Determinant representations of spin-operator matrix elements in the XX spin chain and their applications

Article

关键词: NONLINEAR OPTICAL-RESPONSE;    FRENKEL EXCITONS;    SUPERRADIANCE;    STATES;    MODEL;   

DOI  :  10.1103/PhysRevB.97.014301

来源: SCIE

【 摘 要 】

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) x (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 N <= 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.

【 授权许可】

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