Finite-Size Corrections and Spin Correlations ofMagnetized<i>S</i>=1 Antiferromagnetic Heisenberg Chain

Abstract

The S =1 antiferromagnetic Heisenberg chain in a magnetic field along the z -axis at T =0 is studied by numerical diagonalizations up to N =16 and an analysis of size corrections. We check that the system obeys the conformal field theory with the central charge c =1 in a magnetic state (0< m <1). We investigate the asymptotic form of the transverse and parallel spin correlations and give the exponents η and η z , defined by < S 0 x S _r^x>≃(-1)^rr^-η a n d <S_0^zS_r^z>-m^2≃cos (2k_Fr)r^-η^z. W e d e t e r m i n e η=1/2 a n d η^z=2 a t m=0 a n d 1. I n a d d i t i o n , w e c h e c k t h e r e l a t i o n ηη^z=1, w h i c h i s c o n s i s t e n t w i t h t h e L u t t i n g e r l i q u i d c o n c e p t . I n t e r m s o f t h e c o n c e p t , t h e a n o m a l i e s o f m a g n e t i z a t i o n a t m=0 a n d 1 a r e d i s c u s s e d .