By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by the system during its evolution are distributed according to a multinomial probability density. The class includes (i) the uniformly fully connected models, namely a collection of states all connected with equal hopping coefficients and in the presence of a potential operator with arbitrary levels and degeneracies, and (ii) the random potential systems, in which the hopping operator is generic and arbitrary potential levels are assigned randomly to the states with arbitrary probabilities. For this class of models we find a universal thermodynamic limit characterized only by the levels of the potential, rescaled by the ground-state energy of the system for zero potential, and by the corresponding degeneracies (probabilities). If the degeneracy (probability) of the lowest potential level tends to zero, the ground state of the system undergoes a quantum phase transition between a normal phase and a frozen phase with zero hopping energy. In the frozen phase the ground state condenses into the subspace spanned by the states of the system associated with the lowest potential level.

The exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit / Massimo, Ostilli; Presilla, Carlo. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2006:11(2006), pp. P11012-P11012. [10.1088/1742-5468/2006/11/p11012]

The exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit

PRESILLA, Carlo
2006

Abstract

By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by the system during its evolution are distributed according to a multinomial probability density. The class includes (i) the uniformly fully connected models, namely a collection of states all connected with equal hopping coefficients and in the presence of a potential operator with arbitrary levels and degeneracies, and (ii) the random potential systems, in which the hopping operator is generic and arbitrary potential levels are assigned randomly to the states with arbitrary probabilities. For this class of models we find a universal thermodynamic limit characterized only by the levels of the potential, rescaled by the ground-state energy of the system for zero potential, and by the corresponding degeneracies (probabilities). If the degeneracy (probability) of the lowest potential level tends to zero, the ground state of the system undergoes a quantum phase transition between a normal phase and a frozen phase with zero hopping energy. In the frozen phase the ground state condenses into the subspace spanned by the states of the system associated with the lowest potential level.
2006
anderson model (theory); disordered systems (theory); quantum phase transitions (theory)
01 Pubblicazione su rivista::01a Articolo in rivista
The exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit / Massimo, Ostilli; Presilla, Carlo. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2006:11(2006), pp. P11012-P11012. [10.1088/1742-5468/2006/11/p11012]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/67387
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
social impact