Prokof'ev, Nikolai
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Professor, Physics Department
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Prokof'ev
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Nikolai
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Physics
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Publication Exact quantum Monte Carlo process for the statistics of discrete systems(1996) Prokof'ev, Nikolai; Svistunov, Boris; Tupitsyn, IWe propose an exact Monte Carlo approach for the statistics of discrete quantum systems that does not employ the standard partition of the imaginary time into a mesh and does not contain small parameters. The method operates with discrete objects — kinks, describing virtual transitions at different moments in time. The global statistics of the kinks is reproduced by exact local procedures, the main one being based on the known solution for an asymmetric two-level system.Publication Critical Temperature of Interacting Bose Gases in Two and Three Dimensions(2008-01-01) Pilati, S; Giorgini, S; Prokof’ev, NWe calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=105 particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3≲10-4. This value is different from the estimate na3≲10-6 for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |ψ|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.Publication Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model(2010-01-01) Tupitsyn, I; Kitaev, A; Prokof'ev, Nikolai; Stamp, P.C.EWe construct a mapping between the two-dimensional toric code model in external magnetic fields, hz and hx, and the three-dimensional classical Ising system with plaquette interactions, which is equivalent to the three-dimensional Z2 gauge Higgs model with anisotropy between the imaginary time and spatial directions. The isotropic limit of the latter model was studied using Monte Carlo simulations on large (up to 603) lattices in order to determine the stability of the topological phase against generic magnetic field perturbations and to resolve fine details of the phase diagram. We find that the topological phase is bounded by second-order transition lines, which merge into a first-order line at what appears to be a multicritical point arising from the competition between the Higgs and confinement transitions in the Z2 gauge system. An effective field theory for this type of multicritical point (if one actually exists) is not known. Our results have potential applications to frustrated magnets, quantum computation, lattice gauge models in particle physics, and critical phenomena.Publication Truncated-Determinant Diagrammatic Monte Carlo for Fermions with Contact Interaction(2004-01-01) Bourovski, E; Prokof'ev, Nikolai; Svistunov, BorisFor 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 attractive Hubbard model within the MC scheme based on partially summed Feynman diagrams. We conjecture that similar approach may be useful in other implementations of the sign-free determinant schemes.Publication Frustrated Spin Model as a Hard-Sphere Liquid(2003-01-01) Mostovoy, M; Khomskii, D; Knoester, J; Prokof'ev, NikolaiWe show that one-dimensional topological objects (kinks) are natural degrees of freedom for an antiferromagnetic Ising model on a triangular lattice. Its ground states and the coexistence of spin ordering with an extensive zero-temperature entropy can easily be understood in terms of kinks forming a hard-sphere liquid. Using this picture we explain effects of quantum spin dynamics on that frustrated model, which we also study numerically.Publication Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment(1997) Tupitsyn, I; Prokof'ev, Nikolai; Stamp, PWe consider here the problem of a "giant spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic grains or magnetic macromolecules (ferromagnetically or antiferromagnetically ordered) interacting with a surrounding spin environment, such as nuclear spins. Our aim is to give a general method for truncating the model to another one, valid at low energies, in which a two-level system interacts with the environmental spins, and higher energy terms are absorbed into a new set of couplings. This is done using an instanton technique. We then study the accuracy of this technique, by comparing the results for the low energy effective Hamiltonian, with results derived for the original giant spin, coupled to a macroscopic spin, using exact diagonalization techniques. We find that the low energy central spin effective Hamiltonian gives very accurate results (with increasing accuracy for large S), provided the typical coupling energies between the giant spin and the microscopic spins are not too large, and provided temperature and external field are sufficiently low. The essential limitation to the applicability of the low-energy effective Hamiltonian is just the semiclassical WKB approximation itself, which inevitably fails for very small S. Our results thus justify previous use of this effective Hamiltonian in calculations of the effects of nuclear spins on the dynamics of nanomagnetic systems.Publication Superfluid-Insulator Transition in a Commensurate One-Dimensional Bosonic System with Off-Diagonal Disorder(2005-01-01) Balabanyan, K; Prokof'ev, Nikolai; Svistunov, BorisWe 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.Publication Diagrammatic Monte Carlo(2008-01-01) Houcke, K; Kozik, E; Prokof'ev, Nikolai; Svistunov, BorisDiagrammatic Monte Carlo (DiagMC) is a numeric technique that allows one to calculate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is typically fatal to Monte Carlo approaches, appears to be manageable with DiagMC. Starting with a general introduction to the principles of DiagMC, we present a detailed description of the DiagMC scheme for interacting fermions (Hubbard model), as well as the first illustrative results for the equations of state.Publication Superfluid-Insulator Transition in Commensurate Disordered Bosonic Systems: Large-Scale Worm Algorithm Simulations(2004-01-01) Prokof'ev, Nikolai; Svistunov, BorisWe 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 smaller clusters mimicked a direct superfluid–Mott-insulator transition.Publication Berezinskii-Kosterlitz-Thouless Transition in Two-Dimensional Dipole Systems(2010-01-01) Filinov, A; Prokof'ev, N; Bonitz, MThe superfluid to normal fluid transition of dipolar bosons in two dimensions is studied in a broad density range by using path integral Monte Carlo simulations and summarized in the phase diagram. While at low densities we find good agreement with the universal results depending only on the scattering length as, at moderate and high densities the transition temperature is strongly affected by interactions and the excitation spectrum of quasiparticles. The results are expected to be of relevance to dipolar atomic and molecular systems and indirect excitons in quantum wells.