CRITICAL-BEHAVIOR OF THE APERIODIC QUANTUM ISING CHAIN IN A TRANSVERSE MAGNETIC-FIELD

We consider the quantum spin-1/2 Ising chain in a uniform transverse m agnetic field, with an aperiodic sequence of ferromagnetic exchange co uplings. This system is a limiting anisotropic case of the classical t wo-dimensional Ising model with an arbitrary layered modulation. Its f ormal solution via a Jordan-Wigner transformation enables us to obtain a detailed description of the influence of the aperiodic modulation o n the singularity of the ground-state energy at the critical point. Th e key concept is that of the fluctuation of the sums of any number of consecutive couplings at the critical point. When the fluctuation is b ounded, the model belongs to the ''Onsager universality class'' of the uniform chain. The amplitude of the logarithmic divergence in the spe cific heat is proportional to the velocity of the fermionic excitation s, for which we give explicit expressions in most cases of interest, i ncluding the periodic and quasiperiodic cases, the Thue-Morse chain, a nd the random dimer model. When the couplings exhibit an unbounded flu ctuation, the critical singularity is shown to be generically similar to that of the disordered chain: the ground-state energy has finite de rivatives of all orders at the critical point, and an exponentially sm all singular part, for which we give a quantitative estimate. In the m arginal case of a logarithmically divergent fluctuation, e.g., for the period-doubling sequence or the circle sequence, there is a negative specific heat exponent alpha, which varies continuously with the stren gth of the aperiodic modulation.