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

arXiv:0711.0569 · Physical Review B

Thermodynamic properties of the XXZ model in a transverse field

Mohammad Siahatgar, A. Langari

Published Feb 27, 2008• 9 citations
arXivHTMLPDF

Abstract

We have numerically studied the thermodynamic properties of the spin $\frac{1}{2}$ $XXZ$ chain in the presence of a transverse (noncommuting) magnetic field. The thermal, field dependence of specific heat and correlation functions for chains up to 20 sites has been calculated. The area where the specific heat decays exponentially is considered as a measure of the energy gap. We have also obtained the exchange interaction between chains in a bulk material using the random phase approximation and derived the phase diagram of the three-dimensional material with this approximation. The behavior of the structure factor at different momenta verifies the antiferromagnetic long-range order in the $y$ direction for the three-dimensional case. Moreover, we have concluded that the low temperature Lanczos results [M. Aichhorn et al., Phys. Rev. B 67, 161103(R) (2003)] are more accurate for low temperatures and closer to the full diagonalization ones than the results of finite temperature Lanczos method [J. Jaklic and P. Prelovsek, Phys. Rev. B 49, 5065 (1994)].

DOI
10.1103/physrevb.77.054435

Related papers

Thermodynamic Properties of the Transverse-Crystal-Field Ising Model on a Chain: -- Three Peak Structure in the Specific Heat --

Y. Fukumoto, Akihide Oguchi

The specific heat of the S = 1 transverse-crystal-field Ising model with an antiferro-magnetic exchange interaction J on a ∆-chain is studied by using the exact-diagonalization, quantum Monte Carlo and finite-temperature Lanczos methods. We find that when the strength of the transverse crystal field Γ is chosen to be sufficiently small, the specific heat exhibits a three-peak structure as a function of temperature, with peaks at T ∼ 0.05Γ, 0.2Γ and 0.7J. In addition to the two energy scales Γ and J, a new energy scale ∼ 0.1 × Γ appears due to the geometrical frustration and the existence of the Sz = 0 states in the present system. Geometrically frustrated spin systems have attracted considerable attention for a long time. It is expected that the introduction of quantum fluctuations into a clas-sically degenerate manifold leads to exotic properties of ground states and thermo-dynamics. From this point of view, S = 1/2 transverse-field Ising antiferromagnets

Progress of Theoretical Physics•May 1, 2006•2 citations

Thermodynamic properties of the XXZ ferromagnetic chain with long-range interactions

Lei Shu-guo

The one-dimensional spin-1/2 Heisenberg XXZ ferromagnetic chain with uniform long-range interactions among the z components of the spins in the transverse field was studied by using the mean-field Jordan-Wigner transformation.The analytic expressions and the numerical results of the thermodynamic quantities,including the Helmholtz free energy,internal energy,specific heat,magnetization and isothermal susceptibility,were obtained.We also discussed the phase transitions of the system at a finite temperature.Our results agreed with that from other literatures in the degenerate condition.

Journal of Anhui University•Jan 1, 2008•0 citations

Thermodynamic behavior of theXXZHeisenbergs= 1/2 chain around the factorizing magnetic field

Jahanfar Abouie, A. Langari, Mohammad Siahatgar

We have investigated the zero-and finite-temperature behaviors of the anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of a transverse magnetic field (h). The attention is concentrated on an interval of magnetic field between the factorizing field (h(f)) and the critical one (h(c)). The model presents a spin-flop phase for 0 < h < h(f) with an energy scale which is defined by the long range antiferromagnetic order while it undergoes an entanglement phase transition at h = h(f). The entanglement estimators clearly show that the entanglement is lost exactly at h = h(f), which justifies different quantum correlations on both sides of the factorizing field. As a consequence of zero entanglement (at h = h(f)) the ground state is known exactly as a product of single-particle states which is the starting point for initiating a spin wave theory. The linear spin wave theory is implemented to obtain the specific heat and thermal entanglement of the model in the interested region. A double-peak structure is found in the specific heat around h = h(f), which manifests the existence of two energy scales in the system as a result of two competing orders before the critical point. These results are confirmed by the low temperature Lanczos data which we have computed.

arXiv:0809.1987•Journal of Physics Condensed Matter•May 5, 2010•14 citations

Magnetic Properties of an Antiferromagnetic Spin-1/2 XYZ Model in the Presence of Different Magnetic Fields: Finite-Size Effects of Inhomogeneity Property*

Hamid Arian Zad, Azam Zoshki, Moones Sabeti

Abstract Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility, and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse, and transverse staggered magnetic fields. The magnetization, susceptibility, and the specific heat of the model are investigated under two conditions separately: (i) When the model is putted in the presence of homogeneous magnetic fields. (ii) When finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak, and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.

arXiv:1812.11468•Communications in Theoretical Physics•Oct 1, 2019•3 citations

Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

Ozan S. Sarıyer

Phase diagram, critical properties and thermodynamic functions of the two-dimensional field-free quantum-spin-1/2 XXZ model has been calculated globally using a numerical renormalisation group theory. The nearest-neighbour spin-spin correlations and entanglement properties, as well as internal energy and specific heat are calculated globally at all temperatures for the whole range of exchange interaction anisotropy, from XY limit to Ising limits, for both antiferromagnetic and ferromagnetic cases. We show that there exists long-range (quasi-long-range) order at low-temperatures, and the low-lying excitations are gapped (gapless) in the Ising-like easy-axis (XY-like easy-plane) regime. Besides, we identify quantum phase transitions at zero-temperature.

arXiv:1807.03250•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Apr 17, 2019•36 citations

Finite-temperature and dynamical properties of the random transverse-field Ising spin chain

A. P. Young

We study numerically the paramagnetic phase of the spin-$1/2$ random transverse-field Ising chain, using a mapping to noninteracting fermions. We extend our earlier work, Phys. Rev. B 53, 8486 (1996), to finite temperatures and to dynamical properties. Our results are consistent with the idea that there are Griffiths-McCoy singularities in the paramagnetic phase described by a continuously varying exponent $z(\ensuremath{\delta}),$ where \ensuremath{\delta} measures the deviation from criticality. There are some discrepancies between the values of $z(\ensuremath{\delta})$ obtained from different quantities, but this may be due to corrections to scaling. The average on-site time dependent correlation function decays with a power law in the paramagnetic phase, namely, ${\ensuremath{\tau}}^{\ensuremath{-}1/z(\ensuremath{\delta})},$ where \ensuremath{\tau} is imaginary time. However, the typical value decays with a stretched exponential behavior, $\mathrm{exp}(\ensuremath{-}c{\ensuremath{\tau}}^{1/\ensuremath{\mu}}),$ where \ensuremath{\mu} may be related to $z(\ensuremath{\delta}).$ We also obtain results for the full probability distribution of time dependent correlation functions at different points in the paramagnetic phase.

arXiv:cond-mat/9707060•Physical review. B, Condensed matter•Nov 1, 1997•58 citations
We have numerically studied the thermodynamic properties of the spin 12\frac{1}{2}21​ XXZXXZXXZ chain in the presence of a transverse (noncommuting) magnetic field. The thermal, field dependence of specific heat and correlation functions for chains up to 20 sites has been calculated. The area where the specific heat decays exponentially is considered as a measure of the energy gap. We have also obtained the exchange interaction between chains in a bulk material using the random phase approximation and derived the phase diagram of the three-dimensional material with this approximation. The behavior of the structure factor at different momenta verifies the antiferromagnetic long-range order in the yyy direction for the three-dimensional case. Moreover, we have concluded that the low temperature Lanczos results [M. Aichhorn et al., Phys. Rev. B 67, 161103(R) (2003)] are more accurate for low temperatures and closer to the full diagonalization ones than the results of finite temperature Lanczos method [J. Jaklic and P. Prelovsek, Phys. Rev. B 49, 5065 (1994)].
The specific heat of the S = 1 transverse-crystal-field Ising model with an antiferro-magnetic exchange interaction J on a ∆-chain is studied by using the exact-diagonalization, quantum Monte Carlo and finite-temperature Lanczos methods. We find that when the strength of the transverse crystal field Γ is chosen to be sufficiently small, the specific heat exhibits a three-peak structure as a function of temperature, with peaks at T ∼ 0.05Γ, 0.2Γ and 0.7J. In addition to the two energy scales Γ and J, a new energy scale ∼ 0.1 × Γ appears due to the geometrical frustration and the existence of the Sz = 0 states in the present system. Geometrically frustrated spin systems have attracted considerable attention for a long time. It is expected that the introduction of quantum fluctuations into a clas-sically degenerate manifold leads to exotic properties of ground states and thermo-dynamics. From this point of view, S = 1/2 transverse-field Ising antiferromagnets
The one-dimensional spin-1/2 Heisenberg XXZ ferromagnetic chain with uniform long-range interactions among the z components of the spins in the transverse field was studied by using the mean-field Jordan-Wigner transformation.The analytic expressions and the numerical results of the thermodynamic quantities,including the Helmholtz free energy,internal energy,specific heat,magnetization and isothermal susceptibility,were obtained.We also discussed the phase transitions of the system at a finite temperature.Our results agreed with that from other literatures in the degenerate condition.
We have investigated the zero-and finite-temperature behaviors of the anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of a transverse magnetic field (h). The attention is concentrated on an interval of magnetic field between the factorizing field (h(f)) and the critical one (h(c)). The model presents a spin-flop phase for 0 < h < h(f) with an energy scale which is defined by the long range antiferromagnetic order while it undergoes an entanglement phase transition at h = h(f). The entanglement estimators clearly show that the entanglement is lost exactly at h = h(f), which justifies different quantum correlations on both sides of the factorizing field. As a consequence of zero entanglement (at h = h(f)) the ground state is known exactly as a product of single-particle states which is the starting point for initiating a spin wave theory. The linear spin wave theory is implemented to obtain the specific heat and thermal entanglement of the model in the interested region. A double-peak structure is found in the specific heat around h = h(f), which manifests the existence of two energy scales in the system as a result of two competing orders before the critical point. These results are confirmed by the low temperature Lanczos data which we have computed.
Abstract Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility, and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse, and transverse staggered magnetic fields. The magnetization, susceptibility, and the specific heat of the model are investigated under two conditions separately: (i) When the model is putted in the presence of homogeneous magnetic fields. (ii) When finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak, and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.
Phase diagram, critical properties and thermodynamic functions of the two-dimensional field-free quantum-spin-1/2 XXZ model has been calculated globally using a numerical renormalisation group theory. The nearest-neighbour spin-spin correlations and entanglement properties, as well as internal energy and specific heat are calculated globally at all temperatures for the whole range of exchange interaction anisotropy, from XY limit to Ising limits, for both antiferromagnetic and ferromagnetic cases. We show that there exists long-range (quasi-long-range) order at low-temperatures, and the low-lying excitations are gapped (gapless) in the Ising-like easy-axis (XY-like easy-plane) regime. Besides, we identify quantum phase transitions at zero-temperature.
We study numerically the paramagnetic phase of the spin-1/21/21/2 random transverse-field Ising chain, using a mapping to noninteracting fermions. We extend our earlier work, Phys. Rev. B 53, 8486 (1996), to finite temperatures and to dynamical properties. Our results are consistent with the idea that there are Griffiths-McCoy singularities in the paramagnetic phase described by a continuously varying exponent $z(\ensuremath{\delta}),$ where \ensuremath{\delta} measures the deviation from criticality. There are some discrepancies between the values of $z(\ensuremath{\delta})$ obtained from different quantities, but this may be due to corrections to scaling. The average on-site time dependent correlation function decays with a power law in the paramagnetic phase, namely, ${\ensuremath{\tau}}^{\ensuremath{-}1/z(\ensuremath{\delta})},$ where \ensuremath{\tau} is imaginary time. However, the typical value decays with a stretched exponential behavior, $\mathrm{exp}(\ensuremath{-}c{\ensuremath{\tau}}^{1/\ensuremath{\mu}}),$ where \ensuremath{\mu} may be related to $z(\ensuremath{\delta}).$ We also obtain results for the full probability distribution of time dependent correlation functions at different points in the paramagnetic phase.