Universality of the topological phase transition in mixed-spin tetramer Heisenberg chains

Abstract

The ground-state features of a mixed-spin Heisenberg bond-alternating chain with unit cell consisting of spin-1/2 and general spin-S dimers are investigated using density matrix renormalization group (DMRG) calculations. Similar spin units are considered to interact via an isotropic antiferromagnetic coupling constant J1, while an exchange constant J2 accounts for the interaction between distinct spin units. With increasing values of an external magnetic field, the system presents a sequence of magnetic-field-driven transitions between gapped plateau and gapless spin-liquid phases. At zero field, a quantum phase transition emerges between two topologically distinct gapped phases at a quantum critical point Jc=(J2/J1)|c at which the energy spin-gap closes. We employ a tangential finite-size scaling analysis of the relevant energy gap to precisely locate the quantum critical point and to estimate the correlation length critical exponent for several magnitudes of the spin S. While the critical value of the coupling constant ratio decreases with S, the scaling of the correlation length presents a universal power-law with a logarithmic correction scaling.