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

Acta Physica Polonica A

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

M. Topilko, Oleg Derzhko, Taras Krokhmalskii

Published Jun 1, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.119.868

Related papers

Spin-1/2 XX Chains with Three-Spin Interactions

Taras Krokhmalskii, Oleg Derzhko, Taras Verkholyak +1 more

We consider a spin-1/2 XX chain with three-spin interactions which is equivalent to a system of noninteracting spinless fermions.We examine some dynamic quantities of the spin model.In particular,we calculate analytically the dynamic transverse (zz) structure factor which is governed by a two-fermion excitation continuum.Moreover,we compute numerically the dynamic xx structure factor which is a many-fermion dynamic quantity.We illustrate how the three-spin interactions manifest themselves in the dynamic probes.

Acta Physica Polonica A•Jan 1, 2008•3 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

Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction

Oleg Derzhko, Taras Verkholyak, Taras Krokhmalskii +1 more

We consider the spin-$\frac{1}{2}$ anisotropic $XY$ chain in a transverse $(z)$ field with the Dzyaloshinskii-Moriya interaction directed along the $z$ axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the $zz$, $xx$, and $yy$ dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures.

arXiv:0712.3361•Physical Review B•Jun 6, 2006•51 citations

Dynamics of dimer and z spin component fluctuations in spin-1/2 XY chain

Oleg Derzhko, Taras Krokhmalskii, Petro A. Hlushak

One-dimensional quantum spin-1/2 XY models admit the rigorous analysis not only of their static properties (i.e. the thermodynamic quantities and the equal-time spin correlation functions) but also of their dynamic properties (i.e. the different-time spin correlation functions, the dynamic susceptibilities, the dynamic structure factors).This becomes possible after exploiting the Jordan-Wigner transformation which reduces the spin model to a model of spinless noninteracting fermions.A number of dynamic quantities (e.g.related to transverse spin operator or dimer operator fluctuations) are entirely determined by two-fermion excitations and can be examined in much detail.We consider the spin-1/2 XY chain in a transverse ( z) magnetic field with the Hamiltonianand calculate the dynamic structure factorsis the dimer operator.The results for the dynamic transverse structure factor S zz (κ, ω) and for the dynamic dimer structure factor S DD (κ, ω) are known, whereas the analysis of the dynamic structure factor S zD (κ, ω) = (S Dz (κ, ω)) has not been reported so far.We compare different two-fermion dynamic quantities contrasting their generic and specific features.

Condensed Matter Physics•Jan 1, 2005•0 citations

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY–YZX three-site interactions

Kaiyuan Cao, Ming Zhong, Peiqing Tong

We study the dynamical quantum phase transitions (DQPTs) in the XY chains with the Dzyaloshinskii–Moriya interaction and the XZY–YZX type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan–Wigner and Bogoliubov transformations with the form H = ∑ k ε k ( η k † η k − 1 2 ) , where the quasiparticle excitation spectra εk may be smaller than 0 for some k and are asymmetrical (εk ≠ ε –k ). It is found that the factors of Loschmidt echo equal 1 for some k corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying εk ⋅ ε –k < 0, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.

Chinese Physics B•Jan 12, 2022•8 citations

Dynamic properties of the dimerized spin-½ isotropicXYchain in a transverse field

Oleg Derzhko, Taras Krokhmalskii, Joachim Stolze

The zz and xx ( yy ) dynamic structure factors of the dimerized spin-½ isotropic XY chain in a transverse ( z ) field are calculated for arbitrary temperatures. The zz structure factor can be given in analytical terms, involving a single integration, whereas the xx dynamic structure factor can be evaluated completely numerically for very long chains. We compare the two structure factors and discuss in some detail how a dimerization manifests itself in the dynamic structure factors at different external fields and temperatures. We compare our results to corresponding results for the dimerized Heisenberg chain obtained by approximate techniques.

Journal of Physics A Mathematical and General•Apr 12, 2002•12 citations
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.
We consider a spin-1/2 XX chain with three-spin interactions which is equivalent to a system of noninteracting spinless fermions.We examine some dynamic quantities of the spin model.In particular,we calculate analytically the dynamic transverse (zz) structure factor which is governed by a two-fermion excitation continuum.Moreover,we compute numerically the dynamic xx structure factor which is a many-fermion dynamic quantity.We illustrate how the three-spin interactions manifest themselves in the dynamic probes.
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.
We consider the spin-12\frac{1}{2}21​ anisotropic XYXYXY chain in a transverse (z)(z)(z) field with the Dzyaloshinskii-Moriya interaction directed along the zzz axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the zzzzzz, xxxxxx, and yyyyyy dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures.
One-dimensional quantum spin-1/2 XY models admit the rigorous analysis not only of their static properties (i.e. the thermodynamic quantities and the equal-time spin correlation functions) but also of their dynamic properties (i.e. the different-time spin correlation functions, the dynamic susceptibilities, the dynamic structure factors).This becomes possible after exploiting the Jordan-Wigner transformation which reduces the spin model to a model of spinless noninteracting fermions.A number of dynamic quantities (e.g.related to transverse spin operator or dimer operator fluctuations) are entirely determined by two-fermion excitations and can be examined in much detail.We consider the spin-1/2 XY chain in a transverse ( z) magnetic field with the Hamiltonianand calculate the dynamic structure factorsis the dimer operator.The results for the dynamic transverse structure factor S zz (κ, ω) and for the dynamic dimer structure factor S DD (κ, ω) are known, whereas the analysis of the dynamic structure factor S zD (κ, ω) = (S Dz (κ, ω)) has not been reported so far.We compare different two-fermion dynamic quantities contrasting their generic and specific features.
We study the dynamical quantum phase transitions (DQPTs) in the XY chains with the Dzyaloshinskii–Moriya interaction and the XZY–YZX type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan–Wigner and Bogoliubov transformations with the form H = ∑ k ε k ( η k † η k − 1 2 ) , where the quasiparticle excitation spectra εk may be smaller than 0 for some k and are asymmetrical (εk ≠ ε –k ). It is found that the factors of Loschmidt echo equal 1 for some k corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying εk ⋅ ε –k < 0, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.
The zz and xx ( yy ) dynamic structure factors of the dimerized spin-½ isotropic XY chain in a transverse ( z ) field are calculated for arbitrary temperatures. The zz structure factor can be given in analytical terms, involving a single integration, whereas the xx dynamic structure factor can be evaluated completely numerically for very long chains. We compare the two structure factors and discuss in some detail how a dimerization manifests itself in the dynamic structure factors at different external fields and temperatures. We compare our results to corresponding results for the dimerized Heisenberg chain obtained by approximate techniques.