Entanglement properties of spin models in triangular lattices

The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement spectrum is linked to the symmetries that protect the different quantum phases. This relation extends even further at the phase transitions where a direct link associates the entanglement spectrum to the conformal field theory describing the former. For 2D systems much less is known. The lattice geometry becomes a crucial aspect to consider when studying entanglement and phase transitions. Here, we analyze the entanglement properties of triangular spin lattice models by also considering concepts borrowed from quantum information theory such as geometric entanglement.

Case study of the uniaxial anisotropic spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice

We study the spin-1 model on a triangular lattice in the presence of a uniaxial anisotropy field using a cluster mean-field (CMF) approach. The interplay among antiferromagnetic exchange, lattice geometry, and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF method yields two supersolid phases compatible with those present in the spin-1/2 XXZ model onto which the spin-1 system maps. Between these two supersolid phases, the three-sublattice order is broken and the results of the CMF approach depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

Dense spectrum of resonances and spin-1/2 particle capture in a near-black-hole metric

We show that a spin-1/2 particle in the gravitational field of a massive body of radius R which slightly exceeds the Schwarzschild radius rs, possesses a dense spectrum of narrow resonances. Their lifetimes and density tend to infinity in the limit R → rs. We determine the cross section of the particle capture into these resonances and show that it is equal to the spin-1/2 absorption cross section for a Schwarzschild black hole. Thus black-hole properties may emerge in a non-singular static metric prior to the formation of a black hole.

The Rossiter-McLaughlin effect reloaded: Probing the 3D spin-orbit geometry, differential stellar rotation, and the spatially-resolved stellar spectrum of star-planet systems

When a planet transits its host star, it blocks regions of the stellar surface from view; this causes a distortion of the spectral lines and a change in the line-of-sight (LOS) velocities, known as the Rossiter-McLaughlin (RM) effect. Since the LOS velocities depend, in part, on the stellar rotation, the RM waveform is sensitive to the star-planet alignment (which provides information on the system’s dynamical history). We present a new RM modelling technique that directly measures the spatially-resolved stellar spectrum behind the planet. This is done by scaling the continuum flux of the (HARPS) spectra by the transit light curve, and then subtracting the infrom the out-of-transit spectra to isolate the starlight behind the planet. This technique does not assume any shape for the intrinsic local profiles. In it, we also allow for differential stellar rotation and centre-to-limb variations in the convective blueshift. We apply this technique to HD 189733 and compare to 3D magnetohydrodynamic (MHD) simulations. We reject rigid body rotation with high confidence (>99% probability), which allows us to determine the occulted stellar latitudes and measure the stellar inclination. In turn, we determine both the sky-projected (λ ≈ −0.4 ± 0.2◦) and true 3D obliquity (ψ ≈ 7+12 −4 ◦ ). We also find good agreement with the MHD simulations, with no significant centre-to-limb variations detectable in the local profiles. Hence, this technique provides a new powerful tool that can probe stellar photospheres, differential rotation, determine 3D obliquities, and remove sky-projection biases in planet migration theories. This technique can be implemented with existing instrumentation, but will become even more powerful with the next generation of high-precision radial velocity spectrographs.