scholarly journals Matrix product wave function of the ground state and elementary excitations in the spin- 12 chain

2021 ◽  
Vol 103 (12) ◽  
Author(s):  
Jintae Kim ◽  
Minsoo Kim ◽  
Pramod Padmanabhan ◽  
Jung Hoon Han ◽  
Hyun-Yong Lee
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Matrix Product ◽  
Elementary Excitations

scholarly journals Finitely Correlated Generalized Spin Ladders

1998 ◽  
Vol 12 (23) ◽  
pp. 2325-2348 ◽  
Author(s):  
A. K. Kolezhuk ◽  
H.-J. Mikeska
Keyword(s):  
Ground State ◽  
Ground States ◽  
Exchange Interactions ◽  
Second Order ◽  
Order Transition ◽  
Matrix Product ◽  
Elementary Excitations ◽  
Degenerate Ground State ◽  
Second Order Transition ◽  
Isotropic Exchange

We study two-leg S=1/2 ladders with general isotropic exchange interactions between spins on neighboring rungs, whose ground state can be found exactly in a form of finitely correlated (matrix product) wave function. Two families of models admitting an exact solution are found: one yields translationally invariant ground states and the other describes spontaneously dimerized models with twofold degenerate ground state. Several known models with exact ground states (Majumdar–Ghosh and Shastry–Sutherland spin-1/2 chains, Affleck–Kennedy–Lieb–Tasaki spin-1 chain, Δ-chain, Bose–Gayen ladder model) can be obtained as particular cases from the general solution of the first family, which includes also a set of models with only bilinear interactions. Those two families of models have nonzero intersection, which enables us to determine exactly the phase boundary of the second-order transition into the dimerized phase and to study the properties of this transition. The structure of elementary excitations in the dimerized phase is discussed on the basis of a variational ansatz. For a particular class of models, we present exact wave functions of the elementary excitations becoming gapless at second-order transition lines. We also propose a generalization of the Bose–Gayen model which has a rich phase diagram with all phase boundaries being exact.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

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