Non-periodic Ising quantum chains and conformal invariance
arXiv:cond-mat/9902126 · doi:10.1007/BF02188226
Abstract
A while ago, Luck (J. Stat. Phys. 72 (1993) 417) investigated the critical behaviour of one-dimensional Ising quantum chains with couplings constants modulated according to general non-periodic sequences. In this short note, we take a closer look at the case where the sequences are obtained from (two-letter) substitution rules and at the consequences of Luck's results at criticality. They imply that only for a certain class of substitution rules the long-distance behaviour is still described by the c=1/2 conformal field theory of a free Majorana fermion as for the periodic Ising quantum chain, whereas the general case does not lead to a conformally invariant scaling limit.
13 pages, 4 figures; five years old but still correct; for more recent developments see cond-mat/9706106