnetic effect, the description of anomalous transport coefficients, superconductivity in extreme magnetic fields, the properties of neutron stars, the evolution of heavy-ion collisions, as well as effects on the QCD phase diagram. We describe recent theory and phenomenological developments using effective models as well as LQCD methods. The work represents a state-of-the-art review of the field, motivated by presentations and discussions during the "Workshop on Strongly Interacting Matter in Strong Electromagnetic Fields" that took place in the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in the city of Trento, Italy, September 25-29, 2023.

nucl-th↗

arXiv2024

High-precision Quantum Monte-Carlo study of charge transport in a lattice model of molecular organic semiconductors

We use first-principle Quantum Monte-Carlo (QMC) simulations and numerical exact diagonalization to analyze the low-frequency charge carrier mobility within a simple tight-binding model of molecular organic semiconductors on a two-dimensional triangular lattice. These compounds feature transient localization, an unusual charge transport mechanism driven by dynamical disorder. The challenges of studying the transient localization of charge carriers in the low-frequency/long-time limit from first principles are discussed. We demonstrate that a combination of high-precision QMC data with prior estimates of frequency-dependent charge carrier mobility based on the static disorder approximation for phonon fields allows for improved estimates of mobility in the low-frequency limit. We also point out that a simple relaxation time approximation for charge mobility in organic semiconductors is not consistent with the QMC data. Physical similarities with charge transport in quark-gluon plasma are highlighted.

cond-mat.mtrl-sci↗

arXiv2024

First-principle quantum Monte-Carlo study of charge carrier mobility in organic molecular semiconductors

We present a first-principle numerical study of charge transport in a realistic two-dimensional tight-binding model of organic molecular semiconductors. We use the Hybrid Monte Carlo (HMC) algorithm to simulate the full quantum dynamics of phonons and either a single or multiple charge carriers without any tunable parameters. We introduce a number of algorithmic improvements, including efficient Metropolis updates for phonon fields based on analytic insights, which lead to negligible autocorrelation times and allow to reach sub-permille precisions at small computational cost of $O(1)$ CPU-hour. Our simulations produce charge mobility estimates that are in good agreement with experiment and that also justify the phenomenological Transient Localisation approach.

cond-mat.mtrl-sci↗

arXiv2024

Synthetic images aid the recognition of human-made art forgeries

Previous research has shown that Artificial Intelligence is capable of distinguishing between authentic paintings by a given artist and human-made forgeries with remarkable accuracy, provided sufficient training. However, with the limited amount of existing known forgeries, augmentation methods for forgery detection are highly desirable. In this work, we examine the potential of incorporating synthetic artworks into training datasets to enhance the performance of forgery detection. Our investigation focuses on paintings by Vincent van Gogh, for which we release the first dataset specialized for forgery detection. To reinforce our results, we conduct the same analyses on the artists Amedeo Modigliani and Raphael. We train a classifier to distinguish original artworks from forgeries. For this, we use human-made forgeries and imitations in the style of well-known artists and augment our training sets with images in a similar style generated by Stable Diffusion and StyleGAN. We find that the additional synthetic forgeries consistently improve the detection of human-made forgeries. In addition, we find that, in line with previous research, the inclusion of synthetic forgeries in the training also enables the detection of AI-generated forgeries, especially if created using a similar generator.

cs.CV↗

arXiv2022

Quantum chaos in supersymmetric Yang-Mills-like model: equation of state, entanglement, and spectral form-factors

We analyze in detail a sharp transition between the low-energy, low-dimensional eigenstates and the high-energy chaotic bulk of the spectrum for a simple supersymmetric quantum-mechanical model with Hamiltonian $\hat{H}_S = \left(\hat{p}_1^2 + \hat{p}_2^2 + \hat{x}_1^2 \, \hat{x}_2^2 \right) \otimes I + \hat{x}_1 \otimes σ_1 + \hat{x}_2 \otimes σ_3$, which mimics the structure of the Banks-Fischler-Susskind-Stanford (BFSS) matrix model, the spatially compactified $\mathcal{N} = 1$ super-Yang-Mills theory. We conjecture that this transition might be similar to the transition between the $D0$-brane and $M$-theory regimes in the BFSS model, and find that it does not lead to irregularities in the thermodynamic equation of state. We demonstrate that real-time spectral form-factor for our supersymmetric model exhibits the ``ramp'' behavior typical for quantum chaos. We also analyze the entanglement entropy and the spectrum of the reduced density matrix of the eigenstates of $\hat{H}_S$, considering one of the bosonic degrees of freedom as a subsystem. The entanglement entropy of low-energy eigenstates appears to be practically energy-independent. Exactly at the onset of random-matrix-type level spacing fluctuations, this behavior rapidly changes into a steady growth of entanglement with energy. We demonstrate that the spectrum of the reduced density matrix also exhibits universal level-spacing fluctuations towards its higher end, even for the ground state of the supersymmetric model. Thus even the regularly spaced, non-chaotic eigenstates contain some information about semi-classical chaotic dynamics at high energies.

hep-lat↗

arXiv2022

Reduced critical slowing down for statistical physics simulations

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called "slow mode", which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for the Ising model and the linear-log-relaxation (LLR) method as simulation algorithm. We firstly demonstrate super critical slowing down in a phase with spontaneously broken symmetry and for the heatbath algorithms, for which autocorrelation times grow exponentially with system size. By contrast, using the magnetisation as collective coordinate, we present evidence that super critical slowing down is absent. We still observe a polynomial increase of the autocorrelation time with volume (critical slowing down), which is however reduced by orders of magnitude when compared to local update techniques.

cond-mat.stat-mech↗

arXiv2022

Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches

We put the Density-of-States (DoS) approach to Monte-Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real time evolution of a non-integrable quantum spin chain. Benchmarks against numerical exact diagonalisation and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as $L=40$, far beyond exact diagonalisability, though only for short evolution times $t\lesssim 1$. We identify discontinuities of the density of states as one of the key problems in the MC simulations and propose to calculate some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements the density of states is found highly non-smooth and therefore the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real time simulations with discrete degrees of freedom.

cond-mat.stat-mech↗

arXiv2021

Quantum phase transitions on the hexagonal lattice

Hubbard-type models on the hexagonal lattice are of great interest, as they provide realistic descriptions of graphene and other related materials. Hybrid Monte Carlo simulations offer a first-principles approach to study their phase structure. Here, we review the present status of our work in this direction.

cond-mat.str-el↗

arXiv2019

Lattice study of Rényi entanglement entropy in $SU(N_c)$ lattice Yang-Mills theory with $N_c = 2, 3, 4$

We consider the second Rényi entropy $S^{(2)}$ in pure lattice gauge theory with $SU(2)$, $SU(3)$ and $SU(4)$ gauge groups, which serves as a first approximation for the entanglement entropy and the entropic $C$-function. We compare the results for different gauge groups using scale setting via the string tension. We confirm that at small distances $l$ our approximation for the entropic $C$-function $C(l)$, calculated for the slab-shaped entangled region of width $l$, scales as $N_c^2 - 1$ in accordance with its interpretation in terms of free gluons. At larger distances $l$ $C(l)$ is found to approach zero for $N_c = 3, 4$, somewhat more rapidly for $N_c = 4$ than for $N_c = 3$. This finding supports the conjectured discontinuity of the entropic $C$-function in the large-$N$ limit, which was found in the context of AdS/CFT correspondence and which can be interpreted as transition between colorful quarks and gluons at small distances and colorless confined states at long distances. On the other hand, for $SU(2)$ gauge group the long-distance behavior of the entropic $C$-function is inconclusive so far. There exists a small region of lattice spacings yielding results consistent with $N_c=3,4$, while results from other lattice spacings deviate without clear systematics. We discuss several possible causes for discrepancies between our results and the behavior of entanglement entropy in holographic models.

hep-lat↗

arXiv2019

Numerical evidence of conformal phase transition in graphene with long-range interactions

Using state of the art Hybrid-Monte-Carlo (HMC) simulations we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement.

cond-mat.str-el↗

arXiv2018

Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice

Using first-principle Hybrid-Monte-Carlo (HMC) simulations, we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in the extended Hubbard model on the two dimensional hexagonal lattice at half filling. We determine the phase diagram in the space of on-site and nearest-neighbor couplings $U$ and $V$ in the region $V<U/3$, which can be simulated without a fermion sign problem, and find that a transition from semimetal to a SDW phase occurs at sufficiently large $U$ for basically all $V$. Tracing the corresponding phase boundary from $V=0$ to the $V=U/3$ line, we find evidence for critical scaling in the Gross-Neveu universality class for the entire boundary. With rather high confidence we rule out the existence of the CDW ordered phase anywhere in the range of parameters considered. We also discuss several improvements of the HMC algorithm which are crucial to reach these conclusions, in particular the improved fermion action with exact sublattice symmetry and the complexification of the Hubbard-Stratonovich field to ensure the ergodicity of the algorithm.

cond-mat.str-el↗

arXiv2018

Schur complement solver for Quantum Monte-Carlo simulations of strongly interacting fermions

We present a non-iterative solver based on the Schur complement method for sparse linear systems of special form which appear in Quantum Monte-Carlo (QMC) simulations of strongly interacting fermions on the lattice. While the number of floating-point operations for this solver scales as the cube of the number of lattice sites, for practically relevant lattice sizes it is still significantly faster than iterative solvers such as the Conjugate Gradient method in the regime of strong inter-fermion interactions, for example, in the vicinity of quantum phase transitions. The speed-up is even more dramatic for the solution of multiple linear systems with different right-hand sides. We present benchmark results for QMC simulations of the tight-binding models on the hexagonal graphene lattice with on-site (Hubbard) and non-local (Coulomb) interactions, and demonstrate the potential for further speed-up using GPU.

cond-mat.str-el↗

arXiv2017

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

We describe a numerical method which allows us to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound $λ_L < 2 πT$, while the classical dynamics inevitably breaks the bound.

hep-th↗

arXiv2017

A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density

We report on Hybrid-Monte-Carlo simulations at finite spin density of the $π$-band electrons in monolayer graphene with realistic inter-electron interactions. Unlike simulations at finite charge-carrier density, these are not affected by a fermion-sign problem. Our results are in qualitative agreement with an interaction-induced warping of the Fermi contours, and a reduction of the bandwidth as observed in angle resolved photoemission spectroscopy experiments on charge-doped graphene systems. Furthermore, we find evidence that the neck-disrupting Lifshitz transition, which occurs when the Fermi level traverses the van Hove singularity (VHS), becomes a true quantum phase transition due to interactions. This is in-line with an instability of the VHS towards the formation of electronic ordered phases, which has been predicted by a variety of different theoretical approaches.

cond-mat.str-el↗

arXiv2017

Inter-electron interactions and the RKKY potential between H adatoms in graphene

We use first-principles Quantum Monte-Carlo simulations to study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between hydrogen adatoms attached to a graphene sheet. We find that the pairwise RKKY interactions at distances of a few lattice spacings are strongly affected by inter-electron interactions, in particular, the potential barrier between widely separated adatoms and the dimer configuration becomes wider and thus harder to penetrate. We also point out that anti-ferrromagnetic and charge density wave orderings have very different effects on the RKKY interaction. Finally, we analyze the stability of several regular adatom superlattices with respect to small displacements of a single adatom, distinguishing the cases of adatoms which populate either both or only one sublattice of the graphene lattice.

cond-mat.str-el↗

arXiv2016

Competing order in the fermionic Hubbard model on the hexagonal graphene lattice

We study the phase diagram of the fermionic Hubbard model on the hexagonal lattice in the space of on-site and nearest neighbor couplings with Hybrid-Monte-Carlo simulations. With pure on-site repulsion this allows to determine the critical coupling strength for spin-density wave formation with the standard approach of introducing a small mass term, explicitly breaking the sublattice symmetry. The analogous mass term for charge-density wave formation above a critical nearest-neighbor repulsion, on the other hand, would introduce a fermion sign problem. The competition between the two and the phase diagram in the space of the two coouplings can however be studied in simulations without explicit sublattice symmetry breaking. Our results compare qualitatively well with the Hartree-Fock phase diagram. We furthermore demonstrate how spin-symmetry breaking by the Euclidean time discretization can be avoided also, when using an improved fermion action based on an exponetial transfer matrix with exact sublattice symmetry.

hep-lat↗

arXiv2010

Path Integral over Reparametrizations: Levy Flights versus Random Walks

We investigate the properties of the path integral over reparametrizations (= the boundary value of the Liouville field in open string theory). Discretizing the path integral, we apply the Metropolis-Hastings algorithm to numerical simulations of a proper (subordinator) stochastic process and find that typical trajectories are not Brownian but rather have discontinuities of the type of Levy's flights. We study a fractal structure of these trajectories and show that their Hausdorff dimension is zero. We confirm thereby the discretization and heuristic consideration of QCD scattering amplitudes by analytical and numerical calculations. We also perform Monte Carlo simulations of the path integral over reparametrization in the effective-string ansatz for a circular Wilson loop and discuss their subtleties associated with the discretization of Douglas' functional.

hep-th↗