Heavy Spins For 1 Hour In A Perfect Loop
Here, we prove analytically that a SOC-induced spin-dependent hopping, which previously made the bands dispersive, perfectly flattens the energy bands of pyrochlore and kagome lattices when it becomes comparable to other transfer integrals. Most importantly, the SOC generates an SU(2) gauge field29 and strictly selects the relative angles of electron spins. When electron wave functions have these spin angles, they destructively interefere30 and localize in real space. We obtain an analytical form of such spin-twisted flat band wave function, allowing us to access the important but most unreachable physical regime, the strongest correlation. In analogy to the flat band ferromagnetism, the SOC flat band may select its form by polarizing its spins in a site-dependent manner avoiding the loss of on-site Coulomb energy, resulting in a stiff spin chirality. When the nearest neighbor Coulomb energy is introduced at quarter-filling, the wave function further optimizes its form to a trimerized shape by fully occupying half of the flat band wave functions, and becoming a spin-singlet state. This mechanism may explain the exotic trimerized charge ordering found in 5d pyrochlore CsW2O631, where one-quarter of the pyrochlore sites become perfectly vacant. The present model may provide a platform for testing the interplay of strong correlation and spin topology.
heavy spins for 1 hour in a perfect loop
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The above discussion and force analysis applies to the circular-like motion of a roller coaster car in a clothoid loop. The second section along a roller coaster track where circular motion is experienced is along the small dips and hills. These sections of track are often found near the end of a roller coaster ride and involve a series of small hills followed by a sharp drop. Riders often feel heavy as they ascend the hill (along regions A and E in the diagram below). Then near the crest of the hill (regions B and F), their upward motion makes them feel as though they will fly out of the car; often times, it is only the safety belt that prevents such a mishap. As the car begins to descend the sharp drop, riders are momentarily in a state of free fall (along regions C and G in the diagram below). And finally as they reach the bottom of the sharp dip (regions D and H), there is a large upwards force that slows their downward motion. The cycle is often repeated mercilessly, churning the riders' stomachs and mixing the afternoon's cotton candy into a slurry of ... . These small dips and hills combine the physics of circular motion with the physics of projectiles in order to produce the ultimate thrill of acceleration - rapidly changing magnitudes and directions of acceleration. The diagram below shows the various directions of accelerations that riders would experience along these hills and dips. 041b061a72