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arXiv:1601.07611 · Journal of Statistical Mechanics Theory and Experiment

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

Rona F. Barbarona, Francis N. C. Paraan

Published May 1, 2016• 2 citations
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Abstract

Abstract We report distinctive nonanalytic signatures in the spin–orbit entanglement of a 2D electron gas with Rashba interactions at integer values of the filling factor and at certain level crossings. The accompanying sharp changes in the bulk spin–orbit entanglement entropy can be probed by measuring the fluctuation in the transverse spin polarization of the electron gas.

DOI
10.1088/1742-5468/2016/05/053104

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Abstract We report distinctive nonanalytic signatures in the spin–orbit entanglement of a 2D electron gas with Rashba interactions at integer values of the filling factor and at certain level crossings. The accompanying sharp changes in the bulk spin–orbit entanglement entropy can be probed by measuring the fluctuation in the transverse spin polarization of the electron gas.
We study the fractional quantum Hall phases of a pseudospin-1/2 Bose gas in an artificial gauge field. In addition to an external magnetic field, the gauge field mimics an intrinsic spin–orbit coupling of the Rashba type. While the spin degeneracy of the Landau levels is lifted by the spin–orbit coupling, the crossing of two Landau levels at certain coupling strengths gives rise to a new degeneracy. We therefore take into account two Landau levels and perform exact diagonalization of the many-body Hamiltonian. We study and characterize the quantum Hall phases which occur in the vicinity of the degeneracy point. Notably, we describe the different states appearing at the Laughlin fillings, ν = 1/2 and ν = 1/4. While for these filling factors incompressible phases disappear at the degeneracy point, we find gaps in the spectra of denser systems at ν = 3/2 and ν = 2. For filling factors ν = 2/3 and ν = 4/3, we discuss the connection of the exact ground states to the non-Abelian spin singlet states, obtained as the ground states of ( k + 1)-body contact interactions.
This investigation delves into the dynamics of quantum correlations and coherence within a two-dimensional electron gas (2DEG) system, taking into account the influence of Rashba spin–orbit coupling (SOC). We utilize metrics such as logarithmic negativity ([Formula: see text]), local quantum uncertainty (LQU ([Formula: see text])), and relative entropy of coherence ([Formula: see text]) to specifically assess these quantum resources among electron spins within non-interacting electron gases. Our study investigates how the separation distance (R) between electrons and the intensity of Rashba SOC ([Formula: see text]), impact the behavior of quantum properties within the 2DEG system. We find that specific strengths of Rashba SOC can effectively regulate quantum correlations and coherence within this system. Particularly significant is our observation that optimal quantum indicators emerge when electron proximity is minimized, underscoring the substantial influence of electron distance on quantum characteristics. Conversely, as electron separation increases, these quantum metrics diminish. Therefore, by adjusting the Rashba parameter, we can enhance the resilience of these quantum measurements against increasing electron separations, providing valuable insights into the potential for controlling and manipulating quantum behavior in similar 2DEG systems.
The entanglement entropy of the ν=1/3 and ν=5/2 quantum Hall states in the presence of short-range random disorder has been calculated using direct diagonalization. A microscopic model of electron–electron interaction is used and spin-polarized electrons are confined to a single Landau level and interact with long-range Coulomb interaction. In the case of very weak disorder, the values of topological entanglement entropy are roughly consistent with the expected theoretical results. By considering a broad range of disorder strengths, entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a signature of the transition as the function of the disorder strength for the ν=5/2 state. Prospects of using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.
We theoretically investigate a two-dimensional harmonically trapped gas of identical atoms with Rashba spin-orbit coupling and no interatomic interactions. In analogy with the spin Hall effect in uniform space, the gas exhibits a spin Hall mode. In particular, in response to a displacement of the center of mass of the system, spin-dipole moment oscillations occur. We determine the properties of these oscillations exactly and find that their amplitude strongly depends on the spin-orbit-coupling strength and the quantum statistics of the particles.
We analyze the entanglement entropy, in real space, for the higher-dimensional integer quantum Hall effect on CPk{\mathbb{C}\mathbb{P}}^{k}CPk (any even dimension) for Abelian and non-Abelian magnetic background fields. In the case of $\ensuremath{\nu}=1$ we perform a semiclassical calculation which gives the entropy as proportional to the phase-space area. This exhibits a certain universality in the sense that the proportionality constant is the same for any dimension and for any background, Abelian or non-Abelian. We also point out some distinct features in the profiles of the eigenfunctions of the two-point correlator that underline the difference in the value of entropies between $\ensuremath{\nu}=1$ and higher Landau levels.
We study the correlations of a two-dimensional electron gas with Rashba spin-orbit coupling (SOC). We obtain the two-particle density matrix and use it to derive the exchange hole. We find a nontrivial correlation for electrons with opposite spin projections that does not occur without Rashba SOC. The two-particle density matrix allows us to further study the quantum correlations of the system. We use it to obtain the concurrence and the entanglement of formation in order to quantify the entanglement of the electron spins. Additionally, we calculate the quantum discord and compare it with the entanglement and classical correlations.