arXiv:0904.3843 · Physical Review B

Factorized ground state for a general class of ferrimagnets

Mohammad Rezai, A. Langari, Jahanfar Abouie

Published Feb 4, 2010• 13 citations

Abstract

We have found the exact (factorized) ground state of a general class of ferrimagnets in the presence of a magnetic field which includes the anisotropic and long-range interactions for arbitrary dimensional space. In particular cases our model represents many spin chains with bond alternation of antiferromagnetic-ferromagnetic coupling, ferrimagnetic spin ladders, and also homogeneous spin-$s$ models. The factorized ground state is a product of single-particle kets on a bipartite lattice composed of two different spins $(\ensuremath{\rho},\ensuremath{\sigma})$ which is characterized by two angles, a biangle state. The spin-wave analysis around the exact ground state shows two branch of excitations which are the origin of two dynamics of the model. The signature of these dynamics is addressed as a peak and a broaden bump in the specific heat.

DOI: 10.1103/physrevb.81.060401

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arXiv:0904.3843 · Physical Review B

Factorized ground state for a general class of ferrimagnets

Mohammad Rezai, A. Langari, Jahanfar Abouie

Published Feb 4, 2010• 13 citations

arXiv HTML PDF

Abstract

s

models. The factorized ground state is a product of single-particle kets on a bipartite lattice composed of two different spins

(\ensuremath{\rho},\ensuremath{\sigma})

which is characterized by two angles, a biangle state. The spin-wave analysis around the exact ground state shows two branch of excitations which are the origin of two dynamics of the model. The signature of these dynamics is addressed as a peak and a broaden bump in the specific heat.

DOI: 10.1103/physrevb.81.060401

Related papers

Ground State Factorization of Heterogeneous Spin Models in Magnetic Fields

J. Abouie, M. Rezai, A. Langari

The exact factorized ground state of a heterogeneous (ferrimagnetic) spin model which is composed of two spins (ρ, σ) has been presented in detail. The Hamiltonian is not necessarily translational invariant and the exchange couplings can be competing antiferromagnetic and ferromagnetic arbitrarily between different sublattices to build many practical models such as dimerized and tetramerized materials and ladder compounds. The condition to get a factorized ground state is investigated for non-frustrated spin models in the presence of a uniform and a staggered magnetic field. According to the lattice model structure we have categorized the spin models in two different classes and obtained their factorization conditions. The first class contains models in which their lattice structures do not provide a single uniform magnetic field to suppress the quantum correlations. Some of these models may have a factorized ground state in the presence of a uniform and a staggered magnetic field. However, in the second class there are several spin models in which their ground state could be factorized whether a staggered field is applied to the system or not. For the latter case, in the absence of a staggered field the factorizing uniform field is unique. However, the degrees of freedom for obtaining the factorization conditions are increased by adding a staggered magnetic field.The exact factorized ground state of a heterogeneous (ferrimagnetic) spin model which is composed of two spins (ρ, σ) has been presented in detail. The Hamiltonian is not necessarily translational invariant and the exchange couplings can be competing antiferromagnetic and ferromagnetic arbitrarily between different sublattices to build many practical models such as dimerized and tetramerized materials and ladder compounds. The condition to get a factorized ground state is investigated for non-frustrated spin models in the presence of a uniform and a staggered magnetic field. According to the lattice model structure we have categorized the spin models in two different classes and obtained their factorization conditions. The first class contains models in which their lattice structures do not provide a single uniform magnetic field to suppress the quantum correlations. Some of these models may have a factorized ground state in the presence of a uniform and a staggered magnetic field. However, in the second class there are several spin models in which their ground state could be factorized whether a staggered field is applied to the system or not. For the latter case, in the absence of a staggered field the factorizing uniform field is unique. However, the degrees of freedom for obtaining the factorization conditions are increased by adding a staggered magnetic field.

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Interacting spin chains and ladders are known to support a plethora of quantum phases with complex ground-state phase diagrams. In this work, we study a large family of such models and determine precise, explicit conditions under which an exact dimer state is guaranteed to be the ground state. These general conditions are validated for various generalizations of the Majumdar-Ghosh model using exact diagonalization. Our results provide exact reference points in the phase diagrams of a wide class of spin chains and ladders, including those with anisotropic and arbitrary-range interactions.Interacting spin chains and ladders are known to support a plethora of quantum phases with complex ground-state phase diagrams. In this work, we study a large family of such models and determine precise, explicit conditions under which an exact dimer state is guaranteed to be the ground state. These general conditions are validated for various generalizations of the Majumdar-Ghosh model using exact diagonalization. Our results provide exact reference points in the phase diagrams of a wide class of spin chains and ladders, including those with anisotropic and arbitrary-range interactions.

arXiv:2607.01081Jul 1, 20260 citations

s

models. The factorized ground state is a product of single-particle kets on a bipartite lattice composed of two different spins

(\ensuremath{\rho},\ensuremath{\sigma})

{S}_{z}=0

in the

\mathrm{XY}

regime and two degenerate ground states with nonzero magnetization in the Ising regime, respectively. Therefore, the isotropic point of this model is a bifurcation point for its ground states. Furthermore, we also show that, if magnetization of the ground states in the Ising regime is a macroscopic quantity in the thermodynamic limit, then these states have both ferromagnetic and antiferromagnetic long-range order. In other words, they are ferrimagnetically ordered. These conclusions confirm the previous results derived by numerical calculations on small one-dimensional mixed-spin chains.

We state the conditions under which the general spin-s quantum XYZ ferromagnet (${H}_{\mathrm{\ensuremath{-}}}$) and antiferromagnet (

{H}_{+}

) with an external magnetic field along one axis, specified by the Hamiltonian ${H}_{\ifmmode\pm\else\textpm\fi{}}$=\ifmmode\pm\else\textpm\fi{}

{\mathcal{J}}_{l=1}^{N}

(

{J}_{x}

{S}_{l}^{x}

{S}_{l+1}^{x}

{J}_{y}

{S}_{l}^{y}

_{l+1}^{y}

{J}_{z}

{S}_{l}^{z}

{S}_{l+1}^{z}

)-h

{\mathcal{J}}_{l=1}^{N}

{S}_{l}^{z}

exhibits a fully ordered ground state described by a wave function which is a direct product of single-site wave functions. We present a detailed analysis of the implications for the zero-temperature dynamical properties of this model. In particular, we derive a rigorous relation between the three dynamic structure factors ${S}_{\ensuremath{\mu}\ensuremath{\mu}}$(q,\ensuremath{\omega}), \ensuremath{\mu}=x,y,z at T=0. For the special case of the s=(1/2) anisotropic XY model (

{J}_{z}

=0), these relations are used to determine the dynamic structure factors

{S}_{\mathrm{xx}}

(q,\ensuremath{\omega}) and

{S}_{\mathrm{yy}}

(q,\ensuremath{\omega}) at T=0 and h=(

{J}_{x}

{J}_{y}

{)}^{1/2}

in terms of the known dynamic structure factor

{S}_{\mathrm{zz}}

(q,\ensuremath{\omega}).

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins, 1 and

1/2,

antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact-diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of the ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.

We construct a class of spin-1/2 antiferromagnetic two-chain ladder models consisting of blocks of n-spin tetrahedral clusters alternating with two-spin rungs. For

n=4

and 6 and in extended parameter regimes, the exact ground state of the ladder is shown to be a product of the ground states of the rungs and the n-spin blocks, in both zero and finite magnetic fields. In the latter case, magnetization/site m versus magenetic field h plot exhibits well-defined magnetization plateaus.