Topological quantum phase transition in a mixed-spin Heisenberg tetramer chain with alternating spin-1/2 and spin-5/2 dimers

We investigate magnetic quantum phases and the topological quantum phase transition between two distinct valence-bond solid (VBS) phases of a minimal interacting spin-chain model that captures a magnetic behavior of the novel low-dimensional quantum ferrimagnetic material Cu2Fe2Ge4O13. The studied mixed-spin Heisenberg tetramer chain consists of a 4-period array of spins involving two types of dimers sa - sa (sa = 1/2) and Sb - Sb (Sb = 5/2) under the assumption of unique intra-and inter-dimer coupling constants J1 and J2, respectively. Using the tensor-network formulation of the density-matrix renormalization group method, we have constructed the ground-state phase diagram in the parameter space magnetic field versus the interaction ratio J = J2/J1, whereby all ground states are in accordance with the Oshikawa-Yamanaka-Affleck theorem for a given period. In addition, we have implemented the recent tangential finite-size scaling method in order to characterize the critical behavior of the topological VBS transition through calculation of the critical point Jc and the critical exponent of the correlation length v. Our results are consistent with the topological quantum phase transition from the SU(2) Wess-Zumino-Witten universality class with the critical exponent of correlation length v = 2/3 by assuming the proper logarithmic correction.