Ground-state phase diagram and thermodynamics of coupled trimer chains

TL;DR

This paper uses advanced computational methods to map the phase diagram and thermodynamics of coupled trimer chains in a magnetic field, revealing rich magnetic phases and correlating with experimental data.

Contribution

It presents a detailed ground-state phase diagram of coupled trimer chains, including new insights into magnetic phases and excitations, supported by numerical and experimental comparisons.

Findings

Identification of ferrimagnetic and singlet ground states depending on J

Observation of a 1/3-plateau in magnetization curves

Correlation with experimental neutron scattering data

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 vs. 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 $0<J\leq 1$, and is a singlet for $-1\leq J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law 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 $1/\pi^2$ as the temperature $T\rightarrow 0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound Pb$_3$Cu$_3$(PO$_4$)$_4$ and estimate the model exchange couplings: J1=74.8 K 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 Pb$_3$Cu$_3$(PO$_4$)$_4$ for two excitation modes. The 1/3-plateau closes only at 1/|J|=0 with J<0.