Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
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Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials. / Burrello, M.; Fulga, Ion Cosma; Lepori, L.; Trombettoni, A.
I: Journal of Physics A: Mathematical and Theoretical, Bind 50, 455301, 10.10.2017.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
AU - Burrello, M.
AU - Fulga, Ion Cosma
AU - Lepori, L.
AU - Trombettoni, A.
N1 - [Qdev]
PY - 2017/10/10
Y1 - 2017/10/10
N2 - We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general spaceindependent non-Abelian gauge potential. We first review and analyze the case of purely Abelian potentials, showing also that the so-called Hasegawa gauge yields a decomposition of the Hamiltonian into sub-matrices having minimal dimension. Explicit expressions for such matrices are derived, also for general anisotropic fluxes. Later on, we show that the introduction of a translational invariant non-Abelian coupling for multi-component spinors does not affect the dimension of the minimal Hamiltonian blocks, nor the dimension of the magnetic Brillouin zone. General formulas are presented for the U(2) case and explicit examples are investigated involving π and 2π/3 magnetic fluxes. Finally, we numerically study the effect of random flux perturbations.
AB - We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general spaceindependent non-Abelian gauge potential. We first review and analyze the case of purely Abelian potentials, showing also that the so-called Hasegawa gauge yields a decomposition of the Hamiltonian into sub-matrices having minimal dimension. Explicit expressions for such matrices are derived, also for general anisotropic fluxes. Later on, we show that the introduction of a translational invariant non-Abelian coupling for multi-component spinors does not affect the dimension of the minimal Hamiltonian blocks, nor the dimension of the magnetic Brillouin zone. General formulas are presented for the U(2) case and explicit examples are investigated involving π and 2π/3 magnetic fluxes. Finally, we numerically study the effect of random flux perturbations.
KW - gauge potentials
KW - lattice models
KW - ultracold quantum gases
U2 - 10.1088/1751-8121/aa8d26
DO - 10.1088/1751-8121/aa8d26
M3 - Journal article
AN - SCOPUS:85032224417
VL - 50
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
M1 - 455301
ER -
ID: 186320082