Many body models undergoing a quantum phase transition to a broken-symmetry phase that survives up to a critical temperature must possess, in the ordered phase, symmetric as well as non-symmetric eigenstates. We predict, and explicitly show in the fully-connected Ising model in a transverse field, that these two classes of eigenstates do not overlap in energy, and therefore that an energy edge exists separating low-energy symmetry-breaking eigenstates from high-energy symmetry-invariant ones. This energy is actually responsible, as we show, for the dynamical phase transition displayed by this model under a sudden large increase of the transverse field. A second situation we consider is the opposite, where the symmetry-breaking eigenstates are those in the high-energy sector of the spectrum, whereas the low-energy eigenstates are symmetric. In that case too a special energy must exist marking the boundary and leading to unexpected out-of-equilibrium dynamical behavior. An example is the fermionic repulsive Hubbard model Hamiltonian H. Exploiting the trivial fact that the high energy spectrum of H is also the low energy one of -H, we conclude that the high energy eigenstates of the Hubbard model are superfluid. Simulating in a time-dependent Gutzwiller approximation the time evolution of a high energy BCS-like trial wave function, we show that a small superconducting order parameter will actually grow in spite of the repulsive nature of interaction.

Dynamical quantum phase transitions and broken-symmetry edges in the many-body eigenvalue spectrum / Mazza, Giacomo; Fabrizio, Michele. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - 86:18(2012), pp. 184303.1-184303.9. [10.1103/PhysRevB.86.184303]

Dynamical quantum phase transitions and broken-symmetry edges in the many-body eigenvalue spectrum

Mazza, Giacomo;Fabrizio, Michele
2012-01-01

Abstract

Many body models undergoing a quantum phase transition to a broken-symmetry phase that survives up to a critical temperature must possess, in the ordered phase, symmetric as well as non-symmetric eigenstates. We predict, and explicitly show in the fully-connected Ising model in a transverse field, that these two classes of eigenstates do not overlap in energy, and therefore that an energy edge exists separating low-energy symmetry-breaking eigenstates from high-energy symmetry-invariant ones. This energy is actually responsible, as we show, for the dynamical phase transition displayed by this model under a sudden large increase of the transverse field. A second situation we consider is the opposite, where the symmetry-breaking eigenstates are those in the high-energy sector of the spectrum, whereas the low-energy eigenstates are symmetric. In that case too a special energy must exist marking the boundary and leading to unexpected out-of-equilibrium dynamical behavior. An example is the fermionic repulsive Hubbard model Hamiltonian H. Exploiting the trivial fact that the high energy spectrum of H is also the low energy one of -H, we conclude that the high energy eigenstates of the Hubbard model are superfluid. Simulating in a time-dependent Gutzwiller approximation the time evolution of a high energy BCS-like trial wave function, we show that a small superconducting order parameter will actually grow in spite of the repulsive nature of interaction.
2012
86
18
1
9
184303
https://arxiv.org/abs/1210.2034
Mazza, Giacomo; Fabrizio, Michele
File in questo prodotto:
File Dimensione Formato  
PhysRevB.86.184303.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 834.56 kB
Formato Adobe PDF
834.56 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
1210.2034.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Non specificato
Dimensione 604.91 kB
Formato Adobe PDF
604.91 kB Adobe PDF Visualizza/Apri

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/20.500.11767/11749
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? 25
social impact