Integer effects in the entanglement and spin fluctuations of a quantum Hall system with Rashba interactions

Barbarona, Rona F.; Paraan, Francis N. C.

doi:10.1088/1742-5468/2016/05/053104

Cited by 2 publications

(2 citation statements)

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“…Remarkably, the DTWA gives the same results we have just described for the case of a one-dimensional model with short range interactions, as we discuss in detail in Appendix B. In that case, the model is known to show no long-range order in the excited states [37], and m x is doomed to vanish whichever is the value of h, as can be shown explicitly in the thermodynamic limit using the Jordan-Wigner transformation [38,39]. Our DTWA numerics suggests that the situation is also the same for the long-range model with α 2, but, for sure, this is not a proof and the question is still debated [10,40].…”

Section: A Long-range Model In One Dimensionsupporting

confidence: 71%

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Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench

et al. 2020

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By means of the discrete truncated Wigner approximation, we study dynamical phase transitions arising in the steady state of transverse-field Ising models after a quantum quench. Starting from a fully polarized ferromagnetic initial condition, these transitions separate a phase with nonvanishing magnetization along the ordering direction from a disordered symmetric phase upon increasing the transverse field. We consider two paradigmatic cases, a one-dimensional long-range model with power-law interactions ∝ 1/r α decaying algebraically as a function of distance r and a two-dimensional system with short-range nearest-neighbor interactions. In the former case, we identify dynamical phase transitions for α 2 and we extract the critical exponents from a data collapse of the steady-state magnetization for up to 1200 lattice sites. We find identical exponents for α 0.5, suggesting that the dynamical transitions in this regime fall into the same universality class as the nonergodic mean-field limit. The two-dimensional Ising model is believed to be thermalizing, which we also confirm using exact diagonalization for small system sizes. Thus, the dynamical transition is expected to correspond to the thermal phase transition, which is consistent with our data upon comparing to equilibrium quantum Monte Carlo simulations. We further test the accuracy of the discrete truncated Wigner approximation by comparing against numerically exact methods such as exact diagonalization, tensor network, as well as artificial neural network states and we find good quantitative agreement on the accessible time scales. Finally, our work provides an additional contribution to the understanding of the range and the limitations of qualitative and quantitative applicability of the discrete truncated Wigner approximation.

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Section: A Long-range Model In One Dimensionsupporting

confidence: 71%

“…In the case of spin chain with short-range interaction, there is no ordered nonequilibrium steady state [37][38][39] (it corresponds to the long-range one-dimensional model studied in the limit of very large α). It is useful to check this result with DTWA as an additional test of its quality.…”

Section: Appendix B: Short-range Model In One Dimensionmentioning

confidence: 99%