We study two coupled Su-Schrieffer-Heeger (SSH) chains system, which is shown to contain rich quantum phases associated with topological invariants protected by symmetries. In the weak coupling region, the system supports two non-trivial topological insulating phases, characterized by winding number N = ±1, and two types of edge states. The boundary between the two topological phases arises from two band closing points, which exhibit topological characteristics in onedimensional k space. By mapping Bloch states on a vector field in k space, the band degenerate points correspond to a pair of kinks of the field, with opposite topological charges. Two topological nodal points move and merge as the inter-chain coupling strength varies. This topological invariant is protected by the translational and inversion symmetries, rather than the antiunitary operation. Furthermore, we find that when a pair of nodal points is created, a second order quantum phase transition (QPT) occurs, associating with a gap closing and spontaneously symmetry breaking. This simple model demonstrates several central concepts in the field of quantum materials and provides a theoretical connection between them.

No abstract

Dynamical phase transitions, characterized by non-analytic behaviors in time domain, extend the equilibrium phase transitions to far-from-equilibrium situations 1, 2 . Furthermore, it's predicted that the dynamical phase transitions can be precisely identified by discontinuities of Pancharatnam geometric phase during the time evolution, even in a general nonadiabatic and non-cyclic process 3-5 . Here, we report the observation of dynamical phase transitions via directly measuring Pancharatnam geometric phase in a quenched topological nanomechanical system. We present a flexible strategy based on eight strong-coupled high-quality-factor nanomechanical oscillators to realize an one-dimensional reconfigurable lattice described by the Su-Schrieffer-Heeger Hamiltonian. Due to the chiral symmetry, the dynamical phase of the time-evolved state quenching from an initial topological edge state is 1 arXiv:1807.04483v2 [quant-ph]

The midposterior fundus of the Sylvian fissure in the human brain is central to the cortical processing of vestibular cues. At least two vestibular areas are located at this site: the parietoinsular vestibular cortex (PIVC) and the posterior insular cortex (PIC). It is now well established that activity in sensory systems is subject to cross-modal attention effects. Attending to a stimulus in one sensory modality enhances activity in the corresponding cortical sensory system, but simultaneously suppresses activity in other sensory systems. Here, we wanted to probe whether such cross-modal attention effects also target the vestibular system. To this end, we used a visual multiple-object tracking task. By parametrically varying the number of tracked targets, we could measure the effect of attentional load on the PIVC and the PIC while holding the perceptual load constant. Participants performed the tracking task during functional magnetic resonance imaging. Results show that, compared with passive viewing of object motion, activity during object tracking was suppressed in the PIVC and enhanced in the PIC. Greater attentional load, induced by increasing the number of tracked targets, was associated with a corresponding increase in the suppression of activity in the PIVC. Activity in the anterior part of the PIC decreased with increasing load, whereas load effects were absent in the posterior PIC. Results of a control experiment show that attention-induced suppression in the PIVC is stronger than any suppression evoked by the visual stimulus per se. Overall, our results suggest that attention has a cross-modal modulatory effect on the vestibular cortex during visual object tracking.