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

Journal of Physics Conference Series

Spin-1/2XXchain with three-site interactions: Spin-Peierls instability

Oleg Derzhko, Taras Krokhmalskii, Joachim Stolze, Taras Verkholyak

Published Mar 1, 2009• 0 citations
Publisher

Abstract

We discuss the effect of multisite interactions on the spin-Peierls instability for a spin-1/2 XX chain with three-site interactions of ( XZX + Y ZY )-type. By a Jordan-Wigner transformation we arrive at a model of spinless fermions on a chain with nearest-neighbor and next-nearest-neighbor hoppings. We compute the ground-state energy of the model for static lattice distortion patterns corresponding to dimerization and trimerization in order to identify the ground-state configuration of the lattice. The additional three-site interactions cause a number of new phases to appear in the ground-state phase diagram, including trimerized phases.

DOI
10.1088/1742-6596/150/4/042024

Related papers

Deformable spin- 12 XX chain with three-site interactions at zero and finite temperatures

Oleg Derzhko, Taras Krokhmalskii, Joachim Stolze +1 more

We study spin-Peierls structural lattice instabilities for a spin-1/2 isotropic $XY$ chain with three-site interactions of $(XZX+YZY)$ type. Within the adopted adiabatic treatment we have to examine the ground-state energy or the Helmholtz free energy of the spin chain with exchange couplings varying coherently with a possible static lattice distortion pattern. Since the considered spin model can be converted into a system of noninteracting spinless fermions the required ground-state energy or the Helmholtz free energy can be calculated accurately without making any approximations. We examine rigorously several lattice distortion patterns focusing on dimerized and trimerized ones, which owe their presence to the spin-Peierls mechanism. We present phase diagrams illustrating the effect of the three-site interaction on the spin-Peierls lattice distortions. Finally we discuss some properties of the deformable spin chain in the ground state and at finite temperatures. In particular, we examine the transverse magnetization, the static transverse susceptibility and the specific heat illustrating the changes in these quantities due to lattice instabilities.

Physical Review B•Mar 11, 2009•16 citations

Two-Dimensional Spin-1/2 J1 – J'1 – J2 Heisenberg Model within Jordan–Wigner Transformation

O. R. Baran, Taras Verkholyak

The Jordan–Wigner transformation is applied to the spatially anisotropic spin-1/2 Heisenberg model on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions. The transformed Hamiltonian describes the interacting spinless fermions that hop between neighbor sites in a gauge field. Using the mean-field-type approximation to both the direct interaction between fermions and the phase factors, which represent the gauge field, the problem is reduced to that concerning a free Fermi gas. Two types of antiferromagnetic ordering (the N´eel and collinear ones) are considered. By calculating the ground-state energies, the phase transitions induced by the interaction frustration were analyzed.

Ukrainian Journal of Physics•Jul 1, 2016•1 citation

Phase diagram of S=12XXZ chain with next-nearest-neighbor interaction

Shunsaku Hirata, K. Nomura

The ground-state properties of the one-dimensional $\mathrm{XXZ}$ model with next-nearest-neighbor coupling $\ensuremath{\alpha}$ and anisotropy $\ensuremath{\Delta}$ is studied. A direct transition between the ferromagnetic phase and the spontaneously dimerized phase is found. The effect of bond alternation which arises in realistic systems due to lattice distortion is discussed also. The results suggest that transitions between the ferromagnetic and spin-Peierls phases occur.

arXiv:cond-mat/9909290•Physical review. B, Condensed matter•Apr 1, 2000•30 citations

Dynamic properties of the spin- 12 XY chain with three-site interactions

Taras Krokhmalskii, Oleg Derzhko, Joachim Stolze +1 more

We consider a spin-$\frac{1}{2}$ $XY$ chain in a transverse $(z)$ field with multisite interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan--Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and, hence, the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model, which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First, we consider the $zz$ dynamic structure factor, reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum, which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the $xx$ dynamic structure factor, which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors, which are signatures of the presence of the three-site interactions.

arXiv:0812.4601•Physical Review B•May 2, 2008•43 citations

Quantum lattice fluctuations in the ground state of an XY spin-Peierls chain

H. Zheng

An analytical approach, based on the unitary transformation method, has been developed to study the effect of quantum lattice fluctuations on the ground state of an $\mathrm{XY}$ spin-Peierls chain, which is equivalent to the spinless Su-Schrieffer-Heeger model in half-filling after the Jordan-Wigner transformation. We show that when the spin-phonon coupling constant ${\ensuremath{\alpha}}^{2}/4K$ decreases or the phonon frequency ${\ensuremath{\omega}}_{\ensuremath{\pi}}$ increases, the lattice dimerization and the gap in the fermion spectrum decrease gradually. At some critical value $({\ensuremath{\alpha}}^{2}{/4K)}_{c}$ or ${\ensuremath{\omega}}_{\ensuremath{\pi}c},$ the system becomes gapless and the lattice dimerization disappears. This can be attributed to the fact that the ground state fails to develop the spin-Peierls long-range order because of the quantum lattice fluctuations.

Physical review. B, Condensed matter•Dec 1, 1997•18 citations

Frustrated mixed-spin chains: Three-site interactions and flat-band magnons

S. Seyedi, Fatemeh Heydarinasab, Jahanfar Abouie

We investigate the ground-state phase diagram of frustrated mixed-spin (1, 1/2) chains with three-site four-spin interactions employing different approaches, such as cluster mean field theory, cluster variational method, and spin-wave theory. The interplay of next-nearest-neighbor and three-site interactions leads to a plethora of magnetic and nonmagnetic phases in the ground-state phase diagram. We show that aside from the ferromagnetic and Neel orders, the ground state possesses a magnetic phase in which magnon excitations are dispersionless. The emergence of flat-band magnons is a consequence of the inhomogeneity of our frustrated mixed-spin chains and does not occur in similar uniform spin chains. We also demonstrate that the presence of three-site interaction gives rise to various nonmagnetic phases, such as antiferroquadrupole order and quantum spin-liquid phase.

Physical review. B./Physical review. B•Sep 14, 2022•2 citations
We discuss the effect of multisite interactions on the spin-Peierls instability for a spin-1/2 XX chain with three-site interactions of ( XZX + Y ZY )-type. By a Jordan-Wigner transformation we arrive at a model of spinless fermions on a chain with nearest-neighbor and next-nearest-neighbor hoppings. We compute the ground-state energy of the model for static lattice distortion patterns corresponding to dimerization and trimerization in order to identify the ground-state configuration of the lattice. The additional three-site interactions cause a number of new phases to appear in the ground-state phase diagram, including trimerized phases.
We study spin-Peierls structural lattice instabilities for a spin-1/2 isotropic XYXYXY chain with three-site interactions of (XZX+YZY)(XZX+YZY)(XZX+YZY) type. Within the adopted adiabatic treatment we have to examine the ground-state energy or the Helmholtz free energy of the spin chain with exchange couplings varying coherently with a possible static lattice distortion pattern. Since the considered spin model can be converted into a system of noninteracting spinless fermions the required ground-state energy or the Helmholtz free energy can be calculated accurately without making any approximations. We examine rigorously several lattice distortion patterns focusing on dimerized and trimerized ones, which owe their presence to the spin-Peierls mechanism. We present phase diagrams illustrating the effect of the three-site interaction on the spin-Peierls lattice distortions. Finally we discuss some properties of the deformable spin chain in the ground state and at finite temperatures. In particular, we examine the transverse magnetization, the static transverse susceptibility and the specific heat illustrating the changes in these quantities due to lattice instabilities.
The Jordan–Wigner transformation is applied to the spatially anisotropic spin-1/2 Heisenberg model on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions. The transformed Hamiltonian describes the interacting spinless fermions that hop between neighbor sites in a gauge field. Using the mean-field-type approximation to both the direct interaction between fermions and the phase factors, which represent the gauge field, the problem is reduced to that concerning a free Fermi gas. Two types of antiferromagnetic ordering (the N´eel and collinear ones) are considered. By calculating the ground-state energies, the phase transitions induced by the interaction frustration were analyzed.
The ground-state properties of the one-dimensional XXZ\mathrm{XXZ}XXZ model with next-nearest-neighbor coupling $\ensuremath{\alpha}$ and anisotropy $\ensuremath{\Delta}$ is studied. A direct transition between the ferromagnetic phase and the spontaneously dimerized phase is found. The effect of bond alternation which arises in realistic systems due to lattice distortion is discussed also. The results suggest that transitions between the ferromagnetic and spin-Peierls phases occur.
We consider a spin-12\frac{1}{2}21​ XYXYXY chain in a transverse (z)(z)(z) field with multisite interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan--Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and, hence, the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model, which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First, we consider the zzzzzz dynamic structure factor, reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum, which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xxxxxx dynamic structure factor, which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors, which are signatures of the presence of the three-site interactions.
An analytical approach, based on the unitary transformation method, has been developed to study the effect of quantum lattice fluctuations on the ground state of an XY\mathrm{XY}XY spin-Peierls chain, which is equivalent to the spinless Su-Schrieffer-Heeger model in half-filling after the Jordan-Wigner transformation. We show that when the spin-phonon coupling constant ${\ensuremath{\alpha}}^{2}/4K$ decreases or the phonon frequency ${\ensuremath{\omega}}_{\ensuremath{\pi}}$ increases, the lattice dimerization and the gap in the fermion spectrum decrease gradually. At some critical value $({\ensuremath{\alpha}}^{2}{/4K)}_{c}$ or ${\ensuremath{\omega}}_{\ensuremath{\pi}c},$ the system becomes gapless and the lattice dimerization disappears. This can be attributed to the fact that the ground state fails to develop the spin-Peierls long-range order because of the quantum lattice fluctuations.
We investigate the ground-state phase diagram of frustrated mixed-spin (1, 1/2) chains with three-site four-spin interactions employing different approaches, such as cluster mean field theory, cluster variational method, and spin-wave theory. The interplay of next-nearest-neighbor and three-site interactions leads to a plethora of magnetic and nonmagnetic phases in the ground-state phase diagram. We show that aside from the ferromagnetic and Neel orders, the ground state possesses a magnetic phase in which magnon excitations are dispersionless. The emergence of flat-band magnons is a consequence of the inhomogeneity of our frustrated mixed-spin chains and does not occur in similar uniform spin chains. We also demonstrate that the presence of three-site interaction gives rise to various nonmagnetic phases, such as antiferroquadrupole order and quantum spin-liquid phase.