An analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion
Abstract
We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy as well as the correlation functions in the ground state are exactly determined as series expansions in the cumulants of the multiplicities of the potential and hopping energies assumed by the system during its long-time evolution. Once these cumulants are known, even at a finite order, our approach provides the ground state analytically as a function of the Hamiltonian parameters. A scenario of possible applications of the analytic character of the present approach is discussed.
- Publication:
-
Journal of Statistical Mechanics: Theory and Experiment
- Pub Date:
- April 2005
- DOI:
- 10.1088/1742-5468/2005/04/P04007
- arXiv:
- arXiv:cond-mat/0412157
- Bibcode:
- 2005JSMTE..04..007O
- Keywords:
-
- 02.50.-r;
- 05.40.-a;
- 71.10.Fd correlation functions rigorous results in statistical mechanics other numerical approaches series expansions;
- Condensed Matter - Other Condensed Matter;
- High Energy Physics - Lattice;
- Mathematics - Probability;
- Quantum Physics
- E-Print:
- 26 pages, 5 figures