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

Condensed Matter Physics

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

Oleg Derzhko, Taras Krokhmalskii, Petro A. Hlushak

Published Jan 1, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.5488/cmp.8.4.859

Related papers

Jordan-Wigner Fermions and Dynamic Probes of Quantum Spin Chains

Oleg Derzhko, Taras Verkholyak

With the help of the Jordan–Wigner transformation the spin-12 XY chains can be reformulated in terms of noninteracting spinless fermions and, as a result, many statistical-mechanics calculations can be performed rigorously, i.e. without making any simplifying approximations. We are interested in dynamic properties of such chains (time-dependent spin correlation functions, dynamic structure factors, dynamic susceptibilities) which are of great importance for interpretation of experimental data. We have worked out a number of dynamic quantities explicitly as well as have performed a general analysis of the two-fermion continua which are relevant for different dynamic quantities.

Presented at•Jan 1, 2003•0 citations

JORDAN-WIGNER FERMIONIZATION AND THE THEORY OF LOW-DIMENSIONAL QUANTUM SPIN MODELS. DYNAMIC PROPERTIES

Oleg Derzhko

The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner fermionization technique for calculating dynamic quantities of low-dimensional quantum spin models. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one-half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several lowdimensional quantum spin models. We start from the famous s = 1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to the dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two-fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four-fermion excitation continua. The four-fermion dynamic quantities are of intermediate complexity between simple two-fermion (like the zz dynamic structure factor) and enormously complex multi-fermion (like the xx or xy dynamic structure factors) dynamic quantities. Further we discuss the effects of dimerization, anisotropy of XY interaction, and additional Dzyaloshinskii-Moriya interaction on various dynamic quantities. Finally we consider the dynamic transverse spin structure factor Szz(k, ω) for the s = 1/2 XX model on a spatially anisotropic square lattice which allows one to trace a one-to-two-dimensional crossover in dynamic quantities.

•Jan 1, 2008•2 citations

JORDAN-WIGNER FERMIONIZATION AND THE THEORY OF LOW-DIMENSIONAL QUANTUM SPIN MODELS.: DYNAMIC PROPERTIES

O. DERZHKO

The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner fermionization technique for calculating dynamic quantities of low-dimensional quantum spin models. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one-half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several low-dimensional quantum spin models. We start from the famous s=1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to the dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two-fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four-fermion excitation continua. The four-fermion dynamic quantities are of intermediate complexity between simple two-fermion (like the zz dynamic structure factor) and enormously complex multi-fermion (like the xx or xy dynamic structure factors) dynamic quantities. Further we discuss the effects of dimerization, anisotropy of XY interaction, and additional Dzyaloshinskii-Moriya interaction on various dynamic quantities. Finally we consider the dynamic transverse spin structure factor $S_{zz}({\bf{k}},ω)$ for the s=1/2 XX model on a spatially anisotropic square lattice which allows one to trace a one-to-two-dimensional crossover in dynamic quantities.

arXiv:0812.4750•Jun 1, 2008•3 citations

Dimer and trimer fluctuations in the s=12 transverse XX chain

Oleg Derzhko, Taras Krokhmalskii, Joachim Stolze +1 more

Exact results for the dynamic dimer and trimer structure factors of the one-dimensional $s=\frac{1}{2}\phantom{\rule{0.3em}{0ex}}XX$ model in a transverse magnetic field $(\ensuremath{\Vert}z)$ are presented and discussed in relation to known exact results for the dynamic spin structure factors. In the framework of the Jordan-Wigner representation, the accessible spectrum of the dimer fluctuation operator is limited to two-fermion excitations, whereas that of the trimer fluctuation operator involves two- and four-fermion excitations. The spectral boundaries, soft modes, and singularity structure of the four-fermion excitation continuum as probed by the dynamic trimer structure factor are examined and compared to corresponding properties of the two-fermion excitation continuum, as probed by the dynamic dimer and transverse spin structure factors.

arXiv:cond-mat/0507203•Physical Review B•Mar 31, 2005•7 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 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
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.
With the help of the Jordan–Wigner transformation the spin-12 XY chains can be reformulated in terms of noninteracting spinless fermions and, as a result, many statistical-mechanics calculations can be performed rigorously, i.e. without making any simplifying approximations. We are interested in dynamic properties of such chains (time-dependent spin correlation functions, dynamic structure factors, dynamic susceptibilities) which are of great importance for interpretation of experimental data. We have worked out a number of dynamic quantities explicitly as well as have performed a general analysis of the two-fermion continua which are relevant for different dynamic quantities.
The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner fermionization technique for calculating dynamic quantities of low-dimensional quantum spin models. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one-half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several lowdimensional quantum spin models. We start from the famous s = 1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to the dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two-fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four-fermion excitation continua. The four-fermion dynamic quantities are of intermediate complexity between simple two-fermion (like the zz dynamic structure factor) and enormously complex multi-fermion (like the xx or xy dynamic structure factors) dynamic quantities. Further we discuss the effects of dimerization, anisotropy of XY interaction, and additional Dzyaloshinskii-Moriya interaction on various dynamic quantities. Finally we consider the dynamic transverse spin structure factor Szz(k, ω) for the s = 1/2 XX model on a spatially anisotropic square lattice which allows one to trace a one-to-two-dimensional crossover in dynamic quantities.
The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner fermionization technique for calculating dynamic quantities of low-dimensional quantum spin models. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one-half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several low-dimensional quantum spin models. We start from the famous s=1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to the dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two-fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four-fermion excitation continua. The four-fermion dynamic quantities are of intermediate complexity between simple two-fermion (like the zz dynamic structure factor) and enormously complex multi-fermion (like the xx or xy dynamic structure factors) dynamic quantities. Further we discuss the effects of dimerization, anisotropy of XY interaction, and additional Dzyaloshinskii-Moriya interaction on various dynamic quantities. Finally we consider the dynamic transverse spin structure factor Szz(k,ω)S_{zz}({\bf{k}},ω)Szz​(k,ω) for the s=1/2 XX model on a spatially anisotropic square lattice which allows one to trace a one-to-two-dimensional crossover in dynamic quantities.
Exact results for the dynamic dimer and trimer structure factors of the one-dimensional s=12XXs=\frac{1}{2}\phantom{\rule{0.3em}{0ex}}XXs=21​XX model in a transverse magnetic field $(\ensuremath{\Vert}z)$ are presented and discussed in relation to known exact results for the dynamic spin structure factors. In the framework of the Jordan-Wigner representation, the accessible spectrum of the dimer fluctuation operator is limited to two-fermion excitations, whereas that of the trimer fluctuation operator involves two- and four-fermion excitations. The spectral boundaries, soft modes, and singularity structure of the four-fermion excitation continuum as probed by the dynamic trimer structure factor are examined and compared to corresponding properties of the two-fermion excitation continuum, as probed by the dynamic dimer and transverse spin structure factors.
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.
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.