arXiv:cond-mat/0112145 · Physical review. B, Condensed matter

Gap generation in the XXZ model in a transverse magnetic field

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников

Published Apr 18, 2002• 85 citations

Abstract

The ground-state phase diagram of the one-dimensional $\mathrm{XXZ}$ model in a transverse magnetic field is obtained. It consists of the gapped phases with different types of long-range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of critical lines.

DOI: 10.1103/physrevb.65.172409

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Scaling behavior of the energy gap of the XXZ model in a transverse magnetic field

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arXiv:cond-mat/0112145 · Physical review. B, Condensed matter

Gap generation in the XXZ model in a transverse magnetic field

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников

Published Apr 18, 2002• 85 citations

arXiv HTML PDF

Abstract

The ground-state phase diagram of the one-dimensional

\mathrm{XXZ}

model in a transverse magnetic field is obtained. It consists of the gapped phases with different types of long-range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of critical lines.

DOI: 10.1103/physrevb.65.172409

Related papers

One-dimensional anisotropic Heisenberg model in the transverse magnetic field

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников +1 more

The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.

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Antiferromagnetic Ising chain in a mixed transverse and longitudinal magnetic field

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We have studied the antiferromagnetic Ising chain in a transverse magnetic field ${h}_{x}$ and uniform longitudinal field ${h}_{z}.$ Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in ${(h}_{x}{,h}_{z})$ plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in ${h}_{z}$ the scaling behavior of the mass gap in the vicinity of the critical point ${(h}_{x}{=1/2,h}_{z}=0)$ is established. It is found that the form of the transition line near the classical multicritical point ${(h}_{x}{=0,h}_{z}=1)$ is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.We have studied the antiferromagnetic Ising chain in a transverse magnetic field ${h}_{x}$ and uniform longitudinal field ${h}_{z}.$ Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in ${(h}_{x}{,h}_{z})$ plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in ${h}_{z}$ the scaling behavior of the mass gap in the vicinity of the critical point ${(h}_{x}{=1/2,h}_{z}=0)$ is established. It is found that the form of the transition line near the classical multicritical point ${(h}_{x}{=0,h}_{z}=1)$ is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.

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G. I. Japaridze, Hadi Cheraghi, S. Mahdavifar

We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the z[over ̂] axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite (C1) phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite (C2) phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite (C1) in favor of the composite gapped (C2) phase.

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Thermodynamic properties of the XXZ model in a transverse field

Mohammad Siahatgar, A. Langari

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)].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)].

arXiv:0711.0569Physical Review BFeb 27, 20089 citations

Critical properties and phase diagram of quantum anisotropic XY spin chain in a random magnetic field: A density-matrix renormalization-group analysis

Aušrius Juozapavičius, Laura Urba, S. Caprara +1 more

The spin-1/2 quantum anisotropic $\mathrm{XY}$ spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.The spin-1/2 quantum anisotropic $\mathrm{XY}$ spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.

Physical review. B, Condensed matterDec 1, 199911 citations

The ground-state phase diagram of the one-dimensional

\mathrm{XXZ}

We have studied the antiferromagnetic Ising chain in a transverse magnetic field

{h}_{x}

and uniform longitudinal field

{h}_{z}.

Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in

{(h}_{x}{,h}_{z})

plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in

{h}_{z}

the scaling behavior of the mass gap in the vicinity of the critical point

{(h}_{x}{=1/2,h}_{z}=0)

is established. It is found that the form of the transition line near the classical multicritical point

{(h}_{x}{=0,h}_{z}=1)

is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.

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)].

The spin-1/2 quantum anisotropic

\mathrm{XY}

spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.