Exact short-distance correlations of the Heisenberg chain by means of the fermionic basis / vorgelegt von Raphael Kleinemühl. Wuppertal, November 2020
Content
Introduction
Operators on the Finite Chain
Basic Definitions
Construction of k
Analytic Structure of k, q and t*
Partial Fraction Decomposition
Construction of c, b and f
Creation Operators
Reduction Relations
Shift in alpha
Commutation Relations
Operators on the Infinite Chain
Expectation Values
Construction on the Computer
Form
Construction of t*
Construction of k
Construction of rho and kappa
Construction of the Fermionic Annihilation Operators
Construction of the Fermionic Creation Operators
Elements of the Fermionic Basis
Change of Basis
Expectation Values of Basis Elements
Construction of Omega1
Parallelization
Prospects for the Case n=6
The Function omega
Results of the Computation
Proof of the Exponential Form
Proof of the Vacuum Property
Expectation Values for Vanishing External Field
Operators Even Under Spin Reversal and the Operator t
Relations for Modes of t
Conclusion
Fermionic Basis for n=4
Correlation Functions for n=5
Crossover Temperatures
Bibliography