Anisotropic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>model on the inhomogeneous periodic chain

Lima, J.P. de; Gonçalves, L. L.; Alves, T. F. A.

doi:10.1103/physrevb.75.214406

Cited by 17 publications

(16 citation statements)

References 26 publications

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“…The interest about such a system, belonging to a more general class of models, [13][14][15] is motivated by experimental work on quasicrystals and quasiperiodic superlattices. 16,17 First of all, we show that the model admits the existence of a factorized ground state, and then we discuss the exact solution.…”

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Ground-state factorization and quantum phase transition in dimerized spin chains

Giorgi

2009

Phys. Rev. B

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We study the occurrence of ground-state factorization in dimerized XY spin chains in a transverse field. Together with the usual ferromagnetic and antiferromagnetic regimes, a third case emerges, with no analogous in translationally invariant systems, consisting of an antiferromagnetic Neél-type ground state where pairs of spins represent the unitary cell. Then, we calculate the exact solution of the model and show that the factorizing field represent an accidental degeneracy point of the Hamiltonian. Finally, we extend the study of the existence of ground-state factorization to a more general class of models. The study of zero-temperature critical phenomena in quantum magnetic systems represents since long time a major research subject. [1][2][3][4] In particular, the XY model is a very rich source of information about the quantum behavior of spin chains because of the availability of an exact analytical solution.3,5 During the last years, the main interest about spin chains concerned the relationship between quantum phase transitions and entanglement. 6-9 Among a number of interesting properties of such systems, it is worth citing the existence of special values of the external magnetic field, the parameter which drives the phase transition, which give rise to ground-state factorization, discovered by Kurmann et al. 10 This phenomenon has been observed in two-dimensional lattices through quantum Monte Carlo methods 11 and fully analyzed by Giampaolo et al. 12 in a recent publication, where the factorizing field has been determined for a quite general class of models. They developed an appropriate measure of entanglement which vanishes at the factorizing point. So far, the existence of a factorized ground state has been predicted only in translationally invariant Hamiltonian models.Moreover, critical properties of physical systems are discussed by taking the thermodynamic limit from the beginning. On the other hand, the knowledge of a finite-size solution clarifies important aspects of this limit. For example, it is known that the quantum phase diagram of the XY chain in a transverse field exhibits two different symmetry-broken regions characterized by different behaviors of two-body correlation functions. This dissimilarity has a microscopic origin easily understood in the finite-size case. Besides these considerations, the study of finite systems is relevant by itself for the realization of mesoscopic qubits of contemporary interest.In this Rapid Communication we discuss a finite-size dimerized XY spin chain in a transverse field, and analyze ground-state properties. The interest about such a system, belonging to a more general class of models, 13-15 is motivated by experimental work on quasicrystals and quasiperiodic superlattices. 16,17 First of all, we show that the model admits the existence of a factorized ground state, and then we discuss the exact solution. The factorizing field turns out to be an accidental degeneracy point of the Hamiltonian and falls on a border surface between two regions tha...

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“…We discuss explicitly the finite-size limit. 14,19 The first step is the introduction of the Jordan-Wigner transformation, mapping spins into spinless fermions, 3 …”

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Ground-state factorization and quantum phase transition in dimerized spin chains

Giorgi

2009

Phys. Rev. B

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“…As pointed out by Derzhko et al [18] and in the references therein, quantum spin systems with multiple spin interactions work as effective spin models for the standard Hubbard model under certain conditions. On the other hand, models with longrange interactions are important to understand the process of quantum information in spin chains, as well as for the study of the classical and/or quantum crossover, as it was explained by de Lima and Gonc -alves [19]. Another importance of the long-range interaction is that it can induce first order QPT, which play an important role in the quantum critical behavior [20].…”

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confidence: 98%

Quantum phase transitions of the extended isotropic XY model with long-range interactions

Ribeiro

Lima

Gonçalves

2011

Journal of Magnetism and Magnetic Materials

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a b s t r a c tThe one-dimensional extended isotropic XY model (s¼ 1/2) in a transverse field with uniform longrange interactions among the z components of the spin is considered. The model is exactly solved by introducing the Gaussian and Jordan-Wigner transformations, which map it in a non-interacting fermion system. The partition function can be determined in closed form at arbitrary temperature and for arbitrary multiplicity of the multiple spin interaction. From this result, all relevant thermodynamic functions are obtained and, due to the long-range interactions, the model can present classical and quantum transitions of first and second orders. The study of its critical behavior is restricted to the quantum transitions, which are induced by the transverse field at T¼ 0. The phase diagram is explicitly obtained for multiplicities p¼ 2,3,4 and 1, as a function of the interaction parameters, and, in these cases, the critical behavior of the model is studied in detail. Explicit results are also presented for the induced magnetization and isothermal susceptibility w zz T , and a detailed analysis is also carried out for the static longitudinal /S z j S z l S and transversal /S x j S x l S correlation functions. The different phases presented by the model can be characterized by the spatial decay of these correlations, and from these results some of these can be classified as quantum spin liquid phases. The static critical exponents and the dynamic one, z, have also been determined, and it is shown that, besides inducing first order phase transition, the long-range interaction also changes the universality class of the model.

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“…It was first introduced and analyzed by Perk et al [23]. See also [27,[38][39][40] for related more recent work on different versions of the model. The most recent comprehensive analysis of the ground-state phase diagram of the model at γ a = 0 and its local and nonlocal order parameters is given in [25].…”

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confidence: 99%

Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields

Pandey,

Chitov

2020

Preprint

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The XY Z antiferromagnetic spin-1/2 chain with alternation of the exchange and anisotropy couplings in the presence of uniform and staggered axial magnetic fields is studied. The analysis is done using the effective quadratic fermionic Hamiltonian resulting from the Hartee-Fock approximation. Combining the exact and the mean-field methods, the local and string order parameters on the ground-state phase diagram of the model are identified and calculated. We found a topological phase with oscillating string order with a period of four lattice spacings, not reported before for this model. A detailed analysis of patterns of the string order is given. The special XXZ limit of the model with additional U (1) symmetry brings about, in agreement with the Lieb-Schultz-Mattis theorem and its extensions, plateaux of magnetization and some additional conserving quantities. We have shown that in the XY Z chain, where the plateaux are smeared, the robust oscillating string order parameter is continuously connected to its XXZ limit. Also, the non-trivial winding number and zero-energy localized Majorana edge states, as additional attributes of topological order, are robust in that phase, even off the line of U (1) symmetry.

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AnisotropicXYmodel on the inhomogeneous periodic chain

Abstract: The static and dynamic properties of the anisotropic XY-model (s = 1/2) on the inhomogeneous periodic chain, composed of N cells with n different exchange interactions and magnetic moments, in a transverse field h, are determined exactly at arbitrary temperatures.

Cited by 17 publications

References 26 publications

Ground-state factorization and quantum phase transition in dimerized spin chains

Ground-state factorization and quantum phase transition in dimerized spin chains

Quantum phase transitions of the extended isotropic XY model with long-range interactions

Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields

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