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

Physical Review B

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

Oleg Derzhko, Taras Krokhmalskii, Joachim Stolze, Taras Verkholyak

Published Mar 11, 2009• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.79.094410

Related papers

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

Oleg Derzhko, Taras Krokhmalskii, Joachim Stolze +1 more

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.

Journal of Physics Conference Series•Mar 1, 2009•0 citations

Regularly alternating spin- 12 anisotropic XY chains: The ground-state and thermodynamic properties

Oleg Derzhko, Johannes Richter, Taras Krokhmalskii +1 more

Using the Jordan-Wigner transformation and continued fractions we calculate rigorously the thermodynamic quantities for the spin-1/2 transverse Ising chain with periodically varying intersite interactions and/or on-site fields. We consider in detail the properties of the chains having a period of the transverse field modulation equal to 3. The regularly alternating transverse Ising chain exhibits several quantum phase transition points, where the number of transition points for a given period of alternation strongly depends on the specific set of the Hamiltonian parameters. The critical behavior in most cases is the same as for the uniform chain. However, for certain sets of the Hamiltonian parameters the critical behavior may be changed and weak singularities in the ground-state quantities appear. Due to the regular alternation of the Hamiltonian parameters the transverse Ising chain may exhibit plateaulike steps in the zero-temperature dependence of the transverse magnetization vs transverse field and many-peak temperature profiles of the specific heat. We compare the ground-state properties of regularly alternating transverse Ising and transverse XX chains and of regularly alternating quantum and classical chains. Making use of the corresponding unitary transformations we extend the elaborated approach to the study of thermodynamics of regularly alternating spin-1/2 anisotropic XY chains without field. We use the exact expression for the ground-state energy of such a chain of period 2 to discuss how the exchange interaction anisotropy destroys the spin-Peierls dimerized phase.

arXiv:cond-mat/0408033•Physical Review E•Jun 4, 2004•19 citations

Dynamic Properties of Spin-1/2 XX Chain with Three-Site Interactions of (XZY - YZX)-Type

M. Topilko, Oleg Derzhko, Taras Krokhmalskii

We consider the spin-1/2 isotropic XY chain in a transverse field with three-site interactions of (XZY -Y ZX)--type, which can be transformed into a system of noninteracting spinless fermions.We study dynamic properties of the spin model.In particular, we calculate the dynamic structure factors which are governed by a two-fermion excitation continuum.We demonstrate how the three-site interactions manifest themselves in the dynamic properties of the quantum spin chain.

Acta Physica Polonica A•Jun 1, 2011•0 citations

Thermal Phase Transitions in a Deformable Quantum Spin-1/2 XX Chain in a Transverse Magnetic Field

Dávid Sivý, Jozef Strečka

We investigate the deformable quantum spin-1/2 XX chain in a transverse magnetic field, which is exactly solvable via the Jordan-Wigner transformation under the assumption of a linear dependence of the exchange interaction on uniform lattice distortion. By calculating the magnetization, magnetic susceptibility, distortion parameter, and inverse compressibility, we explore the coupled magnetic and elastic properties of the deformable quantum spin chain. It is demonstrated that the deformable spin-1/2 XX chain in a transverse magnetic field exhibits a line of discontinuous phase transitions emerging at low but finite temperatures, which terminates at a critical point corresponding to a continuous phase transition. The discontinuous thermal phase transitions are accompanied by magnetic hysteresis due to metastable states, which gradually vanishes as the temperature increases.

IEEE Transactions on Magnetics•Nov 3, 2025•0 citations

Spin-Peierls instability in a quantum spin chain with Dzyaloshinskii-Moriya interaction

Oleg Derzhko, Johannes Richter, O. Zaburannyi

We analysed the ground-state energy of some dimerized spin-1/2 transverse XX and Heisenberg chains with Dzyaloshinskii-Moriya (DM) interaction to study the influence of the latter interaction on the spin-Peierls instability. We found that DM interaction may act either in favour of the dimerization or against it. The actual result depends on the dependence of the DM interaction on the distortion amplitude in comparison with such dependence for the isotropic exchange interaction.

arXiv:cond-mat/0010118•Journal of Physics Condensed Matter•Sep 19, 2000•22 citations

Incommensurate Spin-Peierls Phases in the One-Dimensional Quantum Isotropic XY Model

Oleg Derzhko, Taras Krokhmalskii

Using the numerical approach for a study of the thermodynamic properties of the nonuniform one-dimensional spin-1/2 isotropic XY model in a transverse field we examine different lattice distortions to reveal which spin-Peierls phases are realized in the magnetic chain at zero temperature in the presence of external field.

arXiv:cond-mat/0009331•Sep 21, 2000•0 citations
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.
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.
Using the Jordan-Wigner transformation and continued fractions we calculate rigorously the thermodynamic quantities for the spin-1/2 transverse Ising chain with periodically varying intersite interactions and/or on-site fields. We consider in detail the properties of the chains having a period of the transverse field modulation equal to 3. The regularly alternating transverse Ising chain exhibits several quantum phase transition points, where the number of transition points for a given period of alternation strongly depends on the specific set of the Hamiltonian parameters. The critical behavior in most cases is the same as for the uniform chain. However, for certain sets of the Hamiltonian parameters the critical behavior may be changed and weak singularities in the ground-state quantities appear. Due to the regular alternation of the Hamiltonian parameters the transverse Ising chain may exhibit plateaulike steps in the zero-temperature dependence of the transverse magnetization vs transverse field and many-peak temperature profiles of the specific heat. We compare the ground-state properties of regularly alternating transverse Ising and transverse XX chains and of regularly alternating quantum and classical chains. Making use of the corresponding unitary transformations we extend the elaborated approach to the study of thermodynamics of regularly alternating spin-1/2 anisotropic XY chains without field. We use the exact expression for the ground-state energy of such a chain of period 2 to discuss how the exchange interaction anisotropy destroys the spin-Peierls dimerized phase.
We investigate the deformable quantum spin-1/2 XX chain in a transverse magnetic field, which is exactly solvable via the Jordan-Wigner transformation under the assumption of a linear dependence of the exchange interaction on uniform lattice distortion. By calculating the magnetization, magnetic susceptibility, distortion parameter, and inverse compressibility, we explore the coupled magnetic and elastic properties of the deformable quantum spin chain. It is demonstrated that the deformable spin-1/2 XX chain in a transverse magnetic field exhibits a line of discontinuous phase transitions emerging at low but finite temperatures, which terminates at a critical point corresponding to a continuous phase transition. The discontinuous thermal phase transitions are accompanied by magnetic hysteresis due to metastable states, which gradually vanishes as the temperature increases.