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 / Pinto Barros, Joao C.; Dalmonte, Marcello; Trombettoni, Andrea. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2018:10(2018), pp. 1-25. [10.1088/1742-5468/aae2de]

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

Pinto Barros, Joao C.;Dalmonte, Marcello;Trombettoni, Andrea
2018

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.
2018
10
1
25
103103
https://iopscience.iop.org/article/10.1088/1742-5468/aae2de/meta
https://arxiv.org/abs/1708.06585
Pinto Barros, Joao C.; Dalmonte, Marcello; Trombettoni, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/88160
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