Ground-state phase diagram and thermodynamics of coupled trimer chains

Abstract

The density matrix renormalization group and quantum Monte Carlo method are used to describe coupled trimer chains in a magnetic field h. The Hamiltonian contains exchange terms involving the intra-trimer coupling J1 (taken as the unit of energy) and the inter-trimer coupling J2, plus the Zeeman interaction for a magnetic field h along the z direction. Results for the magnetization per trimer m are calculated in regimes of positive and negative values of the ratio J = J2/J1, from which the rich field-induced ground state phase diagram h versus J is derived, with the presence of Luttinger liquid, the 1/3 -plateau (m = 1/2), and the one of fully polarized magnetization (m = 3/2). Also, the zero-field Lanczos calculation of spin-wave dispersion from the 1/3 -plateau for S z = 1 is shown at the previous regimes of J values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for 0 < J ≤ 1, and is a singlet for −1 ≤ J < 0. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic powerlaw decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by 1/|J| gets closer to 1/π 2 as the temperature T → 0. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound Pb3Cu3(PO4)4 and estimate the model exchange couplings: J1 = 74.8K and J = 0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on Pb3Cu3(PO4)4 for two excitation modes. The 1/3 -plateau closes only at 1/|J| = 0 with J < 0. I. INTRODUCTIONChains of spin-1/2 sites exhibit a rich quantum behavior depending on the way the spins are coupled [1]. The spin-1/2 antiferromagnetic linear chain [2] is a paradigmatic model with a gapless spectrum that unveiled, for example, collective excitations such as the spinons and holons [1]. On the other hand, the physics of shortrange valence bond states manifests in the singlet gapped ground state of a spin-1/2 two-leg ladder [3-5], which has two spins in each unit cell. For ladders with n legs, the ground state is gapped, with a finite correlation length, for n even; while it is gapless, with a power-law decay of correlation functions, for n odd [6,7].