Exact short-distance correlations of the Heisenberg chain by means of the fermionic basis / vorgelegt von Raphael Kleinemühl. Wuppertal, November 2020
Inhalt
- 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