Operator renormalization group

Miscellaneous · Sun Jan 01 00:00:00 EST 1989

OSTI ID:5019891

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}{sub 0}{r angle} has an overlap with the true ground state, matrix elements are guaranteed to converge to their true vacuum expectation values in the limit t {yields} {infinity}. The renormalization group approach is an algorithm for constructing an appropriate choice of the class of trial states in a variational calculation. The idea behind the method is as follows. The author begins by dissecting the lattice into small blocks containing a few sites which are coupled together via the gradient terms in the Hamiltonian. The Hamiltonian for the resulting few degrees of freedom is diagonalized and the degrees of freedom are thinned by a truncation procedure that keeps only an appropriate set of low-lying states. An effective Hamiltonian is then constructed by computing the matrix elements of the original Hamiltonian in the space of states spanned by the lowest-lying states in each block. This procedure is then repeated for this effective Hamiltonian until it goes to a fixed form so that the resulting Hamiltonian can be solved exactly. The operator renormalization group method (ORG) combines these two procedures with the hope of effectively extracting infinite volume physics at t {yields} {infinity} from calculations of only a few powers of t.

• Research Organization: Stanford Univ., CA (United States)
• OSTI ID: 5019891
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HAMILTONIANS
CALCULATION METHODS
ALGORITHMS
COMPARATIVE EVALUATIONS
DEGREES OF FREEDOM
GROUND STATES
HEISENBERG MODEL
ISING MODEL
MANY-BODY PROBLEM
PERTURBATION THEORY
POWER SERIES
QUANTUM MECHANICS
RENORMALIZATION
VARIATIONAL METHODS
CRYSTAL MODELS
ENERGY LEVELS
EVALUATION
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM OPERATORS
SERIES EXPANSION
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics