arXiv subjects

Andrei Alexandru

Publications and source records attributed to Andrei Alexandru.

At least 55 records · Page 3Linked to original sources

arXiv2020

Roper State from Overlap Fermions

The Roper state is extracted with valence overlap fermions on a $2+1$-flavor domain-wall fermion lattice (spacing $a = 0.114$ fm and $m_π = 330$ MeV) using both the Sequential Empirical Bayes (SEB) method and the variational method. The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation. Similar calculations carried out for an anisotropic clover lattice with similar parameters find the Roper $\approx 280$ MeV higher than that of the overlap fermion. The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin $Z$-diagram in the isovector scalar meson ($a_0$) correlator in the quenched approximation. Comparing the $a_0$ correlators for clover and overlap fermions, at a pion mass of 290 MeV, we find that the spectral weight of the ghost state with clover fermions is smaller than that of the overlap at $a = 0.12$ fm and $0.09$ fm, whereas the whole $a_0$ correlators of clover and overlap at $a = 0.06$ fm coincide within errors. This suggests that chiral symmetry is restored for clover at $a \le 0.06$ fm and that the Roper should come down at and below this $a$. We conclude that this work supports a resolution of the "Roper puzzle" due to $Z$-graph type chiral dynamics. This entails coupling to higher components in the Fock space (e.g. $Nπ$, $Nππ$ states) to induce the effective flavor-spin interaction between quarks as prescribed in the chiral quark model, resulting in the parity-reversal pattern as observed in the experimental excited states of $N, Δ$ and $Λ$.

hep-ph↗

arXiv2020

Quantum algorithms for disordered physics

We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body disordered systems in the large volume limit; in particular, Anderson localization. The method requires a number of (error corrected) qubits proportional to the logarithm of the volume of the system, and each time evolution step requires a number of gates polylogarithmic in the volume. We simulate the method to observe the metal-insulator transition on a three-dimensional lattice. Additionally, we demonstrate the algorithm on a one-dimensional lattice, using physical quantum processors.

cond-mat.dis-nn↗

arXiv2019

Possible New Phase of Thermal QCD

Using lattice simulations, we show that there is a phase of thermal QCD, where the spectral density $ρ(λ)$ of Dirac operator changes as $1/λ$ for the infrared eigenvalues $λ<T$. This behavior persists over the entire low energy band we can resolve accurately, over three orders of magnitude on our largest volumes. We propose that in this "IR phase", the well-known non-interacting scale invariance at very short distances (UV, $λ\rightarrow \infty$, asymptotic freedom), coexists with very different interacting type of scale invariance at long distances (IR, $λ<T$). Such dynamics may be responsible for the unusual fluidity properties of the medium observed at RHIC and LHC. We point out its connection to the physics of Banks-Zaks fixed point, leading to the possibility of massless glueballs in the fluid. Our results lead to the classification of thermal QCD phases in terms of IR scale invariance. The ensuing picture naturally subsumes the standard chiral crossover feature at $"\!T_c\!" \,\approx 155$ MeV. Its crucial new aspect is the existence of temperature $T_{IR}$ (200 MeV $< T_{IR} < $ 250 MeV) marking the onset of IR phase and possibly a true phase transition.

hep-lat↗

arXiv2019

Finitely Supported Sets Containing Infinite Uniformly Supported Subsets

The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements named atoms. In this paper we study the properties of finitely supported sets that contain infinite uniformly supported subsets, as well as the properties of finitely supported sets that do not contain infinite uniformly supported subsets. For classical atomic sets, we study whether they contain or not infinite uniformly supported subsets.

math.LO↗

arXiv2019

A cross-channel study of pion scattering from lattice QCD

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 MeV and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain $m_πa_0^{I=0}=0.2132(9)$, and $m_πa_0^{I=2}=0.0433(2)$ as well as $m_σ=443(3)-i221(6)$ MeV and $m_ρ=724(4)-i67(1)$ MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well.

hep-lat↗

arXiv2019

Structure Factors of The Unitary Gas Under Supernova Conditions

We compute with lattice field theory the vector and axial static structure factors of the unitary gas for arbitrary temperature above the superfluid transition and for fugacities 0.1 < z < 1.0. Using the lattice formulation, we calculate beyond the validity of the virial expansion, a commonly used technique in many-body physics. We find qualitative differences in the behavior of the structure factors at high fugacity compared to the predictions of the virial expansion. Due to the large scattering length of neutrons, we expect the unitary gas structure factors to approximate the structure factors of hot neutron gases, and we therefore expect our calculations to be useful in supernova simulations, where neutron gas structure factors are needed to compute in-medium neutrino-neutron scattering rates.

nucl-th↗

arXiv2019

Gluon Field Digitization for Quantum Computers

Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that uses the minimum amount of qubits are desirable. We present a practical scheme for digitizing $SU(3)$ gauge theories via its discrete subgroup $S(1080)$. The $S(1080)$ standard Wilson action cannot be used since a phase transition occurs as the coupling is decreased, well before the scaling regime. We proposed a modified action that allows simulations in the scaling window and carry out classical Monte Carlo calculations down to lattice spacings of order $a\approx 0.08$ fm. We compute a set of observables with sub-percent precision at multiple lattice spacings and show that the continuum extrapolated value agrees with the full $SU(3)$ results. This suggests that this digitization scheme provides sufficient precision for NISQ-era QCD simulations.

hep-lat↗

arXiv2019

Sigma models on quantum computers

We formulate a discretization of sigma models suitable for simulation by quantum computers. Space is substituted by a lattice, as usually done in lattice field theory, while the target space (a sphere) is replaced by the "fuzzy sphere", a construction well known from non-commutative geometry. Contrary to more naive discretizations of the sphere, in this construction the exact $O(3)$ symmetry is maintained, which suggests that the discretized model is in the same universality class as the continuum model. That would allow for continuum results to be obtained for very rough discretizations of the target space as long as the space discretization is made fine enough. The cost of performing time-evolution, measured as the number of CNOT operations necessary, is $12 L T/Δt $, where $L$ is the number of spatial sites, $T$ the maximum time extent and $Δt$ the time spacing.

hep-lat↗

arXiv2019

Infinities within Finitely Supported Structures

The theory of finitely supported algebraic structures is related to Pitts theory of nominal sets (by equipping finitely supported sets with finitely supported internal algebraic laws). It represents a reformulation of Zermelo Fraenkel set theory obtained by requiring every set theoretical construction to be finitely supported according to a certain action of a group of permutations of some basic elements named atoms. Its main purpose is to let us characterize infinite algebraic structures, defined involving atoms, only by analyzing their finite supports. The first goal of this paper is to define and study different kinds of infinities and the notion of `cardinality' in the framework of finitely supported structures. We present several properties of infinite cardinalities. Some of these properties are extended from the non-atomic Zermelo Fraenkel set theory into the world of atomic objects with finite support, while other properties are specific to finitely supported structures. We also compare alternative definitions of `infinite finitely supported set', and we finally provide a characterization of finitely supported countable sets.

math.LO↗

arXiv2019

Solution of the sign problem in the Potts model at fixed fermion number

We consider the heavy-dense limit of QCD at finite fermion density in the canonical formulation and approximate it by a 3-state Potts model. In the strong coupling limit, the model is free of the sign problem. Away from the strong coupling, the sign problem is solved by employing a cluster algorithm which allows to average each cluster over the Z(3) sectors. Improved estimators for physical quantities can be constructed by taking into account the triality of the clusters, that is, their transformation properties with respect to Z(3) transformations.

hep-lat↗

arXiv2018

Lattice Calculation of Nucleon Isovector Axial Charge with Improved Currents

We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling $g^3_A$ with overlap valence on $2+1$-flavor Domain Wall Fermion sea. Using the equality of $g^3_A$ from the spatial and temporal components of the axial-vector current as a normalization condition, we find that $g_A^3$ is increased by a few percent towards the experimental value. The excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges $g_A^{3}(24I)=1.22(4)$ and $g_A^{3}(32I)=1.21(3)$ are obtained on a $24^3\times 64$ lattice at pion mass of 330 MeV and a $32^3\times 64$ lattice at pion mass 300 MeV are increased by $3.4\%$ and $1.7\%$ from their unimproved values, respectively. We have also used clover fermion on the same DWF configurations and find the same behavior for the local axial charge as that of the overlap fermion.

hep-lat↗

arXiv2018

Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds

We present Monte Carlo calculations of the thermodynamics of the (2+1) dimensional Thirring model at finite density. We bypass the sign problem by deforming the domain of integration of the path integral into complex space in such a way as to maximize the average sign within a parameterized family of manifolds. We present results for lattice sizes up to $10^3$ and we find that at high densities and/or temperatures the chiral condensate is abruptly reduced.

hep-lat↗

arXiv2018

Finite Density $QED_{1+1}$ Near Lefschetz Thimbles

One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles -- or somewhat close to them -- the sign problem is alleviated. Gauge theories lack a well-defined thimble decomposition, and therefore it is unclear how to carry out a generalized thimble method. In this paper we discuss some of the conceptual issues involved by applying this method to $QED_{1+1}$ at finite density, showing that the generalized thimble method yields correct results with less computational effort than standard methods.

hep-lat↗

arXiv2018

Anatomy of the $ρ$ resonance from lattice QCD at the physical point

We propose a strategy to access the $q\bar{q}$ component of the $ρ$ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the $q\bar{q}$ component is derived at different valence quark masses, and shows a linear dependence on $m_π^2$. The slope is determined to be $c_1=0.505(3)\,{\rm GeV}^{-1}$, from which the valence $πρ$ sigma term is extracted to be $σ_{πρ}^{(\rm val)}=9.82(6)$ MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the $q\bar{q}$ component is interpolated to be $m_ρ=775.9\pm 6.0\pm 1.8$ MeV, which is close to the $ρ$ resonance mass. We also obtain the leptonic decay constant of the $q\bar{q}$ component to be $f_{ρ^-}=208.5\pm 5.5\pm 0.9$ MeV, which can be compared with the experimental value $f_ρ^{\rm exp}\approx 221$ MeV through the relation $f_ρ^{\rm exp}=\sqrt{Z_ρ}f_{ρ^\pm} $ with $Z_ρ\approx 1.13$ being the on-shell wavefunction renormalization of $ρ$ owing to the $ρ-π$ interaction. We emphasize that $m_ρ$ and $f_ρ$ of the $q\bar{q}$ component, which are obtained for the first time from QCD, can be taken as the input parameters of $ρ$ in effective field theory studies where $ρ$ acts as a fundamental degree of freedom.

hep-ph↗

arXiv2018

Spin Polarized Non-Relativistic Fermions in 1+1 Dimensions

We study by Monte Carlo methods the thermodynamics of a spin polarized gas of non-relativistic fermions in 1+1 dimensions. The main result of this work is that our action suffers no significant sign problem for any spin polarization in the region relevant for dilute degenerate fermi gases. This lack of sign problem allows us to study attractive spin polarized fermions non-perturbatively at spin polarizations not previously explored. For some parameters values we verify results previously obtained by methods which include an uncontrolled step like complex Langevin and/or analytical continuation from imaginary chemical potential. For others, larger values of the polarization, we deviate from these previous results.

hep-lat↗

arXiv2018

Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds

We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign (therefore reducing the sign problem) within a parameterized family of manifolds. We presents results for the $1+1$ dimensional Thirring model with Wilson fermions on lattice sizes up to $40\times 10$. This method reaches higher $μ$ then previous techniques while substantially decreasing the computational time required.

hep-lat↗

arXiv2018

Extraction of isoscalar $ππ$ phase-shifts from lattice QCD

We conduct a two-flavor ($N_f=2$) lattice QCD calculation of the elastic phase-shifts for pion-pion scattering in the scalar, isoscalar channel (the $σ$-meson). The calculation is performed for two quark masses corresponding to a pion mass of $315\text{ MeV}$ and $227\text{ MeV}$. The $σ$-meson parameters are extracted using various parametrizations of the scattering amplitude. The results obtained from a chiral unitary parametrization are extrapolated to the physical point and read $M_σ= (440^{+10}_{-16}(50) - i\,240(20)(25))\text{ MeV}$, where the uncertainties in the parentheses denote the stochastic and systematic ones. The behavior of the $σ$-meson parameters with increasing pion mass is discussed as well.

hep-lat↗

arXiv2017

Scattering phaseshift formulas for mesons and baryons in elongated boxes

We derive Lüscher phaseshift formulas for two-particle states in boxes elongated in one of the dimensions. Such boxes offer a cost-effective way of varying the relative momentum of the particles. Boosted states in the elongated direction, which allow wider access to energies, are also considered. The formulas for the various scenarios (moving and zero-momentum states in cubic and elongated boxes) are compared and relations between them are clarified. The results are applicable to a wide set of meson-meson and meson-baryon elastic scattering processes, with the two-particle system having equal or unequal masses.

hep-lat↗