Lattice Renormalization Research Articles

Perturbative renormalization of the supercurrent operator in lattice N=1 supersymmetric Yang-Mills theory

In this work we perform a perturbative study of the Noether supercurrent operator in the context of supersymmetric $\mathcal{N}=1$ Yang-Mills theory on the lattice. The supercurrent mixes with several other operators, some of which are not gauge invariant, having the same quantum numbers. We determine, to one-loop order, the renormalization and all corresponding mixing coefficients by computing the relevant Green's functions of each one of the mixing operators with external elementary fields. Our calculations are performed both in dimensional and lattice regularization. From the first regularization we obtain the $\overline{\mathrm{MS}}$-renormalized Green's functions; comparison of the latter with the corresponding Green's functions in the lattice regularization leads to the extraction of the lattice renormalization factors and mixing coefficients in the $\overline{\mathrm{MS}}$ scheme. The lattice calculations are performed to lowest order in the lattice spacing, using Wilson gluons and clover improved gluinos. The lattice results can be used in nonperturbative studies of supersymmetric Ward identities.

One-loop structure of parton distribution for the gluon condensate and \u201czero modes\u201d

We present results for one-loop corrections to the recently introduced “gluon condensate” PDF F(x). In particular, we give expression for the gg-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No “zero mode” δ(x) terms were found for the twist-4 gluon PDF F(x). However a q2δ(x) term was found for the ξ = 0 GPD F(x, q2) at nonzero momentum transfer q. Overall, our results do not agree with the original attempt of one-loop calculations of F(x) for gluon states, which sets alarm warning for calculations that use matrix elements with virtual external gluons and for lattice renormalization procedures based on their results.

Lattice renormalization of quantum simulations

With advances in quantum computing, new opportunities arise to tackle challenging calculations in quantum field theory. We show that trotterized time-evolution operators can be related by analytic continuation to the Euclidean transfer matrix on an anisotropic lattice. In turn, trotterization entails renormalization of the temporal and spatial lattice spacings. Based on the tools of Euclidean lattice field theory, we propose two schemes to determine Minkowski lattice spacings, using Euclidean data and thereby overcoming the demands on quantum resources for scale setting. In addition, we advocate using a fixed-anisotropy approach to the continuum to reduce both circuit depth and number of independent simulations. We demonstrate these methods with Qiskit noiseless simulators for a $2+1$D discrete non-Abelian $D_4$ gauge theory with two spatial plaquettes.

Renormalization and mixing of staple-shaped Wilson line operators on the lattice revisited

Transverse-momentum-dependent parton distribution functions and wave functions (TMDPDFs/TMDWFs) can be extracted from lattice calculations of appropriate Euclidean matrix elements of staple-shaped Wilson line operators. We investigate the mixing pattern of such operators under lattice renormalization using symmetry considerations. We perform an analysis for operators with all Dirac structures, which reveals mixings that are not present in one-loop lattice perturbation theory calculations. We also present the relevant one-loop matching in a renormalization scheme that does not introduce extra non-perturbative effects at large distances, both for the TMDPDFs and for the TMDWFs. Our results have the potential to greatly facilitate numerical calculations of TMDPDFs and TMDWFs on the lattice.

Understanding the thermal evolution of defects in carbon-implanted ZnO single crystal

Defects and impurities play a major role in controlling the electrical and optical properties of semiconductor materials. Herein, hydrothermally grown ZnO single crystals have been implanted with carbon (C) dopants at room temperature and then annealed in argon atmosphere at various temperatures between 400 and 800 °C. The thermal evolution of C-related defects and their effects on the structural, optical and electrical properties of ZnO single crystals were systematically characterized and discussed. The results show ion implantation induces serious lattice disorder, and post-implantation annealing could promote the lattice renormalization, accompanied by an increase in crystal quality and average visible transmittance. Furthermore, it is found that the diffusion of octahedral carbon interstitial (Ci) along parallel to c-axis facilitates the growth of carbon sp2 clusters due to its low migration barrier during annealing, which energetically contribute to the decrease of the resistivity. Meanwhile, abundant Ci will be able to enter into VZn to form CZn or combine with lattice O to form (CO)O donor defects upon annealing, dominating the increase of electron carrier concentration and enhancing the anomalous Raman mode at 510-525 cm−1. These findings strengthen the fundamental understanding of the donor behavior of C impurities in ZnO.

Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions

Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a non-analytic cusp in the wave function. Here we develop a transcorrelated approach where the cusp is treated exactly and folded into the many-body Hamiltonian with a similarity transformation that removes the leading order singularity. The resulting transcorrelated Hamiltonian is not hermitian but can be treated numerically with a standard projection approach. The smoothness of the wave function improves by at least one order and thus the convergence rate for the ground state energy improves. By numerical investigation of a one-dimensional gas of spin-$\frac{1}{2}$ fermions we find the error in the transcorrelated energy to scale as $M^{-3}$ with a single-particle basis of $M$ plane waves compared to $M^{-1}$ for the expansion of the original Hamiltonian and $M^{-2}$ using conventional lattice renormalization.

A local and scalable lattice renormalization method for ballistic quantum computation

A recent proposal has shown that it is possible to perform linear-optics quantum computation using a ballistic generation of the lattice. Yet, due to the probabilistic generation of its cluster state, it is not possible to use the fault-tolerant Raussendorf lattice, which requires a lower failure rate during the entanglement-generation process. Previous work in this area showed proof-of-principle linear-optics quantum computation, while this paper presents an approach to it which is more practical, satisfying several key constraints. We develop a classical measurement scheme that purifies a large faulty lattice to a smaller lattice with entanglement faults below threshold. A single application of this method can reduce the entanglement error rate to 7% for an input failure rate of 25%. Thus, we can show that it is possible to achieve fault tolerance for ballistic methods.

Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models

Renormalization group based on the Migdal–Kadanoff bond removal approach is often considered a simple and valuable tool to understand the critical behavior of complicated statistical mechanical models. In presence of quenched disorder, however, predictions obtained with the Migdal–Kadanoff bond removal approach quite often fail to quantitatively and qualitatively reproduce critical properties obtained in the mean-field approximation or by numerical simulations in finite dimensions. In an attempt to overcome this limitation we analyze the behavior of Ising and Blume–Emery–Griffiths models on more structured hierarchical lattices. We find that, apart from some exceptions, the failure is not limited to Midgal–Kadanoff cells but originates right from the hierarchization of Bravais lattices on small cells, and shows up also when in-cell loops are considered.

Doping dependence of the electron–phonon and electron–spin fluctuation interactions in the high-Tc superconductor Bi2Sr2CaCu2O8+δ

Using ultrafast optical techniques, we detect two types of bosons strongly coupled to electrons in the family of Bi2Sr2CaCu2O8+δ (Bi-2212) from the underdoped to overdoped regimes. The different doping dependences of the electron–boson coupling strengths enable us to identify them as phonons and spin fluctuations: electron–phonon coupling (λe−ph) peaks at optimal doping, while electron–spin fluctuation coupling (λe−sf) decreases monotonically with doping. This observation is consistent with two facts: (i) superconductivity is in close proximity with antiferromagnetism at low dopings and (ii) a pronounced lattice renormalization effect at larger dopings.

Noise and ultraviolet divergences in the dynamics of the chiral condensate in QCD

The time evolution of the matter produced in high energy heavy-ion collisions seems to be well described by relativistic viscous hydrodynamics. In addition to the hydrodynamic degrees of freedom related to energy-momentum conservation, degrees of freedom associated with order parameters of broken continuous symmetries must be considered because they are all coupled to each other. Of particular interest is the coupling of degrees of freedom associated with the chiral symmetry of QCD. Quantum and thermal fluctuations of the chiral fields act as noise sources in the classical equations of motion, turning them into stochastic differential equations in the form of Ginzburg-Landau-Langevin (GLL) equations. Analytic solutions of GLL equations are attainable only in very special circumstances and extensive numerical simulations are necessary, usually by discretizing the equations on a spatial lattice. However, a not much appreciated issue in the numerical simulations of GLL equations is that ultraviolet divergences in the form of lattice-spacing dependence plague the solutions. The divergences are related to the well-known Rayleigh-Jeans catastrophe in classical field theory. In the present communication we present a systematic lattice renormalization method to control the catastrophe. We discuss the implementation of the method for a GLL equation derived in the context of a model for the QCD chiral phase transition and consider the nonequilibrium evolution of the chiral condensate during the hydrodynamic flow of the quark-gluon plasma.

Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization

We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg–Landau–Langevin and the subtleties related to the multiplicative noise are investigated.

Lattice renormalization ofO(a)improved heavy-light operators: An addendum

The analytical expressions and the numerical values of the renormalization constants of dimension 3 static-light currents are given at one-loop order of perturbation theory in the framework of heavy quark effective theory and with an improved gauge action: the static quark is described by the HYP-smeared action and the light quark is of Wilson kind. This completes a work started a few years ago and is actually an intermediate step in the measurement of the decay constants ${f}_{B}$ and ${f}_{{B}_{s}}$ by the European Twisted Mass Collaboration (arXiv:1107.1441).

Erratum to: “Lattice renormalization of the static quark derivative operator” [Phys. Lett. B 632 (2006) 319

Erratum to: “Lattice renormalization of the static quark derivative operator” [Phys. Lett. B 632 (2006) 319

Lattice renormalization of the static quark derivative operator

We give the analytical expressions and the numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur–Wise form factors τ1/2(1) and τ3/2(1). These corrections induce an enhancement of renormalized quantities if an hypercubic blocking procedure is used for the Wilson line, while there is a reduction without such a procedure.

Domain wall fermion calculation of nucleon gA/ gV

We present a preliminary domain-wall fermion lattice-QCD calculation of isovector vector and axial charges, g V and g A , of the nucleon. Since the lattice renormalizations, Z V and Z A , of the currents are identical with DWF, the lattice ratio ( g A / g V ) lattice directly yields the continuum value. Indeed Z V determined from the matrix element of the vector current agrees closely with Z A from a non-perturbative renormalization study of quark bilinears. We also obtain spin related quantities Δ q/ g V and δ q/ g V .

RI/MOM renormalization window and Goldstone pole contamination

We perform a comparative study of the ratio of lattice (Wilson fermion) renormalization constants Z P / Z S , obtained non-perturbatively from the RI/MOM renormalization conditions and from Ward Identities of on- and off-shell Green's functions. The off-shell Ward Identity used in this work relies on correlation functions with non-degenerate quark masses. We find that, due to discretization effects, there is a 10–15% discrepancy between the two Ward Identity determinations at current bare couplings ( β values). The RI/MOM result is in the same range and has a similar systematic error of 10–15%. Thus, contrary to a previous claim, the contamination of the RI/MOM result from the presence of a Goldstone pole at renormalization scales μ∼ a −1 is subdominant, compared to finite cutoff effects.

Resummation of cactus diagrams in lattice QCD, to all orders

We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant tadpole-like diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, e.g. the lattice renormalization of some two-fermion operators, this expansion yields results remarkably close to corresponding nonperturbative estimates. We consider in our study both the Wilson and the clover action for fermions.

One loop renormalization for the axial Ward-Takahashi identity in domain-wall QCD

We calculate the one loop correction to the axial Ward-Takahashi identity given by Furman and Shamir in domain-wall QCD. It is shown perturbatively that the renormalized axial Ward-Takahashi identity is satisfied without fine-tuning and the ``conserved'' axial vector current receives no renormalization, giving ${Z}_{A}=1$. This fact will simplify the calculation of the pion decay constant in numerical simulations since the decay constant defined by this current needs no lattice renormalization factor.

Resummation of cactus diagrams in the clover improved lattice formulation of QCD

We extend to the clover improved lattice formulation of QCD the resummation of cactus diagrams, i.e. a certain class of tadpole-like gauge invariant diagrams. Cactus resummation yields an improved perturbative expansion. We apply it to the lattice renormalization of some two-fermion operators improving their one-loop perturbative estimates.

Lattice renormalization of quark operators

We have technically improved the non-perturbative renormalization method, proposed by Martinelli et al., by using quark momentum sources and sinks. Composite two-fermion operators up to three derivatives have been measured for Wilson fermions and Sheikholeslami-Wohlert improved fermions in the quenched approximation. The calculations are performed in the Landau gauge on 16 332 lattices at β = 6.0 for 3 κ values in each case. The improved sources greatly decrease the statistical noise. We extract and discuss here renormalization factors for local operators and moments of the structure functions for Wilson fermions.