Quantum spiral spin-tensor magnetism

Synthetic Hall tube of interacting fermions

“…Since the inter-leg couplings of this synthetic Hall tube generate an interesting spin-tensor Zeeman field, it is very necessary to explore magnetic properties of the system, apart from the interactiondriven topological transition. Due to the coexistence of the spiral spin-vector and -tensor Zeeman fields in the synthetic Hall tube, local magnetic orders with 3 spin-vectors and 5 spin-tensors should be introduced [38]. In terms of the calculated entanglement spectrum, entanglement entropies, energy gaps, and local magnetic orders, we find four new quantum phases such as nontopological spin-vector and -tensor paramagnetic insulators, and topological and nontopological spin-mixed paramagnetic insulators.…”

Observation of spin-tensor induced topological phase transitions of triply degenerate points with a trapped ion

“…is determined by an azimuthal angle φ T , which fixes the orientation of the ellipsoid [22][23][24][25]. Therefore, an arbitrary spin-1 quantum state |Ψ can be characterized by four parameters F, φ F , θ F , φ T .…”

“…On the other hand, the Berry flux and monopole charge cannot be solely determined by the solid angle of spin vector and its covering number on the Bloch sphere as in spin-1/2 case. In fact, the spin-1 vector can go inside the Bloch sphere and the spin tensors must also be taken into account to obtain the Berry flux [22][23][24][25].…”

“…We effectively tune (α, β) and observe the transitions of the A direct measurement of the topological phase transition requires measuring the change of the total Berry flux on the surface enclosing the TDP monopole. A spin-1 quantum state is determined by the mean values of both spin vectors and tensors, which are represented by an arrow and an ellipsoid [22][23][24][25], respectively. The orientation and size of the ellipsoid are given by the eigenvectors and the square root of the eigenvalues of the tensor matrix T ij = Nij − Fi Fj + 2δ ij /3, as shown in Fig.…”

Bright solitons in a spin-tensor-momentum-coupled Bose-Einstein condensate

“…Different from the usual spin-orbit coupling where linear momentum is coupled with spin vectors, STMC is the interaction between linear momentum and spin tensors. Such emergent interaction can be applicable to the discovery of exotic topological matters [42,43].…”