The 17/5 Spectrum Of The Kelvin-Wave Cascade, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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 ...

Regularization Of Diagrammatic Series With Zero Convergence Radius, 2011 University of Massachusetts - Amherst

#### Regularization Of Diagrammatic Series With Zero Convergence Radius, L Pollet, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

The divergence of perturbative expansions which occurs for the vast majority of macroscopic systems and follows from Dyson’s collapse argument prevents the direct use of Feynman’s diagrammatic technique for controllable studies of strongly interacting systems. We show how the problem of divergence can be solved by replacing the original model with a convergent sequence of successive approximations which have a convergent perturbative series while maintaining the diagrammatic structure. As an instructive model, we consider the zero-dimensional |ψ|4 theory.

Kelvin-Wave Cascade And Decay Of Superfluid Turbulence, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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 ...

Monte Carlo Study Of The Two-Dimensional Bose-Hubbard Model, 2011 University of Massachusetts - Amherst

#### Monte Carlo Study Of The Two-Dimensional Bose-Hubbard Model, B Capogrosso-Sansone, S Söyler, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

One of the most promising applications of ultracold gases in optical lattices is the possibility to use them as quantum emulators of more complex condensed matter systems. We provide benchmark calculations, based on exact quantum Monte Carlo simulations, for the emulator to be tested against. We report results for the ground state phase diagram of the two-dimensional Bose-Hubbard model at unity filling factor. We precisely trace out the critical behavior of the system and resolve the region of small insulating gaps, Δ⪡J. The critical point is found to be (J/U)c=0.05974(3), in perfect agreement with ...

The Beliaev Technique For A Weakly Interacting Bose Gas, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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.

Incorporating Dynamic Mean-Field Theory Into Diagrammatic Monte Carlo, 2011 University of Massachusetts - Amherst

#### Incorporating Dynamic Mean-Field Theory Into Diagrammatic Monte Carlo, L Pollet, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feyn- man's diagrammatic series using skeleton diagrams. For lattice models the e#14;ciency of BDMC can be dramatically improved by incorporating dynamic mean-#12;eld theory solutions into renormalized propagators. From the DMFT perspective, combining it with BDCM leads to an unbiased method with well-de#12;ned accuracy. We illustrate the power of this approach by computing the single-particle propagator (and thus the density of states) in the non-perturbative regime of the Anderson local- ization problem, where a gain of the order of 104 is achieved ...

Comment On "Symmetries And Interaction Coefficients Of Kelvin Waves" [Arxiv:1005.4575] By Lebedev And L'Vov, 2011 University of Massachusetts - Amherst

#### 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 ...

Superfluid-Insulator Transition In A Commensurate One-Dimensional Bosonic System With Off-Diagonal Disorder, 2011 University of Massachusetts - Amherst

#### Superfluid-Insulator Transition In A Commensurate One-Dimensional Bosonic System With Off-Diagonal Disorder, K Balabanyan, Nikolai Prokof'ev, Boris Svistunov

*Boris Svistunov*

We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of a large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and the applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.

Truncated-Determinant Diagrammatic Monte Carlo For Fermions With Contact Interaction, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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, 2011 University of Massachusetts - Amherst

#### 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.