T expansion: A nonperturbative analytic tool for Hamiltonian systems

Horn, D; Weinstein, M

doi:10.1103/PhysRevD.30.1256

Title: T expansion: A nonperturbative analytic tool for Hamiltonian systems

Full Record
Other Related Research

Abstract

A systematic nonperturbative scheme is developed to calculate the ground-state expectation values of arbitrary operators for any Hamiltonian system. Quantities computed in this way converge rapidly to their true expectation values. The method is based upon the use of the operator e/sup -t/H to contract any trial state onto the true ground state of the Hamiltonian H. We express all expectation values in the contracted state as a power series in t, and reconstruct t..-->..infinity behavior by means of Pade approximants. The problem associated with factors of spatial volume is taken care of by developing a connected graph expansion for matrix elements of arbitrary operators taken between arbitrary states. We investigate Pade methods for the t series and discuss the merits of various procedures. As examples of the power of this technique we present results obtained for the Heisenberg and Ising models in 1+1 dimensions starting from simple mean-field wave functions. The improvement upon mean-field results is remarkable for the amount of effort required. The connection between our method and conventional perturbation theory is established, and a generalization of the technique which allows us to exploit off-diagonal matrix elements is introduced. The bistate procedure is used to develop a tmore »« less

Authors:: Horn, D; Weinstein, M

Publication Date:: Sat Sep 15 00:00:00 EDT 1984

Research Org.:: Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

OSTI Identifier:: 6349576

DOE Contract Number:: AC03-76SF00515

Resource Type:: Journal Article

Journal Name:: Phys. Rev. D; (United States)

Additional Journal Information:: Journal Volume: 30:6

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; LATTICE FIELD THEORY; HAMILTONIANS; GAUGE INVARIANCE; ISING MODEL; MATRIX ELEMENTS; PADE APPROXIMATION; PERTURBATION THEORY; RENORMALIZATION; VARIATIONAL METHODS; WAVE FUNCTIONS; CRYSTAL MODELS; FIELD THEORIES; FUNCTIONS; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; QUANTUM FIELD THEORY; QUANTUM OPERATORS; 645400* - High Energy Physics- Field Theory

Citation Formats


                    Horn, D, and Weinstein, M. T expansion: A nonperturbative analytic tool for Hamiltonian systems.  United States: N. p., 1984. 
        Web.  doi:10.1103/PhysRevD.30.1256.

Copy to clipboard


                    Horn, D, & Weinstein, M. T expansion: A nonperturbative analytic tool for Hamiltonian systems.  United States.  https://doi.org/10.1103/PhysRevD.30.1256

Copy to clipboard


                    Horn, D, and Weinstein, M. 1984.  
        "T expansion: A nonperturbative analytic tool for Hamiltonian systems".  United States.  https://doi.org/10.1103/PhysRevD.30.1256.

Copy to clipboard


                    
@article{osti_6349576,

  title        = {T expansion: A nonperturbative analytic tool for Hamiltonian systems},

  author       = {Horn, D and Weinstein, M},

  abstractNote = {A systematic nonperturbative scheme is developed to calculate the ground-state expectation values of arbitrary operators for any Hamiltonian system. Quantities computed in this way converge rapidly to their true expectation values. The method is based upon the use of the operator e/sup -t/H to contract any trial state onto the true ground state of the Hamiltonian H. We express all expectation values in the contracted state as a power series in t, and reconstruct t..-->..infinity behavior by means of Pade approximants. The problem associated with factors of spatial volume is taken care of by developing a connected graph expansion for matrix elements of arbitrary operators taken between arbitrary states. We investigate Pade methods for the t series and discuss the merits of various procedures. As examples of the power of this technique we present results obtained for the Heisenberg and Ising models in 1+1 dimensions starting from simple mean-field wave functions. The improvement upon mean-field results is remarkable for the amount of effort required. The connection between our method and conventional perturbation theory is established, and a generalization of the technique which allows us to exploit off-diagonal matrix elements is introduced. The bistate procedure is used to develop a t expansion for the ground-state energy of the Ising model which is, term by term, self-dual.},

  doi          = {10.1103/PhysRevD.30.1256},

  url          = {https://www.osti.gov/biblio/6349576},
  journal      = {Phys. Rev. D; (United States)},
number       = ,

  volume       = 30:6,

  place        = {United States},

  year         = {Sat Sep 15 00:00:00 EDT 1984},

  month        = {Sat Sep 15 00:00:00 EDT 1984}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1103/PhysRevD.30.1256

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Operator renormalization group

Miscellaneous Stubbins, C

A powerful new hybrid method for calculating ground-state energies for lattice Hamiltonians is presented. This method combines the t-expansion with the real space renormalization group approach. The t-expansion is a nonperturbative method that calculates groundstate expectation values of many-body systems in Quantum Mechanics as a power series in the parameter t. The idea behind this method is that for any variational state {vert bar}{psi}{sub 0}{r angle}, the author can construct a new state {vert bar}{psi}{sub t}{r angle}, which is a better approximation to the true ground state for any value of t. As long as the initial state {vert bar}{psi}{submore »« less
Constructing and proving the ground state of a generalized Ising model by the cluster tree optimization algorithm

Journal Article Huang, Wenxuan; Kitchaev, Daniil; Dacek, Stephen; ... - arXiv.org Repository

Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, and fluid mechanics. However, the problem of finding the global ground state of generalized Ising model has remained unresolved, with only a limited number of results for simple systems known. We propose a method to efficiently find the periodic ground state of a generalized Ising model of arbitrary complexity by a new algorithm which we term cluster tree optimization.more »« less
Full Text Available
Hamiltonians, path integrals, and a new renormalization group

Journal Article Weinstein, M - Physical Review, D (Particles Fields); (United States)

New nonperturbative methods for dealing with Hamiltonian systems are introduced. The derivation of these methods requires identities for rewriting exponentials of sums of operators which are different from the usual Campbell-Hausdorff formula. These identities allow one to derive approximations to [ital e][sup [minus][delta][ital H]] which are correct to higher order in [delta] and which contain fewer terms than the Campbell-Hausdorff formula. This allows one to generate path-integral actions which are more accurate for finite-size steps in time and which can be exploited to improve the rate of convergence of Monte Carlo calculations. To show that these methods allow one tomore »« less
https://doi.org/10.1103/PhysRevD.47.5499
Operator renormalization group and spin systems

Journal Article Stubbins, C - Physical Review, D (Particles Fields); (USA)

The results of a new hybrid method for calculating ground-state energies for lattice Hamiltonians are presented. This method combines the {ital t} expansion with the real-space renormalization-group approach, with the hope of extracting infinite-volume physics at {ital t}{r arrow}{infinity} from calculations of only a few powers of {ital t}. We calculate the ground-state energy for the (1+1)-dimensional anisotropic Heisenberg model and the (1+1)-dimensional Ising model. Using a blocking that treats the sites and links symmetrically, we were able to determine the exact critical point of the Ising system. In both of these systems we see that the operator renormalization-group methodmore »« less
https://doi.org/10.1103/PhysRevD.44.488
100kW Energy Transfer Multiplexer Power Converter Prototype Development Project

Technical Report Skeist, S; Baker, Richard; Marini, Anthony

Project Final Report for "100kW Energy Transfer Multiplexer Power Converter Prototype Development Project" prepared under DOE grant number DE-FG36-03GO13138. This project relates to the further development and prototype construction/evaluation for the Energy Transfer Multiplexer (ETM) power converter topology concept. The ETM uses a series resonant link to transfer energy from any phase of a multiphase input to any phase of a multiphase output, converting any input voltage and frequency to any output voltage and frequency. The basic form of the ETM converter consists of an eight (8)-switch matrix (six phase power switches and two ground power switches) and a seriesmore »« less
https://doi.org/10.2172/881570

Full Text Available

Similar Records