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- W2753439821 abstract "For the one-dimensional spin-1/2 XX model with either periodic or open boundary conditions, it is shown by using a fermionic approach that the matrix element of the spin operator $S^-_j$ ($S^-_{j}S^+_{j'}$) between two eigenstates with numbers of excitations $n$ and $n+1$ ($n$ and $n$) can be expressed as the determinant of an appropriate $(n+1)times (n+1)$ matrix whose entries involve the coefficients of the canonical transformations diagonalizing the model. In the special case of a homogeneous periodic XX chain, the matrix element of $S^-_j$ reduces to a variant of the Cauchy determinant that can be evaluated analytically to yield a factorized expression. The obtained compact representations of these matrix elements are then applied to two physical scenarios: (i) Nonlinear optical response of molecular aggregates, for which the determinant representation of the transition dipole matrix elements between eigenstates provides a convenient way to calculate the third-order nonlinear responses for aggregates from small to large sizes compared with the optical wavelength, and (ii) real-time dynamics of an interacting Dicke model consisting of a single bosonic mode coupled to a one-dimensional XX spin bath. In this setup, full quantum calculation up to $Nleq 16$ spins for vanishing intrabath coupling shows that the decay of the reduced bosonic occupation number approaches a finite plateau value (in the long-time limit) that depends on the ratio between the number of excitations and the total number of spins. Our results can find useful applications in various system-bath systems, with the system part inhomogeneously coupled to an interacting XX chain." @default.
- W2753439821 created "2017-09-15" @default.
- W2753439821 creator A5023371171 @default.
- W2753439821 date "2017-09-03" @default.
- W2753439821 modified "2023-09-24" @default.
- W2753439821 title "Spin operator matrix elements in the XX spin chain with application to the dynamics of the interacting Dicke model" @default.
- W2753439821 hasPublicationYear "2017" @default.
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