arXiv:cond-mat/9507036

Bloch Electron on a Triangular Lattice and Quantum Ising Model in a Transverse Field

Jukka A. Ketoja, Indubala I. Satija

Published Jul 12, 1995• 0 citations

Abstract

The tight binding model for an electron on an anisotropic triangular lattice in a uniform magnetic field is studied using a decimation scheme. The model exhibits a transition from critical to localized phase and the phase diagram is described in terms of three nontrivial renormalization fixed points for the band edges. These subcritical, critical, and supercritical universality classes also describe the corresponding states of the quantum Ising chain in a modulating transverse field. The only exception is the conformally invariant point of the Ising model which has no analog in the electron problem.

DOI: 10.48550/arxiv.cond-mat/9507036

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arXiv:cond-mat/9507036

Bloch Electron on a Triangular Lattice and Quantum Ising Model in a Transverse Field

Jukka A. Ketoja, Indubala I. Satija

Published Jul 12, 1995• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9507036

Related papers

The re-entrant phase diagram of the generalized Harper equation

Jukka A. Ketoja, Indubala I. Satija

We study the phase diagram of the tight-binding model for an electron on an anisotropic square lattice with a four-dimensional parameter space defined by two nearest-neighbour and two next-nearest-neighbour couplings. Using a renormalization scheme, we show that the inequality of the two next-nearest-neighbour couplings destroys the fat critical regime found in the isotropic case above the bicritical line and replaces it with another re-entrant extended phase. The scaling properties of the model are those of the corresponding tight-binding models on the nearest-neighbour square and triangular lattices. The triangular universality class also describes the quantum Ising chain in a transverse field with the only exception being the conformally invariant state of the Ising model which has no analogue in the triangular-lattice case.We study the phase diagram of the tight-binding model for an electron on an anisotropic square lattice with a four-dimensional parameter space defined by two nearest-neighbour and two next-nearest-neighbour couplings. Using a renormalization scheme, we show that the inequality of the two next-nearest-neighbour couplings destroys the fat critical regime found in the isotropic case above the bicritical line and replaces it with another re-entrant extended phase. The scaling properties of the model are those of the corresponding tight-binding models on the nearest-neighbour square and triangular lattices. The triangular universality class also describes the quantum Ising chain in a transverse field with the only exception being the conformally invariant state of the Ising model which has no analogue in the triangular-lattice case.

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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.

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Critical properties and phase diagram of the 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 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 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.

arXiv:cond-mat/9812056Dec 3, 19980 citations

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 zero-temperature phase diagram of

\mathrm{XYZ}

model in the presence of transverse magnetic field. We show that small anisotropy $(0<~\ensuremath{\Delta}<1)$ is not relevant to change the universality class. The phase diagram consists of two antiferromagnetic ordering and a paramagnetic phase. We have obtained the critical exponents, fixed points, and running of coupling constants by implementing the standard quantum renormalization group. The continuous phase transition from antiferromagnetic (spin-flop) phase to a paramagnetic one is in the universality class of Ising model in transverse field. Numerical exact diagonalization has been done to justify our results. We have also addressed the application of our findings to the recent experiments on

{\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}.

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.