Low-lying excited states and low-temperature properties of an alternating spin-1–spin-1/2 chain: A density-matrix renormalization-group study

We report spin wave and density-matrix renormalization-group (DMRG) studies of the ground and low-lying excited states of uniform and dimerized alternating spin chains. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of the system. The ground state of a 2N spin system with spin-1 and spin- alternating from site to site and interacting via an antiferromagnetic exchange is found to be ferrimagnetic with total spin ${\mathrm{s}}_{\mathrm{G}}$=N/2 from both DMRG and spin wave analysis. Both the studies also show that there is a gapless excitation to a state with spin ${\mathrm{s}}_{\mathrm{G}}$-1 and a gapped excitation to a state with spin ${\mathrm{s}}_{\mathrm{G}}$+1. Surprisingly, the correlation length in the ground state is found to be very small from both the studies for this gapless system. For this very reason, we show that the ground state can be described by a variational ansatz of the product type. DMRG analysis shows that the chain is susceptible to a conditional spin-Peierls' instability. The DMRG studies of magnetization, magnetic susceptibility (χ), and specific heat show strong magnetic-field dependence. The product χT shows a minimum as a function of temperature (T) at low-magnetic fields and the minimum vanishes at high-magnetic fields. This low-field behavior is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature and the height of the maximum increases sharply at high-magnetic fields. It is hoped that these studies will motivate experimental studies at high-magnetic fields.