Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9712014 · Physical review. B, Condensed matter

Spin-wave series for quantum one-dimensional ferrimagnets

Nedko B. Ivanov

Published Jun 1, 1998• 35 citations
arXivHTMLPDF

Abstract

Second-order spin-wave expansions are used to compute the ground-state energy and sublattice magnetizations of the quantum one-dimensional Heisenberg ferrimagnet with nearest-neighbor antiferromagnetic interactions and two types of alternating sublattice spins ${S}_{1}>{S}_{2}.$ It is found that in the extreme quantum cases ${(S}_{1}{,S}_{2})$=(1,1/2), (3/2,1), and (3/2,1/2), the estimates for the ground-state energy and sublattice magnetizations differ less than 0.03% for the energy and 0.2% for the sublattice magnetizations from the recently published density-matrix renormalization-group numerical calculations. The reported results strongly suggest that the quantum Heisenberg ferrimagnetic chains give another example of a low-dimensional quantum spin system where the spin-wave approach demonstrates a surprising efficiency.

DOI
10.1103/physrevb.57.r14024

Related papers

Quantum Ferrimagnets

Ramin Abolfath, H. Hamidian, A. Langari

We study quantum ferrimagnets in one, two, and three dimensions by using a variety of methods and approximations. These include: (i) a treatment based on the spin coherent state path-integral formulation of quantum ferrimagnets by taking into account the leading order quantum and thermal fluctuations (ii) a field-theoretical (non-linear $σ$-model type) formulation of the special case of one-dimensional quantum ferrimagnets at zero temperature (iii) an effective description in terms of dimers and quantum rotors, and (iv) a quantum renormalization group study of ferrimagnetic Heisenberg chains. Some of the formalism discussed here can be used for a unified treatment of both ferromagnets and antiferromagnets in the semiclassical limit. We show that the low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the phase diagram of quantum ferrimagnets in the presence of an external magnetic field h ($h_{c1} < h < h_{c2}$) and show that the low- and the high-field phases correspond respectively to the classical Néel and the fully polarized ferromagnetic states. We also calculate the transition temperature for the Berezinskii-Kosterlitz-Thouless phase transition in the special case of two-dimensional quantum ferrimagnets.

arXiv:cond-mat/9901063•Jan 8, 1999•1 citation

Frustrated quantum Heisenberg ferrimagnetic chains

Nedko B. Ivanov, Johannes Richter, Ulrich Schollwöck

We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins ${S}_{1}>{S}_{2},$ using $1/S$ spin-wave expansions, density-matrix renormalization group, and exact diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate-incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.

arXiv:cond-mat/9803150•Physical review. B, Condensed matter•Dec 1, 1998•30 citations

Magnon dispersions in quantum Heisenberg ferrimagnetic chains at zero temperature

Nedko B. Ivanov

Within the Dyson-Maleev boson formalism, we study the zero-temperature magnon dispersions in a family of one-dimensional quantum Heisenberg ferrimagnets composed of two different spins ${(S}_{1}{,S}_{2})$ in the elementary cell. It is shown that the spin-wave theory can produce precise quantitative results for the low-energy excitations. The spin-stiffness constant ${\ensuremath{\rho}}_{s}$ and the optical magnon gap $\ensuremath{\Delta}$ of different ${(S}_{1}{,S}_{2})$ ferrimagnetic systems are calculated, respectively, to second and third order in the quasiparticle interaction. The spin-wave results are compared with available numerical estimates.

arXiv:cond-mat/0001441•Physical review. B, Condensed matter•Aug 1, 2000•25 citations

Frustration-Induced Ferrimagnetism in Heisenberg Spin Chains

Tokuro Shimokawa, Hiroki Nakano

We study ground-state properties of the Heisenberg frustrated spin chain with interactions up to fourth nearest neighbors by the exact-diagonalization method and the density matrix renormalization group method. We find that ferrimagnetism is realized not only in the case of S=1/2 but also S=1 despite that there is only a single spin site in each unit cell determined from the shape of the Hamiltonian. Our numerical results suggest that a "multi-sublattice structure" is not required for the occurrence of ferrimagnetism in quantum spin systems with isotropic interactions.

arXiv:1111.3430•Journal of the Physical Society of Japan•Nov 21, 2011•5 citations

Matrix-product-states approach to Heisenberg ferrimagnetic spin chains

Alexei K. Kolezhuk, H.-J. Mikeska, Shoji Yamamoto

We present a method of constructing matrix-product (MP) states and apply it to the ground state of the Heisenberg spin chain with alternating spins 1 and and antiferromagnetic exchange interactions between nearest neighbors (the simplest example of a quantum ferrimagnet). The elementary matrix state is constructed in a way that ensures given transformational properties under rotations, which allows one to fix the total spin, and its z projection, of the entire MP wave function. We compare the variational MP results with the numerical results obtained through a quantum Monte Carlo method; the agreement is found to be within 0.4% for the ground-state energy and 5% for the correlation functions.

arXiv:cond-mat/9610097•Physical review. B, Condensed matter•Feb 1, 1997•121 citations

The ground-state properties of the one-dimensional heterospin chain (5/2, 1/2, 1/2) with alternating exchange

Alexander S. Ovchinnikov, Irina Gennad'evna Bostrem, Valentine E. Sinitsyn +2 more

The ground-state properties of the ferrimagnetic spin chain consisting of (5/2,1/2,1/2) trimers with antiferromagnetic exchange between the 5/2 and 1/2 spins and ferromagnetic exchange between the 1/2 and 1/2 spins are analysed in the framework of the quantum renormalization group in real space and the matrix product method. The results are compared with a spin-wave calculation for a spin chain with two types of spin, (5/2,1). The ground-state energy, the average magnetizations and the correlation length are found as functions of the ratio between the antiferromagnetic and ferromagnetic exchange. The analysis shows that the trimer spin chain is characterized by strong quantum fluctuations reducing the average magnetizations and possesses an extremely short correlation length.

Journal of Physics Condensed Matter•May 18, 2001•6 citations
Second-order spin-wave expansions are used to compute the ground-state energy and sublattice magnetizations of the quantum one-dimensional Heisenberg ferrimagnet with nearest-neighbor antiferromagnetic interactions and two types of alternating sublattice spins S1>S2.{S}_{1}>{S}_{2}.S1​>S2​. It is found that in the extreme quantum cases (S1,S2){(S}_{1}{,S}_{2})(S1​,S2​)=(1,1/2), (3/2,1), and (3/2,1/2), the estimates for the ground-state energy and sublattice magnetizations differ less than 0.03% for the energy and 0.2% for the sublattice magnetizations from the recently published density-matrix renormalization-group numerical calculations. The reported results strongly suggest that the quantum Heisenberg ferrimagnetic chains give another example of a low-dimensional quantum spin system where the spin-wave approach demonstrates a surprising efficiency.
We study quantum ferrimagnets in one, two, and three dimensions by using a variety of methods and approximations. These include: (i) a treatment based on the spin coherent state path-integral formulation of quantum ferrimagnets by taking into account the leading order quantum and thermal fluctuations (ii) a field-theoretical (non-linear σσσ-model type) formulation of the special case of one-dimensional quantum ferrimagnets at zero temperature (iii) an effective description in terms of dimers and quantum rotors, and (iv) a quantum renormalization group study of ferrimagnetic Heisenberg chains. Some of the formalism discussed here can be used for a unified treatment of both ferromagnets and antiferromagnets in the semiclassical limit. We show that the low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the phase diagram of quantum ferrimagnets in the presence of an external magnetic field h (hc1<h<hc2h_{c1} < h < h_{c2}hc1​<h<hc2​) and show that the low- and the high-field phases correspond respectively to the classical Néel and the fully polarized ferromagnetic states. We also calculate the transition temperature for the Berezinskii-Kosterlitz-Thouless phase transition in the special case of two-dimensional quantum ferrimagnets.
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S1>S2,{S}_{1}>{S}_{2},S1​>S2​, using 1/S1/S1/S spin-wave expansions, density-matrix renormalization group, and exact diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate-incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.
Within the Dyson-Maleev boson formalism, we study the zero-temperature magnon dispersions in a family of one-dimensional quantum Heisenberg ferrimagnets composed of two different spins (S1,S2){(S}_{1}{,S}_{2})(S1​,S2​) in the elementary cell. It is shown that the spin-wave theory can produce precise quantitative results for the low-energy excitations. The spin-stiffness constant ${\ensuremath{\rho}}_{s}$ and the optical magnon gap $\ensuremath{\Delta}$ of different (S1,S2){(S}_{1}{,S}_{2})(S1​,S2​) ferrimagnetic systems are calculated, respectively, to second and third order in the quasiparticle interaction. The spin-wave results are compared with available numerical estimates.
We study ground-state properties of the Heisenberg frustrated spin chain with interactions up to fourth nearest neighbors by the exact-diagonalization method and the density matrix renormalization group method. We find that ferrimagnetism is realized not only in the case of S=1/2 but also S=1 despite that there is only a single spin site in each unit cell determined from the shape of the Hamiltonian. Our numerical results suggest that a "multi-sublattice structure" is not required for the occurrence of ferrimagnetism in quantum spin systems with isotropic interactions.
We present a method of constructing matrix-product (MP) states and apply it to the ground state of the Heisenberg spin chain with alternating spins 1 and and antiferromagnetic exchange interactions between nearest neighbors (the simplest example of a quantum ferrimagnet). The elementary matrix state is constructed in a way that ensures given transformational properties under rotations, which allows one to fix the total spin, and its z projection, of the entire MP wave function. We compare the variational MP results with the numerical results obtained through a quantum Monte Carlo method; the agreement is found to be within 0.4% for the ground-state energy and 5% for the correlation functions.
The ground-state properties of the ferrimagnetic spin chain consisting of (5/2,1/2,1/2) trimers with antiferromagnetic exchange between the 5/2 and 1/2 spins and ferromagnetic exchange between the 1/2 and 1/2 spins are analysed in the framework of the quantum renormalization group in real space and the matrix product method. The results are compared with a spin-wave calculation for a spin chain with two types of spin, (5/2,1). The ground-state energy, the average magnetizations and the correlation length are found as functions of the ratio between the antiferromagnetic and ferromagnetic exchange. The analysis shows that the trimer spin chain is characterized by strong quantum fluctuations reducing the average magnetizations and possesses an extremely short correlation length.