Ground State and Finite Temperature Properties of Mixed Diamond Chains with Spins 1 and 1/2 with Single-site Anisotropy

Kazuo Hida

Published Jun 20, 2011• 0 citations

Abstract

Ground states and ﬁnite temperature properties of mixed diamond chains with spins 1 and1/2 which has the single-site anisotropy on spin-1 sites are investigated. There are phaseswhere the ground state is a spin cluster solid, i. e. an array of uncorrelated spin-1 clustersseparated by singlet dimers. The ground state is nonmagnetic for the easy-plane anisotropy,while it is paramagnetic for the easy-axis anisotropy. Also there are the N´eel, Haldane, andlarge-D phases, where the ground state is a single spin cluster of inﬁnite size and the systemis equivalent to the spin-1 Heisenberg chain with alternating anisotropy. The longitudinal andtransverse susceptibilities and entropy are calculated at ﬁnite temperatures in the spin-cluster-solid phases. Their low temperature behaviors are sensitive to the anisotropy.KEYWORDS: mixed diamond chain, anisotropy, frustration, spin cluster solid, N´eel phase, Haldane phase,large-Dphase

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Abstract

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D

phases, where the ground state is a single spin cluster of infinite size and the system is equivalent to the spin-1 Heisenberg chain with alternating anisotropy. The longitudinal and transverse susceptibilities and entropy are calculated at finite temperatures in the spin-cluster-solid phases. Their low-temperature behaviors are sensitive to anisotropy.

S=1

spin, this type of ground state breaks the translational symmetry spontaneously. Although the mechanism leading to this type of ground state is the same as that in the isotropic case, it is nonmagnetic or paramagnetic depending on the competition between two types of anisotropy. We also find the Néel, period-doubled Néel, Haldane, and large-

D

phases, where the ground state is a single spin cluster of infinite size equivalent to the spin-1 Heisenberg chain with alternating anisotropies. The ground-state phase diagrams are determined for typical sets of parameters by numerical analysis. In various limiting cases, the ground-state phase diagrams are determined analytically. The low-temperature behaviors of magnetic susceptibility and entropy are investigated to distinguish each phase by observable quantities. The relationship of the present model with the anisotropic rung-alternating ladder with spin-1/2 is also discussed.

Exact Thermodynamic Properties of

(1,1/2)

Mixed Diamond Chains with Strong Single-Site Anisotropy

m=1/6

and 1/3 per site. The ferrimagnetic state with

m=1/6

is accompanied by a spontaneous translational symmetry breakdown. This phase vanishes for strong bond alternation.

Ground-State Phase Diagram of

(1/2,1/2,1)

Mixed Diamond Chains with Single-Site Anisotropy

The ground-state phases of mixed diamond chains with (

S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)

, where

S

is the magnitude of vertex spins, and

τ^{(1)}

and

τ^{(2)}

are those of apical spins, are investigated with the single-site anisotropy

D

on the

τ^{(2)}

-site. The two apical spins in each unit cell are coupled by an exchange coupling

λ

. The vertex spins are coupled with the top and bottom apical spins by exchange couplings

1+δ

and

1-δ

, respectively. The ground-state phase diagram is determined using the numerical exact diagonalization and DMRG method in addition to the analytical approximations in various limiting cases. The phase diagram consists of a Néel ordered phase, a nonmagnetic Tomonaga-Luttinger liquid phase, and quantized and partial ferrimagnetic phases. A region with anisotropy inversion is found where the Ising-like Néel phase is realized for the easy-plane anisotropy

D >0

and the XY-like Tomonaga-Luttinger liquid phase is realized for the easy-axis anisotropy

D <0

on the

S=1

sites.

The mixed diamond chain is a frustrated Heisenberg chain composed of successive diamond-shaped units with two kinds of spins of magnitudes

S

and

S/2

(

S

: integer). Ratio $\ensuremath{\lambda}$ of two exchange parameters controls the strength of frustration. With varying $\ensuremath{\lambda}$, the Haldane state and several spin-cluster states appear as the ground state. A spin-cluster state is a tensor product of exact local eigenstates of cluster spins. We prove that a spin-cluster state is the ground state in a finite interval of $\ensuremath{\lambda}$. For

S=1

, we numerically determine the total phase diagram consisting of five phases.