arXiv:cond-mat/9507041 · Physical review. B, Condensed matter

Frustrated spin-Peierls chains

Jun Zang, A. R. Bishop, D. Schmeltzer

Published Sep 1, 1995• 22 citations

Abstract

We study the phase diagram, ground-state properties, and excitation gaps of a frustrated spin-Peierls chain, i.e., a spin-Peierls chain with both nearest-neighbor exchange ${\mathit{J}}_{1}$ and next-nearest-neighbor exchange ${\mathit{J}}_{2}$. The phase diagram is calculated using a bosonization renormalization-group method. We propose a bond-operator mean-field approximation to calculate the ground-state properties and excitation gaps.

DOI: 10.1103/physrevb.52.6723

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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

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arXiv:cond-mat/9507041 · Physical review. B, Condensed matter

Frustrated spin-Peierls chains

Jun Zang, A. R. Bishop, D. Schmeltzer

Published Sep 1, 1995• 22 citations

arXiv HTML PDF

Abstract

We study the phase diagram, ground-state properties, and excitation gaps of a frustrated spin-Peierls chain, i.e., a spin-Peierls chain with both nearest-neighbor exchange

{\mathit{J}}_{1}

and next-nearest-neighbor exchange

{\mathit{J}}_{2}

. The phase diagram is calculated using a bosonization renormalization-group method. We propose a bond-operator mean-field approximation to calculate the ground-state properties and excitation gaps.

DOI: 10.1103/physrevb.52.6723

Related papers

Density-matrix renormalization-group studies of the spin-1/2 Heisenberg system with dimerization and frustration

R. Chitra, Swapan Kumar Pati, H. R. Krishnamurthy +2 more

Using the density-matrix renormalization-group technique, we study the ground-state phase diagram and other low-energy properties of an isotropic antiferromagnetic spin-1/2 chain with both dimerization and frustration, i.e., an alternation \ensuremath{\delta} of the nearest-neighbor exchanges and a next-nearest-neighbor exchange ${\mathit{J}}_{2}$ . For \ensuremath{\delta}=0, the system is gapless for ${\mathit{J}}_{2}$ ${\mathit{J}}_{2\mathit{c}}$ and has a gap for ${\mathit{J}}_{2}$ > ${\mathit{J}}_{2\mathit{c}}$ where ${\mathit{J}}_{2\mathit{c}}$ is about 0.241. For ${\mathit{J}}_{2}$ = ${\mathit{J}}_{2\mathit{c}}$ , the gap above the ground state grows as \ensuremath{\delta} to the power 0.667\ifmmode\pm\else\textpm\fi{}0.001. In the ${\mathit{J}}_{2}$ -\ensuremath{\delta} plane, there is a disorder line 2 ${\mathit{J}}_{2}$ +\ensuremath{\delta}=1. To the left of this line, the peak in the static structure factor S(q) is at ${\mathit{q}}_{\mathrm{max}}$ =\ensuremath{\pi} (N\'eel phase), while to the right of the line, ${\mathit{q}}_{\mathrm{max}}$ decreases from \ensuremath{\pi} to \ensuremath{\pi}/2 as ${\mathit{J}}_{2}$ is increased to large values (spiral phase). For \ensuremath{\delta}=1, the system is equivalent to two coupled chains as on a ladder and it is gapped for all values of the interchain coupling.Using the density-matrix renormalization-group technique, we study the ground-state phase diagram and other low-energy properties of an isotropic antiferromagnetic spin-1/2 chain with both dimerization and frustration, i.e., an alternation \ensuremath{\delta} of the nearest-neighbor exchanges and a next-nearest-neighbor exchange ${\mathit{J}}_{2}$. For \ensuremath{\delta}=0, the system is gapless for ${\mathit{J}}_{2}$${\mathit{J}}_{2\mathit{c}}$ and has a gap for ${\mathit{J}}_{2}$>${\mathit{J}}_{2\mathit{c}}$ where ${\mathit{J}}_{2\mathit{c}}$ is about 0.241. For ${\mathit{J}}_{2}$=${\mathit{J}}_{2\mathit{c}}$, the gap above the ground state grows as \ensuremath{\delta} to the power 0.667\ifmmode\pm\else\textpm\fi{}0.001. In the ${\mathit{J}}_{2}$-\ensuremath{\delta} plane, there is a disorder line 2${\mathit{J}}_{2}$+\ensuremath{\delta}=1. To the left of this line, the peak in the static structure factor S(q) is at ${\mathit{q}}_{\mathrm{max}}$=\ensuremath{\pi} (N\'eel phase), while to the right of the line, ${\mathit{q}}_{\mathrm{max}}$ decreases from \ensuremath{\pi} to \ensuremath{\pi}/2 as ${\mathit{J}}_{2}$ is increased to large values (spiral phase). For \ensuremath{\delta}=1, the system is equivalent to two coupled chains as on a ladder and it is gapped for all values of the interchain coupling.

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Phase diagram of theXXZchain with next-nearest-neighbor interactions

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We calculate the quantum phase diagram of an XXZ chain with nearest-neighbor (NN) ${J}_{1}$ and next-NN exchange ${J}_{2}$ with anisotropies ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2},$ respectively. In particular we consider the case ${\ensuremath{\Delta}}_{1}=\ensuremath{-}{\ensuremath{\Delta}}_{2},$ to interpolate between the XX chain $({\ensuremath{\Delta}}_{i}=0)$ and the isotropic model with ferromagnetic phase ${J}_{2}.$ For ${\ensuremath{\Delta}}_{1}<\ensuremath{-}1,$ a ferromagnetic phase and two antiferromagnetic phases exist. For $|{\ensuremath{\Delta}}_{i}|<1,$ the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large ${J}_{2}{/J}_{1},$ this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for ${\ensuremath{\Delta}}_{1}={\ensuremath{\Delta}}_{2}=1$ suggests that a small gap is present.We calculate the quantum phase diagram of an XXZ chain with nearest-neighbor (NN) ${J}_{1}$ and next-NN exchange ${J}_{2}$ with anisotropies ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2},$ respectively. In particular we consider the case ${\ensuremath{\Delta}}_{1}=\ensuremath{-}{\ensuremath{\Delta}}_{2},$ to interpolate between the XX chain $({\ensuremath{\Delta}}_{i}=0)$ and the isotropic model with ferromagnetic phase ${J}_{2}.$ For ${\ensuremath{\Delta}}_{1}<\ensuremath{-}1,$ a ferromagnetic phase and two antiferromagnetic phases exist. For $|{\ensuremath{\Delta}}_{i}|<1,$ the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large ${J}_{2}{/J}_{1},$ this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for ${\ensuremath{\Delta}}_{1}={\ensuremath{\Delta}}_{2}=1$ suggests that a small gap is present.

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Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain

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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

Ground state of an Ising-type spin-1/2 chain with competing interactions

Takashi Tonegawa, H. Matsumoto, Toshiya Hikihara +1 more

The ground state of an Ising-type spin-1/2 chain with ferromagnetic bond-alternating nearest-neighbor and anti-ferromagnetic uniform next-nearest-neighbor interactions is studied by using the exact-diagonalization method and the density-matrix renormalization-group method. The Hamiltonian describing the system is expressed as H = Σi h2i1,2i J1 Σi h2i,2i+1 + J2 Σi hi,i+2 with hi,i' = γ(Six Si'x + Siy Si'y) + Siz Si'z, where J1 0, J2 0, and 1 > γ 0. Special attention is paid to the ground-state phase diagram on the J1 versus J2 plane for a given value of γ. The phase diagram is composed of the ferromagnetic, intermediate, and up-up-down-down phases, the intermediate phase being characterized by its magnetization, which takes finite but unsaturated values. The phase diagram obtained for γ = 0.5 shows that the region of the intermediate phase for a given value of J1 is widest when J1 = 1.0 and becomes narrower rather rapidly as J1 decreases or increases from 1.0. The J2-dependence of the ground-state magnetization for γ = 0.5 and J1 = 0.85 is also discussed. PACS Nos.: 75.10Jm, 75.40MgThe ground state of an Ising-type spin-1/2 chain with ferromagnetic bond-alternating nearest-neighbor and anti-ferromagnetic uniform next-nearest-neighbor interactions is studied by using the exact-diagonalization method and the density-matrix renormalization-group method. The Hamiltonian describing the system is expressed as H = Σi h2i1,2i J1 Σi h2i,2i+1 + J2 Σi hi,i+2 with hi,i' = γ(Six Si'x + Siy Si'y) + Siz Si'z, where J1 0, J2 0, and 1 > γ 0. Special attention is paid to the ground-state phase diagram on the J1 versus J2 plane for a given value of γ. The phase diagram is composed of the ferromagnetic, intermediate, and up-up-down-down phases, the intermediate phase being characterized by its magnetization, which takes finite but unsaturated values. The phase diagram obtained for γ = 0.5 shows that the region of the intermediate phase for a given value of J1 is widest when J1 = 1.0 and becomes narrower rather rapidly as J1 decreases or increases from 1.0. The J2-dependence of the ground-state magnetization for γ = 0.5 and J1 = 0.85 is also discussed. PACS Nos.: 75.10Jm, 75.40Mg

Canadian Journal of PhysicsJan 1, 20015 citations

We study the phase diagram, ground-state properties, and excitation gaps of a frustrated spin-Peierls chain, i.e., a spin-Peierls chain with both nearest-neighbor exchange

{\mathit{J}}_{1}

and next-nearest-neighbor exchange

{\mathit{J}}_{2}

. The phase diagram is calculated using a bosonization renormalization-group method. We propose a bond-operator mean-field approximation to calculate the ground-state properties and excitation gaps.

{\mathit{J}}_{2}

. For \ensuremath{\delta}=0, the system is gapless for

{\mathit{J}}_{2}

{\mathit{J}}_{2\mathit{c}}

and has a gap for

{\mathit{J}}_{2}

{\mathit{J}}_{2\mathit{c}}

where

{\mathit{J}}_{2\mathit{c}}

is about 0.241. For

{\mathit{J}}_{2}

{\mathit{J}}_{2\mathit{c}}

, the gap above the ground state grows as \ensuremath{\delta} to the power 0.667\ifmmode\pm\else\textpm\fi{}0.001. In the

{\mathit{J}}_{2}

-\ensuremath{\delta} plane, there is a disorder line 2

{\mathit{J}}_{2}

+\ensuremath{\delta}=1. To the left of this line, the peak in the static structure factor S(q) is at

{\mathit{q}}_{\mathrm{max}}

=\ensuremath{\pi} (N\'eel phase), while to the right of the line,

{\mathit{q}}_{\mathrm{max}}

decreases from \ensuremath{\pi} to \ensuremath{\pi}/2 as

{\mathit{J}}_{2}

is increased to large values (spiral phase). For \ensuremath{\delta}=1, the system is equivalent to two coupled chains as on a ladder and it is gapped for all values of the interchain coupling.

The ground state properties of an Ising chain with nearest (

{J}_{1}

) and next-nearest neighbor (

{J}_{2}

) interactions in a transverse field are investigated using the density matrix renormalization group and cluster mean-field theory methods. Its quantum phase diagram has two ordered regions (separated by a quantum disordered region), one of which has simple ferromagnetic or N\'eel order depending upon the sign of

{J}_{1}

, and the other is the double-staggered antiferromagnetic phase. The presence of the edge modes in these ordered phases is inferred by calculating the end-to-end spin-spin correlations on open chains. It is found that there occur four edge modes in the double-staggered phase, while the ferromagnetic and N\'eel phases support two edge modes, except very near

{J}_{1}=0

, where it seems they have four edge modes like the exact case at

{J}_{1}=0

itself.

We calculate the quantum phase diagram of an XXZ chain with nearest-neighbor (NN)

{J}_{1}

and next-NN exchange

{J}_{2}

with anisotropies ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2},$ respectively. In particular we consider the case ${\ensuremath{\Delta}}_{1}=\ensuremath{-}{\ensuremath{\Delta}}_{2},$ to interpolate between the XX chain $({\ensuremath{\Delta}}_{i}=0)$ and the isotropic model with ferromagnetic phase

{J}_{2}.

For ${\ensuremath{\Delta}}_{1}<\ensuremath{-}1,$ a ferromagnetic phase and two antiferromagnetic phases exist. For $|{\ensuremath{\Delta}}_{i}|<1,$ the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large

{J}_{2}{/J}_{1},

this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for ${\ensuremath{\Delta}}_{1}={\ensuremath{\Delta}}_{2}=1$ suggests that a small gap is present.

We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-

\frac{1}{2}

Luttinger liquid coupled by a Kondo exchange interaction

{J}_{K}

to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling

{J}_{1}

and a next-nearest-neighbor (frustrating) exchange interaction

{J}_{2}

. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling

{J}_{K}

with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios

{J}_{K}/{J}_{1}

{J}_{2}/{J}_{1}

, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.

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.