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## Full-Text Articles in Physics

Detecting Supercounterfluidity By Ramsey Spectroscopy, A Kuklov, Nikolai Prokof'ev, Boris Svistunov

#### Detecting Supercounterfluidity By Ramsey Spectroscopy, A Kuklov, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

A two-component system of ultracold atoms in an optical lattice at integer total filling factor and strong enough onsite repulsion can form a supercounterfluid (SCF) phase, which can be viewed as the Bose-Einstein condensate (BEC) of pairs formed by particles of one sort and holes of another sort. In this quasimolecular BEC, no single-component BEC exists, and the net atomic flow is prohibited. We show that, in the case of the interconvertible species (like hyperfine states of Rb), the corresponding order parameter can be detected by spatially selective Ramsey spectroscopy. The method can be used, in particular, for revealing a ...

Superfluid Interfaces In Quantum Solids, E Bourovski, E. Kozik, A Kuklov, Nikolai Prokof'ev, Boris Svistunov

#### Superfluid Interfaces In Quantum Solids, E Bourovski, E. Kozik, A Kuklov, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

One scenario for the nonclassical moment of inertia of solid 4He discovered by Kim and Chan [Nature (London) 427, 225 (2004)] is the superfluidity of microcrystallite interfaces. On the basis of the most simple model of a quantum crystal—the checkerboard lattice solid—we show that the superfluidity of interfaces between solid domains can exist in a wide range of parameters. At strong enough interparticle interaction, a superfluid interface becomes an insulator via a quantum phase transition. Under the conditions of particle-hole symmetry, the transition is of the standard U(1) universality class in 3D, while in 2D the onset ...

The 17/5 Spectrum Of The Kelvin-Wave Cascade, E Kozik, Boris Svistunov

#### The 17/5 Spectrum Of The Kelvin-Wave Cascade, E Kozik, Boris Svistunov

*Boris Svistunov*

Direct numeric simulation of the Biot-Savart equation readily resolves the 17/5 spectrum of the Kelvin-wave cascade from the 11/3 spectrum of the non-local (in the wavenumber space) cascade scenario by L’vov and Nazarenko. This result is a clear-cut visualisation of the unphysical nature of the 11/3 solution, which was established earlier on the grounds of symmetry.

Superfluid-Insulator Transition In Commensurate Disordered Bosonic Systems: Large-Scale Worm Algorithm Simulations, Nikolai Prokof'ev, Boris Svistunov

#### Superfluid-Insulator Transition In Commensurate Disordered Bosonic Systems: Large-Scale Worm Algorithm Simulations, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We report results of large-scale Monte Carlo simulations of superfluid-insulator transitions in disordered commensurate 2D bosonic systems. In the off-diagonal disorder case, we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is z=1.5(2). In the diagonal-disorder case, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in crossover to the generic universality class (apparently with z=2). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of ...

Superfluid-Insulator And Roughening Transitions In Domain Walls, S Söyler, Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov

#### Superfluid-Insulator And Roughening Transitions In Domain Walls, S Söyler, Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We have performed quantum Monte Carlo simulations to investigate the superfluid behavior of one- and two-dimensional interfaces separating checkerboard solid domains. The system is described by the hard-core Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with Burovski et al. [Phys. Rev. Lett. 94, 165301 (2005)] we find that (i) the interface remains superfluid in a wide range of interaction strength before it undergoes a superfluid-insulator transition; (ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is accompanied by the roughening transition, driven by proliferation of charge-1∕2 quasiparticles; (iii) in two dimensions, the transition belongs to the ...

Exact, Complete, And Universal Continuous-Time Worldline Monte Carlo Approach To The Statistics Of Discrete Quantum Systems, Nikolai Prokof'ev, Boris Svistunov, Tupitsyn

#### Exact, Complete, And Universal Continuous-Time Worldline Monte Carlo Approach To The Statistics Of Discrete Quantum Systems, Nikolai Prokof'ev, Boris Svistunov, Tupitsyn

*Boris Svistunov*

We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be formulated directly in continuous time, rendering the scheme exact. For an arbitrary system with discrete Hilbert space, none of the configuration update procedures contain small parameters. We find that the most effective update strategy involves the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green’s function. Being based on local updates only, our method nevertheless allows one to work with the grand canonical ensemble and nonzero winding numbers, and to calculate any dynamical ...

Superfluidity Of Grain Boundaries In Solid 4he, L Pollet, M Boninsegni, A Kuklov, Nikolai Prokof'ev, Boris Svistunov, M Troyer

#### Superfluidity Of Grain Boundaries In Solid 4he, L Pollet, M Boninsegni, A Kuklov, Nikolai Prokof'ev, Boris Svistunov, M Troyer

*Boris Svistunov*

By large-scale quantum Monte Carlo simulations we show that grain boundaries in 4He crystals are generically superfluid at low temperature, with a transition temperature of the order of ∼0.5 K at the melting pressure; nonsuperfluid grain boundaries are found only for special orientations of the grains. We also find that close vicinity to the melting line is not a necessary condition for superfluid grain boundaries, and a grain boundary in direct contact with the superfluid liquid at the melting curve is found to be mechanically stable and the grain-boundary superfluidity observed by Sasaki et al. [Science 313, 1098 (2006 ...

Geometric Symmetries In Superfluid Vortex Dynamics, E Kozik, Boris Svistunov

#### Geometric Symmetries In Superfluid Vortex Dynamics, E Kozik, Boris Svistunov

*Boris Svistunov*

Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether’s constants of motion, which—apart from their rather specific expressions in terms of w(z)—are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the ...

Phase Diagram And Thermodynamics Of The Three-Dimensional Bose-Hubbard Model, B Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov

#### Phase Diagram And Thermodynamics Of The Three-Dimensional Bose-Hubbard Model, B Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than has been done in the past. In particular, the position of the critical point at filling factor n=1 is found to be at (U∕t)c=29.34(2), and the insulating gap Δ is measured with accuracy of a few percent of the hopping amplitude t. We obtain the effective mass of particle and hole excitations in the insulating state—with explicit demonstration of the emerging particle-hole symmetry and relativistic ...

Kelvin-Wave Cascade And Decay Of Superfluid Turbulence, E Kozik, Boris Svistunov

#### Kelvin-Wave Cascade And Decay Of Superfluid Turbulence, E Kozik, Boris Svistunov

*Boris Svistunov*

Kelvin waves (kelvons), the distortion waves on vortex lines, play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that nontrivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; a corresponding kinetic equation is derived. We prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.

Fermi-Polaron Problem: Diagrammatic Monte Carlo Method For Divergent Sign-Alternating Series, Nikolai Prokof'ev, Boris Svistunov

#### Fermi-Polaron Problem: Diagrammatic Monte Carlo Method For Divergent Sign-Alternating Series, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We use the diagrammatic Monte Carlo approach to solve the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles. Our solution is important for understanding the phase diagram and properties of the crossover from the BCS regime to the Bose-Einstein condensate in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem-tolerant method for exact numerical solution of polaron-type models. This is a characteristic example of how Monte Carlo methods can be used to simulate divergent sign-alternating diagrammatic series.

Scanning Superfluid-Turbulence Cascade By Its Low-Temperature Cutoff, E Kozik, Boris Svistunov

#### Scanning Superfluid-Turbulence Cascade By Its Low-Temperature Cutoff, E Kozik, Boris Svistunov

*Boris Svistunov*

On the basis of a recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, L, controlled by the frictional coefficient, α(T)≪1, responsible for the cutoff. The curve ln L(lnα) is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wave number regions. Excellent agreement with a recent experiment by Walmsley et al. [Phys. Rev. Lett. 99, 265302 (2007)]—in which L(T) has been measured down to T ...

The Beliaev Technique For A Weakly Interacting Bose Gas, B Capogrosso-Sansone, S Giorgini, S Pilati, L. Pollet, N Prokof'ev, B Svistunov, M Troyer

#### The Beliaev Technique For A Weakly Interacting Bose Gas, B Capogrosso-Sansone, S Giorgini, S Pilati, L. Pollet, N Prokof'ev, B Svistunov, M Troyer

*Boris Svistunov*

Aiming at simplicity of explicit equations and, at the same time, controllable accuracy of the theory, we present our results for all the thermodynamic quantities and correlation functions for a weakly interacting Bose gas at short-to-intermediate distances obtained within an improved version of Beliaev's diagrammatic technique. With a controllably small (but essentially finite) Bogoliubov's symmetry-breaking term, Beliaev's diagrammatic technique becomes regular in the infrared limit. Up to higher-order terms (for which we present parametric order-of-magnitude estimates), the partition function and entropy of the system formally correspond to those of a non-interacting bosonic (pseudo-)Hamiltonian with a temperature-dependent ...

Worm Algorithm For Continuous-Space Path Integral Monte Carlo Simulations, M Boninsegni, Nikolai Prokof'ev, Boris Svistunov

#### Worm Algorithm For Continuous-Space Path Integral Monte Carlo Simulations, M Boninsegni, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC simulations. As an illustrative application of the method, we simulate the superfluid transition of 4He in two dimensions.

Comment On "Symmetries And Interaction Coefficients Of Kelvin Waves" [Arxiv:1005.4575] By Lebedev And L'Vov, E Kozik, Boris Svistunov

#### Comment On "Symmetries And Interaction Coefficients Of Kelvin Waves" [Arxiv:1005.4575] By Lebedev And L'Vov, E Kozik, Boris Svistunov

*Boris Svistunov*

Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether’s constants of motion, which—apart from their rather specific expressions in terms of w(z)—are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the ...

Truncated-Determinant Diagrammatic Monte Carlo For Fermions With Contact Interaction, E Bourovski, Nikolai Prokof'ev, Boris Svistunov

#### Truncated-Determinant Diagrammatic Monte Carlo For Fermions With Contact Interaction, E Bourovski, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

For some models of interacting fermions the known solution to the notorious sign problem in Monte Carlo (MC) simulations is to work with macroscopic fermionic determinants; the price, however, is a macroscopic scaling of the numerical effort spent on elementary local updates. We find that the ratio of two macroscopic determinants can be found with any desired accuracy by considering truncated (local in space and time) matices. In this respect, MC for interacting fermionic systems becomes similar to that for the sign-problem-free bosonic systems with system-size independent update cost. We demonstrate the utility of the truncated-determinant method by simulating the ...

Sign-Alternating Interaction Mediated By Strongly Correlated Lattice Bosons, S Söyler, B Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov

#### Sign-Alternating Interaction Mediated By Strongly Correlated Lattice Bosons, S Söyler, B Capogrosso-Sansone, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We reveal a generic mechanism of generating sign-alternating intersite interactions mediated by strongly correlated lattice bosons. The ground-state phase diagram of the two-component hard-core Bose–Hubbard model on a square lattice at half-integer filling factor for each component, obtained by worm algorithm Monte Carlo simulations, is strongly modified by these interactions and features the solid+superfluid (SF) phase for strong asymmetry between the hopping amplitudes. The new phase is a direct consequence of the effective nearest-neighbor repulsion between 'heavy' atoms mediated by the 'light' SF component. Due to their sign-alternating character, mediated interactions lead to a rich variety of yet ...

Worm Algorithms For Classical Statistical Models, Nikolai Prokof'ev, Boris Svistunov

#### Worm Algorithms For Classical Statistical Models, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We show that high-temperature expansions provide a basis for the novel approach to efficient Monte Carlo simulations. “Worm” algorithms utilize the idea of updating closed-path configurations (produced by high-temperature expansions) through the motion of end points of a disconnected path. An amazing result is that local, Metropolis-type schemes using this approach appear to have dynamical critical exponents close to zero (i.e., their efficiency is comparable to the best cluster methods) as proved by finite-size scaling of the autocorrelation time for various universality classes.

Kolmogorov And Kelvin-Wave Cascades Of Superfluid Turbulence At T=0: What Lies Between, E Kozik, Boris Svistunov

#### Kolmogorov And Kelvin-Wave Cascades Of Superfluid Turbulence At T=0: What Lies Between, E Kozik, Boris Svistunov

*Boris Svistunov*

As long as vorticity quantization remains irrelevant for long-wave physics, superfluid turbulence supports a regime macroscopically identical to the Kolmogorov cascade of a normal liquid. At high enough wave numbers, the energy flux in wavelength space is carried by individual Kelvin-wave cascades on separate vortex lines. We analyze the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, revealing a chain of three distinct intermediate cascades supported by local-induction motion of the vortex lines and distinguished by specific reconnection mechanisms. The most prominent qualitative feature predicted is unavoidable production of vortex rings of a characteristic size.

Local Stress And Superfluid Properties Of Solid 4he, L Pollet, M Boninsegni, A Kuklov, Nikolai Prokof'ev, Boris Svistunov, M Troyer

#### Local Stress And Superfluid Properties Of Solid 4he, L Pollet, M Boninsegni, A Kuklov, Nikolai Prokof'ev, Boris Svistunov, M Troyer

*Boris Svistunov*

We provide a semiquantitative tool, derived from first-principles simulations, for answering the question of whether certain types of defects in solid 4He support mass superflow. Although ideal crystals of 4He are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) can turn superfluid.

Single-Hole Spectral Function And Spin-Charge Separation In The T-J Model, A Mishchenko, Nikolai Prokof'ev, Boris Svistunov

#### Single-Hole Spectral Function And Spin-Charge Separation In The T-J Model, A Mishchenko, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

Worm algorithm Monte Carlo simulations of the hole Green function with subsequent spectral analysis were performed for 0.1<~J/t<~0.4 on lattices with up to L×L=32×32 sites at a temperature as low as T=J/40, and present, apparently, the hole spectral function in the thermodynamic limit. Spectral analysis reveals a δ-function-sharp quasiparticle peak at the lower edge of the spectrum that is incompatible with the power-law singularity and thus rules out the possibility of spin-charge separation in this parameter range. Spectral continuum features two peaks separated by a gap ∼4÷5 t.

The Fermi–Hubbard Model At Unitarity, F Bourovski, Nikolai Prokof'ev, Boris Svistunov, M Troyer

#### The Fermi–Hubbard Model At Unitarity, F Bourovski, Nikolai Prokof'ev, Boris Svistunov, M Troyer

*Boris Svistunov*

We simulate the dilute attractive Fermi–Hubbard model in the unitarity regime using a diagrammatic determinant Monte Carlo (MC) algorithm with worm-type updates. We obtain the dependence of the critical temperature on the filling factor ν and, by extrapolating to ν → 0, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy: Tc/εF = 0.152(7). We also determine the thermodynamic functions and show how the MC results can be used for accurate thermometry of a trapped unitary gas.

Phase Diagram Of The Disordered Bose-Hubbard Model, V Gurarie, L Pollet, Nikolai Prokof'ev, Boris Svistunov, M Troyer

#### Phase Diagram Of The Disordered Bose-Hubbard Model, V Gurarie, L Pollet, Nikolai Prokof'ev, Boris Svistunov, M Troyer

*Boris Svistunov*

We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling which has been controversial for many years. The theorem of inclusions, proven by Pollet et al. [Phys. Rev. Lett. 103, 140402 (2009)] states that the Bose-glass phase always intervenes between the Mott insulating and superfluid phases. Here, we note that assumptions on which the theorem is based exclude phase transitions between gapped (Mott insulator) and gapless phases (Bose glass). The apparent paradox is resolved through a unique mechanism: such transitions have to be of the Griffiths type when the vanishing of the gap at the critical ...

Worm Algorithm For Problems Of Quantum And Classical Statistics, Nikolai Prokof'ev, Boris Svistunov

#### Worm Algorithm For Problems Of Quantum And Classical Statistics, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

This is a chapter of the multi-author book “Understanding Quantum Phase Transitions,” edited by Lincoln Carr and published by Taylor & Francis. In this chapter, we give a general introduction to the worm algorithm and present important results highlighting the power of the approach.

Deconfined Criticality, Runaway Flow In The Two-Component Scalar Electrodynamics And Weak First-Order Superfluid-Solid Transitions, A Kuklov, Nikolai Prokof'ev, Boris Svistunov, M Troyer

#### Deconfined Criticality, Runaway Flow In The Two-Component Scalar Electrodynamics And Weak First-Order Superfluid-Solid Transitions, A Kuklov, Nikolai Prokof'ev, Boris Svistunov, M Troyer

*Boris Svistunov*

We perform a comparative Monte Carlo study of the easy-plane deconfined critical point (DCP) action and its short-range counterpart to reveal close similarities between the two models for intermediate and strong coupling regimes. For weak coupling, the structure of the phase diagram depends on the interaction range: while the short-range model features a tricritical point and a continuous U(1) × U(1) transition, the long-range DCP action is characterized by the runaway renormalization flow of coupling into a first (I) order phase transition. We develop a “numerical flowgram” method for high precision studies of the runaway effect, weakly I-order transitions ...

Bold Diagrammatic Monte Carlo Technique: When The Sign Problem Is Welcome, N Prokof'ev, B Svistunov

#### Bold Diagrammatic Monte Carlo Technique: When The Sign Problem Is Welcome, N Prokof'ev, B Svistunov

*Boris Svistunov*

We introduce a Monte Carlo scheme for sampling a bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo (BMC) technique is significantly broader than that of a simple iterative scheme for solving integral equations. With the BMC technique, a moderate “sign problem” turns out to be an advantage in terms of the convergence of the process. For an illustrative purpose, we solve the one-particle s-scattering problem. As an important application, we obtain the T matrix for a Fermi polaron (one spin-down particle interacting with the spin-up fermionic ...

Superglass Phase Of 4he, M Boninsegni, Nikolai Prokof'ev, Boris Svistunov

#### Superglass Phase Of 4he, M Boninsegni, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We study different solid phases of 4He, by means of path integral Monte Carlo simulations based on a recently developed worm algorithm. Our study includes simulations that start off from a high-T gas phase, which is then “quenched” down to T=0.2 K. The low-T properties of the system crucially depend on the initial state. While an ideal hcp crystal is a clear-cut insulator, the disordered system freezes into a superglass, i.e., a metastable amorphous solid featuring off-diagonal long-range order and superfluidity.

Commensurate Two-Component Bosons In An Optical Lattice: Ground State Phase Diagram, A Kuklov, N Prokof'ev, B Svistunov

#### Commensurate Two-Component Bosons In An Optical Lattice: Ground State Phase Diagram, A Kuklov, N Prokof'ev, B Svistunov

*Boris Svistunov*

Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable superfluid and insulating ground states with rich and nontrivial phase diagram. The structure of the ground state diagram is established by mapping a d-dimensional quantum system onto a (d+1)-dimensional classical loop-current model and Monte Carlo (MC) simulations of the latter. Surprisingly, the quantum phase diagram features, besides second-order lines, first-order transitions and two multicritical points. We explain why first-order transitions are generic for models with pairing interactions using microscopic and mean-field (MF) arguments. In some cases, the MC results strongly deviate from ...

Comment On “Phase Diagram Of A Disordered Boson Hubbard Model In Two Dimensions”, N Prokof’Ev, B Svistunov

#### Comment On “Phase Diagram Of A Disordered Boson Hubbard Model In Two Dimensions”, N Prokof’Ev, B Svistunov

*Boris Svistunov*

In a recent Letter [1] (see also [2]) the authors presented numerical evidence supporting an idea of a direct transition between the superfluid (SF) and Mott insulating (MI) phases in the disordered Bosonic system, and even studied non-trivial properties of the multicritical line where SF, MI and the Bose Glass (BG) phases meet. The results were obtained from Monte Carlo simulations of the (2+1)-dimensional classical loop-current model [3] with the lattice action S = 1 2K ÞE ~ J=0 XrƒÑ #20;~ J2(r, ƒÑ) . 2(ƒÊ + v(r)) ~ JƒÑ (r, ƒÑ)#21; . (1) where r, ƒÑ are spatial ...

Scale-Separation Scheme For Simulating Superfluid Turbulence: Kelvin-Wave Cascade, E Kozik, Boris Svistunov

#### Scale-Separation Scheme For Simulating Superfluid Turbulence: Kelvin-Wave Cascade, E Kozik, Boris Svistunov

*Boris Svistunov*

A Kolmogorov-type cascade of Kelvin waves—the distortion waves on vortex lines—plays a key part in the relaxation of superfluid turbulence at low temperatures. We propose an efficient numeric scheme for simulating the Kelvin-wave cascade on a single vortex line. This idea is likely to be generalizable for a full-scale simulation of different regimes of superfluid turbulence. With the new scheme, we are able to unambiguously resolve the cascade spectrum exponent, and thus to settle the controversy between recent simulations of Vinen, Tsubota, and Mitani [Phys. Rev. Lett. 91, 135301 (2003)] and recently developed analytic theory [Phys. Rev. Lett ...