Boundary-induced spin-density waves in linear Heisenberg antiferromagnetic spin chains with S >= 1

Article

关键词: QUANTUM RENORMALIZATION-GROUPS;    MATRIX RENORMALIZATION;    CRITICAL-BEHAVIOR;    EDGE STATES;    ALGORITHMS;    ENERGY;   

DOI  :  10.1103/PhysRevB.94.144417

来源: SCIE

【 摘 要 】

Linear Heisenberg antiferromagnets (HAFs) are chains of spin-S sites with isotropic exchange J between neighbors. Open and periodic boundary conditions return the same ground-state energy per site in the thermodynamic limit, but not the same spin S-G when S >= 1. The ground state of open chains of N spins has S-G = 0 or S, respectively, for even or odd N. Density-matrix renormalization-group calculations with different algorithms for even and odd N are presented up to N = 500 for the energy and spin densities rho(r, N) of edge states in HAFs with S = 1, 3/2, and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with rho(r, N) proportional to (-1)(r-1) for r = 1,2,..., N. The SDWs are in phase when N is odd, are out of phase when N is even, and have finite excitation energy Gamma(N) that decreases exponentially with N for integer S and faster than 1/N for half integer S. The spin densities and excitation energy are quantitatively modeled for integer S chains longer than 5 xi spins by two parameters, the correlation length xi and the SDW amplitude, with xi = 6.048 for S = 1 and 49.0 for S = 2. The BI-SDWs of S = 3/2 chains are not localized and are qualitatively different for even and odd N. Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases vertical bar Gamma(N)vertical bar and weakens the size dependence. The nonlinear sigma model (NL sigma M) has been applied to the HAFs, primarily to S = 1 with even N, to discuss spin densities and exchange between localized states at the ends as Gamma(N) proportional to (-1)(N) exp(-N/xi). S = 1 chains with odd N are fully consistent with the NL sigma M; S = 2 chains have two gaps Gamma(N) with the same xi as predicted whose ratio is 3.45 rather than 3; the NL sigma M is more approximate for S = 3/2 chains with even N and is modified for exchange between ends for odd N.

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