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Physical review. B, Condensed matter

Quantum phase transitions of a quasiperiodic anisotropic XY chain in a transverse magnetic field

Peiqing Tong, Ming Zhong

Published Jan 18, 2002• 16 citations
Publisher

Abstract

The zero-temperature phase diagram of a quasiperiodic anisotropic $\mathrm{XY}$ quantum spin chain in a transverse magnetic field is studied. In the isotropic limit, the system exhibits an infinite number of quantum phase transitions with a devil's-staircase-like magnetization curve. Anisotropy decreases the number of transitions. A mechanism is proposed for the successive transitions based on the ordering of finite clusters of spins along the chain.

DOI
10.1103/physrevb.65.064421

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The zero-temperature phase diagram of a quasiperiodic anisotropic XY\mathrm{XY}XY quantum spin chain in a transverse magnetic field is studied. In the isotropic limit, the system exhibits an infinite number of quantum phase transitions with a devil's-staircase-like magnetization curve. Anisotropy decreases the number of transitions. A mechanism is proposed for the successive transitions based on the ordering of finite clusters of spins along the chain.
The spin-1/2 quantum anisotropic XY\mathrm{XY}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 partition function zeros of the anisotropic XY chain in a complex transverse field are studied analytically and numerically. It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field. For the periodic and quasiperiodic anisotropic XY chains, the closed curves are split to two or three closed curves as the anisotropic parameter gamma decreases at a given ratio of two kinds of exchange interactions. For the isotropic XX case, the partition function zeros lie on the straight segments which are parallel to the real axis and the segments move towards the real axis as the temperature goes to zero.
Anisotropic quantum XY spin chains in a quasiperiodic (QP) transverse field provide a very interesting and a rich class of one-dimensional models exhibiting extended (E), localized (L), and critical (C) phases in addition to a magnetic transition to long-range order. The interesting feature in this class of models is the fact that the intermediate C phase exists in a finite window of size determined by the magnitude of spin-space anisotropy. Furthermore, even a small amount of anisotropy in the spin space destroys the fractal phase boundary between the E and L phases of the isotropic model.
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.
We study anisotropic quantum spin chains in an aperiodic magnetic field h n = λ cos(2πσ n v ); for 0 < v < 1. For v equal to unity and σ equal to the golden mean, the system is quasiperiodic. In the isotropic limit, the incommensurate behaviour is described by the Harper equation exhibiting the metal-insulator transition whereas in the anisotropic case a new fat critical phase is observed between the extended and localized phases. For v different from unity, the global extended phase of the quasiperiodic anisotropic model is replaced by the metal-insulator transition with mobility edges. The mobility edge corresponding to the isotropic model exhibits a novel intermittency. In addition, a new mobility edge with no analog in the isotropic model appears at energy corresponding to the spin space anisotropy g . Instead of the fat critical phase of the quasiperiodic model we now observe a phase which is localized everywhere except at the energy equal to g . There is no localization-delocalization transition in this case. Various high precision numerical tools suggest the existence of critical states at the onset of metal-insulator transition, along the line where the energy is equal to g as well as at the conformally invariant point. We conjecture that the existence of critical states at a conformal point is a universal phenomenon for all aperiodic potentials.