transverse field ising model "mean field"

Bloch spheres show average spin ⟨S⟩ at select times for two different initial states |θ⟩ (blue and red). We consider both the ferromagnetic (J<0) and the antiferromagnetic (J>0) cases, and set |J|=1 as our energy scale. We only implemented inversion (whenever present). (a) Trajectories S(k) for initial states |θ,ϕ⟩ (square data points) and up to k=4 Floquet cycles, obtained with dressing parameters (Ω,Δ)=2π×(2.8,25)  MHz. A, M. Srednicki, “Chaos and This was possible via a mapping of the site occupation of the bosonic atoms onto pseudo-spins Sachdev et al. (c) Phase shift ϕ vs initial tilt θ for different interaction times τR with fit curves ϕ=−Qcosθ. Download PDF Abstract: We investigate the quench dynamics of the transverse field Ising model on a finite fully connected lattice as a prime example of non-equilibrium mean field dynamics. (1987); Suzuki et al. B. French, P. A. Mello, A. Pandey,  and S. S. M. Wong, “Random-matrix physics: spectrum and strength Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made. In Ref. Many studies of quantum systems, mainly in one-dimensional lattices, have found results consistent with this Rigol (2009a, b); Santos and Rigol (2010a); Neuenhahn and Marquardt (2012); Genway et al. The three-dimensional TFIM was used by DeGennes to characterize the ferroelectric phase of KH2PO2 De Gennes (1963), and the one-dimensional TFIM was recently realized in experiments with ultracold bosons in tilted optical lattices Simon et al. P. Calabrese, F. H. L. Essler,  and M. Fagotti, “Quantum quench 3 and 4, we show the structural entropy for the ferromagnetic and antiferromagnetic models, respectively, for five different systems sizes and eight values of the transverse field. They are in very good agreement with PGOE(r). (2015), one expects the maximal values of (ΔSF)α and (ΔSAF)α to decrease exponentially with system size. We have systematically studied quantum chaos indicators and energy-eigenstate expectation values of structure factors in the ferromagnetic 2D-TFIM, and the antiferromagnetic 2D-TFIM in the presence of a longitudinal field, in the square lattice. We are not aware of studies of the phase diagram of the antiferromagnetic 2D-TFIM with a longitudinal field ε=g. The one-dimensional TFIM has been extensively studied theoretically in recent years in the context of quantum quenches in integrable systems Rossini et al. spacings in random matrix ensembles,” Phys. J. Stat. The feedback must be of minimum 40 characters and the title a minimum of 5 characters, This is a comment super asjknd jkasnjk adsnkj, The feedback must be of minumum 40 characters, Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA, Beijing Computational Science Research Center, Beijing 100193, China, Department of Physics, University of California, Santa Barbara, California, 93106, USA, P. G. De Gennes, “Collective Next, we attempt to address whether the eigenstate expectation values of the structure factors in the ordered phases exhibit eigenstate thermalization. This is a clear signature of quantum chaos. We compute. The elementary excitations, the ground-state energy and the free energy are found. Using the results for Tc(g) from the latter study, we have calculate Ec(g) in all clusters (for g<3.044, which is the critical value for the ground-state phase transition). L. D’Alessio, Y. Kafri, Agreement. effects of fluctuations,”, Journal of Physics C: Solid State Physics. (2) for r smaller (larger) than the value for which PGOE(r) is maximal, in agreement with the analysis in Ref. g and ε are the strength of the transverse and longitudinal fields, respectively. The slope of the linear fit (solid blue) gives the mean-field interaction energy χ=2π×15(1)  kHz. The ϕ=0 contour reveals fixed points of the mean-field dynamics, matching the theoretical prediction (purple dot-dashed, purple dashed, and gray dotted curves for the ferromagnetic ground states, paramagnetic ground state, and unstable fixed points, respectively). Note that, away from the integrable limits g=0 and g=∞, the results are consistent with ⟨r⟩GOE. Copyright © 1991 Published by Elsevier B.V. https://doi.org/10.1016/0375-9601(91)91060-Q. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. electrons in high-temperature superconductors,”, O. Bohigas, M. J. Giannoni,  and C. Schmit, “Characterization For quantum chaotic systems with time-reversal symmetry, for which the relevant random matrices belong to the Gaussian orthogonal ensemble (GOE), the distribution of r is given by the expression Atas et al. Santos and Rigol (2010a) that the structural entropy is a useful quantity to detect quantum chaos in systems with unaccounted symmetries. Time evolution of order parameter eigenstates obey the eigenstate thermalization hypothesis,”, S. Sorg, L. Vidmar, quantum quench from the atomic limit,”, L. F. Santos and M. Rigol, “Onset of quantum chaos in The transverse field Ising model (TFIM) is one of the simplest models that exhibits both ground-state and finite-temperature (in dimensions higher than one) phase transitions between paramagnetic and ordered phases. Our results support the conclusion in Ref. You can find more about that e.g. (2014); Sorg et al. In contrast to the study in Ref. Section IV is devoted to the analysis of eigenstate thermalization indicators and their scaling. Figures 6 and 7 show the eigenstate expectation values of the ferromagnetic and antiferromagnetic structure factors in the ferromagnetic and antiferromagnetic 2D-TFIMs, respectively, as computed in all the eigenstates of the Hamiltonian. 1. We denote the total number of sites in the system by N. First, it is important to mention some symmetries of this model in the square lattice, which is a bipartite lattice. Figure 2 shows the numerical results obtained for P(r) averaged over all momentum sectors excluding k=(0,0) and k=(π,π). Instead, we use structure factors, which reveal order even in the absence of symmetry breaking. (b) Energy level diagrams for a single atom (left) and for a pair of atoms (right). Brown, N. Frazier,  and M. Horoi, “The nuclear shell model as a testing of Three-Dimensional Heisenberg and Transverse-Ising Magnets,” in, Quantum Monte Carlo The Monte-Carlo approach to the Ising model, which completely avoids the use of the mean field approximation, is based on the following algorithm: Step through each atom in the array in turn: For a given atom, evaluate the change in energy of the system, , when …