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• W2897096372 abstract "For the two-mode and $(Nensuremath{-}1)ensuremath{-}mathrm{bosonic}$ Bose-Hubbard quantum system a less usual phase transition controlled by the parameter $ensuremath{varepsilon}$ representing the on-site energy difference is studied. In the literature the parameter is considered either real ($ensuremath{varepsilon}>0$) or purely imaginary (with, say, $ensuremath{gamma}=mathrm{Im}phantom{rule{4pt}{0ex}}ensuremath{varepsilon}>0$), so the phase transition is analyzed here at the interface $ensuremath{varepsilon}=ensuremath{gamma}=0$. The evolution in the $ensuremath{gamma}ensuremath{-}mathrm{controlled}$ phase is required unitary so that the main task for the theory is found in the (quasi-)Hermitization of the Hamiltonian, achieved by a suitable amendment of the inner product in Hilbert space, $ensuremath{langle}ifmmodecdotelsetextperiodcenteredfi{}|ifmmodecdotelsetextperiodcenteredfi{}ensuremath{rangle}ensuremath{rightarrow}ensuremath{langle}ifmmodecdotelsetextperiodcenteredfi{}|mathrm{ensuremath{Theta}}|ifmmodecdotelsetextperiodcenteredfi{}ensuremath{rangle}$. In the most relevant domain of small $ensuremath{gamma}$ the linearized Hilbert-space metric $mathrm{ensuremath{Theta}}(ensuremath{gamma})$ [constrained by the requirement ${lim}_{ensuremath{gamma}ensuremath{rightarrow}0}mathrm{ensuremath{Theta}}(ensuremath{gamma})=I$ of the smoothness of the change of the Hilbert space at the phase transition] is constructed in closed form. Beyond the phase-transition instant, several forms of the systematic non-numerical recurrent construction of the exact metrics $mathrm{ensuremath{Theta}}(ensuremath{gamma})$ are also shown user friendly and feasible, at the not too large matric dimensions $N$ at least." @default.
• W2897096372 created "2018-10-26" @default.
• W2897096372 creator A5075251924 @default.
• W2897096372 date "2018-11-05" @default.
• W2897096372 modified "2023-09-25" @default.
• W2897096372 title "Broken-Hermiticity phase transition in the Bose-Hubbard model" @default.
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• W2897096372 doi "https://doi.org/10.1103/physreva.98.052102" @default.
• W2897096372 hasPublicationYear "2018" @default.
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