# Magnetism and Thermodynamics of Spin-1/2 Heisenberg Diamond Chains in a Magnetic Field

## TL;DR

This paper investigates the magnetic and thermodynamic properties of spin-1/2 Heisenberg diamond chains using advanced numerical methods, revealing coupling-independent peaks in structure factors and temperature-dependent double-peak features in susceptibility and heat capacity.

## Contribution

It provides a comprehensive analysis of different coupling regimes in Heisenberg diamond chains and introduces new fitting equations for the static structure factor based on low-lying excitations.

## Key findings

- Static structure factor peaks at specific wavevectors in zero field
- Coupling-independent peaks at certain wavevectors in magnetization plateau
- Double-peak structures in susceptibility and specific heat at finite temperatures

## Abstract

The magnetic and thermodynamic properties of spin-1/2 Heisenberg diamond chains are investigated in three different cases: (a) J1, J2, J3>0 (frustrated); (b) J1, J3<0, J2>0 (frustrated); and (c) J1, J2>0, J3<0 (non-frustrated). The density matrix renormalization group (DMRG) technique is invoked to study the properties of the system in the ground state, while the transfer matrix renormalization group (TMRG) technique is applied to explore the thermodynamic properties. The local magnetic moments, spin correlation functions, and static structure factors are discussed in the ground state for the three cases. It is shown that the static structure factor S(q) shows peaks at wavevectors $q=a\pi /3$ (a=0,1,2,3,4,5) for different couplings in a zero magnetic field, which, however in the magnetic fields where the magnetization plateau with m=1/6 pertains, exhibits the peaks only at q=0, $2\pi /3$ and $4\pi /3$, which are found to be couplings-independent. The DMRG results of the zero-field static structure factor can be nicely fitted by a linear superposition of six modes, where two fitting equations are proposed. It is observed that the six modes are closely related to the low-lying excitations of the system. At finite temperatures, the double-peak structures of the susceptibility and specific heat against temperature are obtained, where the peak positions and heights are found to depend on the competition of the couplings. It is also uncovered that the XXZ anisotropy of F and AF couplings leads the system of case (c) to display quite different behaviors. In addition, the experimental data of the susceptibility, specific heat and magnetization for the compound Cu$_{3}$(CO$_{3}$)$_{2}$(OH)$_{2}$ are fairly compared with our TMRG results.