Exactly solvable mixed-spin Ising-Heisenberg diamond chain with the biquadratic interactions and single-ion anisotropy

TL;DR

This paper presents an exactly solvable mixed-spin Ising-Heisenberg diamond chain model with biquadratic interactions and single-ion anisotropy, revealing a rich ground state phase diagram and exact thermodynamic properties.

Contribution

It introduces a new exactly solvable model incorporating biquadratic interactions and anisotropy, expanding understanding of quantum spin chains.

Findings

Multiple ground states including saturated and ferrimagnetic phases

Presence of macroscopically degenerated frustrated states at zero field

Exact expressions for thermodynamic functions and phase diagrams

Abstract

An exactly solvable variant of mixed spin-(1/2,1) Ising-Heisenberg diamond chain is considered. Vertical spin-1 dimers are taken as quantum ones with Heisenberg bilinear and biquadratic interactions and with single-ion anisotropy, while all interactions between spin-1 and spin-1/2 residing on the intermediate sites are taken in the Ising form. The detailed analysis of the $T=0$ ground state phase diagram is presented. The phase diagrams have shown to be rather rich, demonstrating large variety of ground states: saturated one, three ferrimagnetic with magnetization equal to 3/5 and another four ferrimagnetic ground states with magnetization equal to 1/5. There are also two frustrated macroscopically degenerated ground states which could exist at zero magnetic filed. Solving the model exactly within classical transfer-matrix formalism we obtain an exact expressions for all thermodynamic function of the system. The thermodynamic properties of the model have been described exactly by exact calculation of partition function within the direct classical transfer-matrix formalism, the entries of transfer matrix, in their turn, contain the information about quantum states of vertical spin-1 XXZ dimer (eigenvalues of local hamiltonian for vertical link).