One-dimensional Quantum Chains Research Articles

N=1 superconformal invariance in the six-state quantum chain with free boundary conditions

The spectrum of a six-state one-dimensional quantum chain with free boundaries at the critical point is studied. Using finite-size scaling and conformal invariance, they find a line in the plane of the coupling constants where the system has N=1 superconformal invariance with c=5/4.

Finite-size scaling functions and conformal invariance

A method to calculate perturbative corrections to the spectrum of a one-dimensional quantum chain in the scaling variable z is developed from the conformal invariance at its fixed point. Then, from the knowledge of certain correlation functions, one can calculate the first coefficients of the scaling functions. The method is applied successfully to the Ising model, where the corrections are also known from the exact solution. The first coefficients of the magnetic scaling functions of the Ising model are also obtained.

The Ashkin-Teller quantum chain and conformal invariance

The authors study the finite-size effects for the fourth-state one-dimensional quantum chain introduced by Kohmoto et al. (1981) using different boundary conditions. From the corrections to the ground-state energy for periodic boundary conditions they verify that the central charge of the Virasoro algebra is equal to one in the whole domain of criticality. Their numerical study suggests a new relation between the corrections to the ground-state energy with free boundary conditions and with periodic boundary conditions. Various critical exponents including the surface ones and those corresponding to the para-fermions are determined.

Conformal invariance and finite one-dimensional quantum chains

Based on previous work of Cardy (1984), the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions. The method is illustrated in the case of the three- and four-state Potts models where the anomalous dimensions of the para-fermionic operators are found.

Determination of Hamiltonian parameters of anisotropic one-dimensional quantum chains by susceptibility measurements

Determination of Hamiltonian parameters of anisotropic one-dimensional quantum chains by susceptibility measurements

Theory of the spin-peierls transition for one-dimensional classical and quantum chains

A spin-lattice coupling induced lattice dimerization (spin-Peierls transition) in exactly soluble linear magnetic models is investigated. The transition can be of first or second order for classical spin model but of second order only for quantum X-Y model.

Dispersion curve for a one-dimensional quantum chain

Dispersion curve for a one-dimensional quantum chain