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Ukrainian Journal of Physics

Asymmetric Diamond Ising-Hubbard Chain with Attraction

Bohdan Lisnyi

Published Feb 1, 2013• 9 citations
Publisher

Abstract

The ground state and thermodynamic properties of an asymmetric diamond Ising–Hubbard chain with the on-site electron-electron attraction has been considered. The problem can be solved exactly using the decoration-iteration transformation. In the case of the antiferromagnetic Ising interaction, the influence of this attraction on the ground state and the temperature dependences of the magnetization, magnetic susceptibility, and specific heat has been studied.

DOI
10.15407/ujpe58.02.0195

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The ground state and thermodynamic properties of an asymmetric diamond Ising–Hubbard chain with the on-site electron-electron attraction has been considered. The problem can be solved exactly using the decoration-iteration transformation. In the case of the antiferromagnetic Ising interaction, the influence of this attraction on the ground state and the temperature dependences of the magnetization, magnetic susceptibility, and specific heat has been studied.
The ground state and the thermodynamics of a spin-1/2 asymmetric diamond Ising--Heisenberg chain are considered. For the XYZXYZXYZ anisotropic Heisenberg interaction, the exact calculations of the free energy, entropy, heat capacity, magnetization, and magnetic susceptibility are performed using the method of decoration-iteration transformation. In the case of antiferromagnetic interactions (Ising and XXZXXZXXZ anisotropic Heisenberg ones), the ground state, magnetization process, temperature dependence of the magnetization, magnetic susceptibility, and heat capacity are investigated. The influence of geometric frustration and quantum fluctuations on these characteristics is studied.
Abstract A symmetric spin‐1/2 Ising–Heisenberg diamond chain with the Ising four‐spin interaction is exactly solved by means of the generalized decoration‐iteration mapping transformation. The ground state, the magnetization process and thermodynamics are particularly examined for the case of antiferromagnetic pair interactions (Ising and isotropic Heisenberg ones). It is shown that an interplay between pair interactions, the four‐spin interaction and the external magnetic field gives rise to several quantum ground states with entangled spin states in addition to some semi‐classically ordered ones. Besides, the temperature dependence of the magnetic susceptibility multiplied by the temperature is studied and the interesting triple‐peak specific heat curve is also detected when considering the zero‐field region rather close to the triple point, where three different ground states coexist.
The exact solution of the distorted Ising-Hubbard model for a diamond chain is obtained by means of transfer matrix method. Based on this solution the magnetic, thermal and concurrence properties of the system are studied. We discuss in detail the ground state varying values of Ising and Hubbard interaction couplings, hopping amplitude, magnetic field, chemical potential and get paramagnetic, ferromagnetic, antiferromagnetic and ferrimagnetic phases of the system. Plateaus in magnetization curves and several-peak structures of the specific heat curve for different values of Hamiltonian parameters are obtained. The dependence of concurrence in Hubbard dimers from chain parameters, external magnetic field and temperature are studied.
The exact solution of the distorted diamond Ising–Hubbard chain is analyzed in the special limit of infinite on-site electron-electron repulsion, where the two-electron Hubbard dimer becomes equivalent to the antiferromagnetic isotropic Heisenberg dimer. The special limit of infinite repulsion for the matrix of the cell Hamiltonian of this model is analytically calculated, and it is demonstrated that the exact solution of the distorted diamond Ising–Hubbard chain in this limit coincides with the exact solution of the spin-1/2 distorted diamond Ising–Heisenberg chain with antiferromagnetic isotropic Heisenberg interaction. The numerical calculation of the special limit of infinite repulsion for the ground-state phase diagram and thermodynamic characteristics of the distorted diamond Ising–Hubbard chain was performed in a way that provides a very fast convergence to the limit results for these characteristics.
The ground state and thermodynamics of a generalized spin‐1/2 Ising–Heisenberg diamond chain with the second‐neighbor interaction between nodal spins are calculated exactly using the mapping method based on the decoration–iteration transformation. Rigorous results for the magnetization, susceptibility, and heat capacity are investigated in dependence on temperature and magnetic field for the frustrated diamond spin chain with the antiferromagnetic Ising and Heisenberg interactions. It is demonstrated that the second‐neighbor interaction between nodal spins gives rise to a greater diversity of low‐temperature magnetization curves, which may include an intermediate plateau at two‐third of the saturation magnetization related to the classical ferrimagnetic (up–up–up–down–up–up– ) ground state with translationally broken symmetry besides an intermediate one‐third magnetization plateau reflecting the translationally invariant quantum ferrimagnetic (monomer–dimer) spin arrangement.