quantum xy model

If so, what type of transition? One theoretical model where it can be well understood is the anisotropic quantum XY model, in one- and two-dimensions, described by the following Hamiltonian: (1) H =-J ∑ n (S n x S n + 1 x + S n y S n + 1 y) + D ∑ n (S n z) 2, where the parameter D represents an xy easy-plane single For example, one can analyze the Hamiltonian by using Subtleties in the exact solution to the 1D quantum XY model, in particular the Bogoliubov transformation. Remarkably, the equivalence between the microscopic spin model and the continuous O(2)-vector model with transverse-Ising model (TIM)-like dynamics, characterized by a dynamic critical exponent z=1, emerges at low temperatures close to the quantum critical point with the single-ion anisotropy parameter D as the non-thermal control parameter. We employ the two-time Green function method by avoiding the Anderson–Callen decoupling of spin operators at the same sites which is of doubtful accuracy. Indeed, at high temperatures this quantity approaches zero since the components of the spins will tend to be randomized and thus sum to zero. insulators, superfluidity, melting, and possibly to the recently Does the two-dimensional quantum XY model  go The transition, due to the Physics in two dimensions is characterized by large fluctuations. It plays an important role both in traditional and symmetry­protected topological phase trans­ itions, received intense study in many aspects [16–29]. physics significantly. In details, spin systems such as the XY model, XXZ model and so on, have been used to investigate the quantum entanglement 29,30,31,32,33,34, quantum discord 35,36,37, and others, while the problem of quantum phase transitions is also addressed. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. We study the entanglement in the quantum Heisenberg XY model in which the so-called W entangled states can be generated for 3 or 4 qubits. discovered high- superconducting transition. For d>2, and in particular for d=3, we determine the finite-temperature critical line ending in the quantum critical point and the related TIM-like shift exponent, consistently with recent renormalization group predictions. Copyright © 2020 Elsevier B.V. or its licensors or contributors. It is well known now that the two-dimensional (2D) classical (planar) XY Here we study the entanglement in the XY model. This is a We also discuss an explicit lower bound on the critical temperature of the quantum XY model. Quantum criticality induced by single-ion anisotropy in a spin-1 XY model is studied. Following the original Devlin procedure we treat exactly the higher order single-site anisotropy Green functions and use Tyablikov-like decouplings for the exchange higher order ones. The related self-consistent equations appear suitable for an analysis of the thermodynamic properties at and around second order phase transition points. And the quantum XY models have the same phases and phase transitions as models of lattice bosons with short-range interactions. The fully anisotropic transverse-field XY model in one dimension (1d) describes an interacting spin system for which many exact results on ground and excited state properties including spin correlations are known [1–3]. Quantum XY model was solved by Lieb, Schultz, Mattis in 1961 [31] and later all the statistical properties were examined by many other authors [32{39]. The Hamiltonian describing the model is given by HXY = − λ 2 XL i=1 (1+γ)σx i σ x i+1 +(1−γ)σ y iσ y +1 − XL i=1 σz i (1) 82B26 1 Introduction and Results Correlation inequalities, initially proposed by Griffiths [4], have been an invaluable tool in the study of several classical spin systems.

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