arXiv:1204.4076 · Physical Review B

Universal low-temperature magnetic properties of the classical and quantum dimerized ferromagnetic spin chain

Д. В. Дмитриев, V. Ya. Krivnov

Published Oct 10, 2012• 8 citations

Abstract

Low-temperature magnetic properties of both classical and quantum dimerized ferromagnetic spin chains are studied. It is shown that at low temperatures the classical dimerized model reduces to the classical uniform model with the effective exchange integral ${J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})$, where $\ensuremath{\delta}$ is the dimerization parameter. The partition function and spin correlation function are calculated by means of mapping to the continuum limit, which is justified at low temperatures. The quantum model is studied using the Dyson-Maleev representation of the spin operators. It is shown that in the long-wavelength limit the Hamiltonian of the quantum dimerized chain reduces to that of the uniform ferromagnetic chain with the effective exchange integral ${J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})$. This fact implies that the known equivalence of the low-temperature magnetic properties of classical and quantum ferromagnetic chains remains for the dimerized chains. The considered model is generalized to include the next-neighbor antiferromagnetic interaction.

DOI: 10.1103/physrevb.86.134407

Related papers

Static and dynamic properties of a dimerized quantum-spin chain

Oliver Fritz, Stephen William Lovesey, Greg I Watson

Journal of Physics Condensed MatterJul 20, 19981 citation

Low-temperature thermodynamics of the classical frustrated ferromagnetic chain in a magnetic field

Д. В. Дмитриев, V. Ya. Krivnov, N. Yu. Kuzminyh

arXiv:1110.0771Physical Review BDec 27, 20114 citations

A dimerized and frustrated spin model with alternating ferromagnetic and antiferromagnetic exchanges: investigating quantum phases of Heisenberg spin chains with s = 1/2 and 1

Shaon Sahoo, V. M. L. Durga Prasad Goli, Diptiman Sen +1 more

May 29, 20130 citations

Quantum Ferrimagnets

Ramin Abolfath, H. Hamidian, A. Langari

arXiv:cond-mat/9901063Jan 8, 19991 citation

Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions

Hiroki Nakano, Masahiro Takahashi

arXiv:cond-mat/9505066Physical review. B, Condensed matterSep 1, 199548 citations

Exact solution for a quantum spin- 12 Ising-Heisenberg orthogonal-dimer chain with Heisenberg intradimer and Ising interdimer interactions

Taras Verkholyak, Jozef Strečka

arXiv:1306.0487Physical Review BOct 21, 201323 citations

arXiv:1204.4076 · Physical Review B

Universal low-temperature magnetic properties of the classical and quantum dimerized ferromagnetic spin chain

Д. В. Дмитриев, V. Ya. Krivnov

Published Oct 10, 2012• 8 citations

arXiv HTML PDF

Abstract

{J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})

, where

\ensuremath{\delta}

is the dimerization parameter. The partition function and spin correlation function are calculated by means of mapping to the continuum limit, which is justified at low temperatures. The quantum model is studied using the Dyson-Maleev representation of the spin operators. It is shown that in the long-wavelength limit the Hamiltonian of the quantum dimerized chain reduces to that of the uniform ferromagnetic chain with the effective exchange integral

{J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})

. This fact implies that the known equivalence of the low-temperature magnetic properties of classical and quantum ferromagnetic chains remains for the dimerized chains. The considered model is generalized to include the next-neighbor antiferromagnetic interaction.

DOI: 10.1103/physrevb.86.134407

Related papers

Static and dynamic properties of a dimerized quantum-spin chain

Oliver Fritz, Stephen William Lovesey, Greg I Watson

Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.

Journal of Physics Condensed MatterJul 20, 19981 citation

Low-temperature thermodynamics of the classical frustrated ferromagnetic chain in a magnetic field

Д. В. Дмитриев, V. Ya. Krivnov, N. Yu. Kuzminyh

Low-temperature magnetization curves of the classical frustrated ferromagnetic chain in the external magnetic field near the transition point between the ferromagnetic and the helical phases is studied. It is shown that the calculation of the partition function in the scaling limit reduces to the solution of the Schr\"odinger equation of the special form for the quantum particle. It is proposed that the magnetization of the classical model in the ferromagnetic part of the phase diagram including the transition point defines the universal scaling function which is valid for the quantum model as well. Explicit analytical formulas for the magnetization are given in the limiting cases of low and high magnetic fields. The influence of the easy-axis anisotropy on the magnetic properties of the model is studied. It is shown that even small anisotropy essentially changes the behavior of the susceptibility in the vicinity of the transition point.Low-temperature magnetization curves of the classical frustrated ferromagnetic chain in the external magnetic field near the transition point between the ferromagnetic and the helical phases is studied. It is shown that the calculation of the partition function in the scaling limit reduces to the solution of the Schr\"odinger equation of the special form for the quantum particle. It is proposed that the magnetization of the classical model in the ferromagnetic part of the phase diagram including the transition point defines the universal scaling function which is valid for the quantum model as well. Explicit analytical formulas for the magnetization are given in the limiting cases of low and high magnetic fields. The influence of the easy-axis anisotropy on the magnetic properties of the model is studied. It is shown that even small anisotropy essentially changes the behavior of the susceptibility in the vicinity of the transition point.

arXiv:1110.0771Physical Review BDec 27, 20114 citations

A dimerized and frustrated spin model with alternating ferromagnetic and antiferromagnetic exchanges: investigating quantum phases of Heisenberg spin chains with s = 1/2 and 1

Shaon Sahoo, V. M. L. Durga Prasad Goli, Diptiman Sen +1 more

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ( $J_1^F$ ) and antiferromagnetic ( $J_1^A$ ) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ( $J_2^F$ ). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$ . The model with site spin $s$ behaves like a Haldane spin chain with site spin 2 $s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$ . We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

May 29, 20130 citations

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.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/9901063Jan 8, 19991 citation

Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions

Hiroki Nakano, Masahiro Takahashi

Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are inves- tigated by means of the Green's frunction method. The model Hamiltonian is given by scrH=-( ${\mathit{J}}_{0}$ /2)${\mathcal{J}}_{\mathit{i}\mathrm{\ensuremath{\ne}}\mathit{j}}$${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathrm{\ensuremath{-}}\mathit{p}}$ ${\mathbf{S}}_{\mathit{i}}$ \ensuremath{\cdot} ${\mathbf{S}}_{\mathit{j}}$ -H ${\mathcal{J}}_{\mathit{j}}$ ${\mathit{S}}_{\mathit{j}}^{\mathit{z}}$ . It is shown that there exists a finite-temperature phase transition in the region dp2d for the d-dimensional case and that no transitions at any finite temperature exist for p\ensuremath{\ge}2d; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on p; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are inves- tigated by means of the Green's frunction method. The model Hamiltonian is given by scrH=-(${\mathit{J}}_{0}$/2)${\mathcal{J}}_{\mathit{i}\mathrm{\ensuremath{\ne}}\mathit{j}}$${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathrm{\ensuremath{-}}\mathit{p}}$${\mathbf{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathbf{S}}_{\mathit{j}}$ -H${\mathcal{J}}_{\mathit{j}}$${\mathit{S}}_{\mathit{j}}^{\mathit{z}}$. It is shown that there exists a finite-temperature phase transition in the region dp2d for the d-dimensional case and that no transitions at any finite temperature exist for p\ensuremath{\ge}2d; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on p; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.

arXiv:cond-mat/9505066Physical review. B, Condensed matterSep 1, 199548 citations

Exact solution for a quantum spin- 12 Ising-Heisenberg orthogonal-dimer chain with Heisenberg intradimer and Ising interdimer interactions

Taras Verkholyak, Jozef Strečka

The quantum spin- $\frac{1}{2}$ orthogonal-dimer chain with the Heisenberg intradimer and Ising interdimer interactions in a magnetic field is considered by a rigorous approach. The model conserves the $z$ component of total spin on vertical Heisenberg bonds, and this property is used to calculate exactly the partition function using the transfer-matrix method. We have found the ground-state phase diagram of the given model in a magnetic field as well as the macroscopic degeneracy along field-induced transitions accompanied with the magnetization jumps. The model exhibits two intermediate fractional plateaux at one quarter and one half of the saturation magnetization. We have examined the effect of the exchange anisotropy in the $XXZ$ Heisenberg intradimer interaction on the ground state. It is shown that the one-quarter and one-half plateaux may disappear from the magnetization curve for the ferromagnetic Heisenberg intradimer interaction. We have also studied rigorously the effect of frustrated interactions on the thermodynamic and magnetic properties of the model and show how the macroscopic degeneracy of the ground state is reflected in the low-temperature behavior of the magnetization, entropy, and specific heat. A possibility of observing enhanced magnetocaloric effect during the adiabatic demagnetization is discussed in detail.The quantum spin-$\frac{1}{2}$ orthogonal-dimer chain with the Heisenberg intradimer and Ising interdimer interactions in a magnetic field is considered by a rigorous approach. The model conserves the $z$ component of total spin on vertical Heisenberg bonds, and this property is used to calculate exactly the partition function using the transfer-matrix method. We have found the ground-state phase diagram of the given model in a magnetic field as well as the macroscopic degeneracy along field-induced transitions accompanied with the magnetization jumps. The model exhibits two intermediate fractional plateaux at one quarter and one half of the saturation magnetization. We have examined the effect of the exchange anisotropy in the $XXZ$ Heisenberg intradimer interaction on the ground state. It is shown that the one-quarter and one-half plateaux may disappear from the magnetization curve for the ferromagnetic Heisenberg intradimer interaction. We have also studied rigorously the effect of frustrated interactions on the thermodynamic and magnetic properties of the model and show how the macroscopic degeneracy of the ground state is reflected in the low-temperature behavior of the magnetization, entropy, and specific heat. A possibility of observing enhanced magnetocaloric effect during the adiabatic demagnetization is discussed in detail.

arXiv:1306.0487Physical Review BOct 21, 201323 citations

{J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})

, where

\ensuremath{\delta}

{J}_{0}=J(1\ensuremath{-}{\ensuremath{\delta}}^{2})

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (

J_1^F

) and antiferromagnetic (

J_1^A

) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (

J_2^F

). In this model frustration is induced by the non-zero

J_2^F

and the effect of dimerization is realized by changing the strength of

J_1^A

for a fixed value of

J_1^F

. The model with site spin

s

behaves like a Haldane spin chain with site spin 2

s

in the limit of vanishing

J_2^F

and large

J_1^F/J_1^A

. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of

J_1^A-J_2^F

is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

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.

Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are inves- tigated by means of the Green's frunction method. The model Hamiltonian is given by scrH=-(

{\mathit{J}}_{0}

/2)${\mathcal{J}}_{\mathit{i}\mathrm{\ensuremath{\ne}}\mathit{j}}$${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathrm{\ensuremath{-}}\mathit{p}}$

{\mathbf{S}}_{\mathit{i}}

\ensuremath{\cdot}

{\mathbf{S}}_{\mathit{j}}

-H

{\mathcal{J}}_{\mathit{j}}

{\mathit{S}}_{\mathit{j}}^{\mathit{z}}

. It is shown that there exists a finite-temperature phase transition in the region dp2d for the d-dimensional case and that no transitions at any finite temperature exist for p\ensuremath{\ge}2d; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on p; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.

The quantum spin-

\frac{1}{2}

orthogonal-dimer chain with the Heisenberg intradimer and Ising interdimer interactions in a magnetic field is considered by a rigorous approach. The model conserves the

z

component of total spin on vertical Heisenberg bonds, and this property is used to calculate exactly the partition function using the transfer-matrix method. We have found the ground-state phase diagram of the given model in a magnetic field as well as the macroscopic degeneracy along field-induced transitions accompanied with the magnetization jumps. The model exhibits two intermediate fractional plateaux at one quarter and one half of the saturation magnetization. We have examined the effect of the exchange anisotropy in the

XXZ

Heisenberg intradimer interaction on the ground state. It is shown that the one-quarter and one-half plateaux may disappear from the magnetization curve for the ferromagnetic Heisenberg intradimer interaction. We have also studied rigorously the effect of frustrated interactions on the thermodynamic and magnetic properties of the model and show how the macroscopic degeneracy of the ground state is reflected in the low-temperature behavior of the magnetization, entropy, and specific heat. A possibility of observing enhanced magnetocaloric effect during the adiabatic demagnetization is discussed in detail.