We show how certain long-range models of interacting fermions in d + 1 dimensions are equivalent to gauge theories in D + 1 dimensions in which gauge fields are defined in a dimension (D) larger than the dimension (d) of the fermionic theory to be simulated. For d = 1 it is possible to obtain an exact mapping, providing an expression of the fermionic interaction potential in terms of half-integer powers of the Laplacian. An analogous mapping can be applied to the kinetic term of the bosonized theory. A diagrammatic representation of the theories obtained by dimensional mismatch is presented, and consequences and applications of the established duality are discussed. Finally, by using a perturbative approach, we address the canonical quantization of fermionic theories presenting non-locality in the interaction term to construct the Hamiltonians for the effective theories found by dimensional reduction. We conclude by showing that one can engineer the gauge fields and the dimensional mismatch in order to obtain long-range effective Hamiltonians with 1/r or 1/r 2 potentials as examples.

Long-range interactions from U (1) gauge fields via dimensional mismatch

Trombettoni, Andrea
2018-01-01

Abstract

We show how certain long-range models of interacting fermions in d + 1 dimensions are equivalent to gauge theories in D + 1 dimensions in which gauge fields are defined in a dimension (D) larger than the dimension (d) of the fermionic theory to be simulated. For d = 1 it is possible to obtain an exact mapping, providing an expression of the fermionic interaction potential in terms of half-integer powers of the Laplacian. An analogous mapping can be applied to the kinetic term of the bosonized theory. A diagrammatic representation of the theories obtained by dimensional mismatch is presented, and consequences and applications of the established duality are discussed. Finally, by using a perturbative approach, we address the canonical quantization of fermionic theories presenting non-locality in the interaction term to construct the Hamiltonians for the effective theories found by dimensional reduction. We conclude by showing that one can engineer the gauge fields and the dimensional mismatch in order to obtain long-range effective Hamiltonians with 1/r or 1/r 2 potentials as examples.
File in questo prodotto:
File Dimensione Formato  
jstat_103103_2018_p_23_10_18.pdf

Accesso chiuso

Tipologia: Documento in Versione Editoriale
Licenza: Copyright Editore
Dimensione 1.33 MB
Formato Adobe PDF
1.33 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
jstat_103103_2018_p_23_10_18-Post_print.pdf

Open Access dal 24/10/2020

Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Digital Rights Management non definito
Dimensione 1.34 MB
Formato Adobe PDF
1.34 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

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/11368/2956758
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact