Related papers: Topological Order Parameters of the Spin-1/2 Dimer…
We begin with an introduction to topological order using Wegner's quantum $Z_2$ gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying $Z_2$ magnetic flux. The interplay between…
A large variety of materials can be approximately described by means of spin-1/2 Heisenberg ladders. Here, the Density Matrix Renormalization Group (DMRG) algorithm together with a previously established numerical self-consistent mean-field…
A spin-1/2 frustrated two-leg ladder with four-spin exchange interaction is studied by quantized Berry phases. We found that the Berry phase successfully characterizes the Haldane phase in addition to the rung-singlet phase, and the…
The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest…
In this paper, we study periodically modulated $s=1/2$ spin chain in a linear gradient potential (LP) that is generated by an external magnetic field. In the absence of the LP, the system has topological states that exhibit a magnetization…
Spin-1/2 orthogonal-dimer chain composed of regularly alternating Ising and Heisenberg dimers is exactly solved in a presence of the magnetic field by the transfer-matrix method. It is shown that the ground-state phase diagram involves in…
We study the topological phase in dipolar-coupled two-dimensional breathing square lattice of magnetic vortices. By evaluating the quantized Chern number and $\mathbb{Z}_{4}$ Berry phase, we obtain the phase diagram and identify that the…
We propose the creation of a two-dimensional topological semimetal in a semiconductor artificial lattice with triangular symmetry. An in-plane magnetic field drives a quantum phase transition between the topological insulating and…
The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe \textit{et al.}, Phys. Rev. B {\bf 103}, 134430 (2021)], we discuss magnetic analogs…
Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-$1/2$ Heisenberg model on the maple-leaf lattice with three…
We consider a two-chain, spin-1/2 antiferromagnetic Heisenberg spin ladder in an external magnetic field H. The spin ladder is known to undergo second order quantum phase transitions (QPTs) at two critical values, Hc1 and Hc2, of the…
Rydberg tweezer arrays provide a platform for realizing spin-1/2 Hamiltonians with long-range tunneling that decays as a power law with distance. We numerically investigate the effects of positional disorder and dimerization on the…
The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a…
We investigate the ground state magnetization plateaux appearing in spin 1/2 two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos…
We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time reversal symmetry, these Berry phases are quantized,…
The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase ($\lambda$)…
Spin-1/2 two-legged ladders respecting inter-leg exchange symmetry and D2 spin rotation symmetry have new symmetry protected topological (SPT) phases which are different from the Haldane phase. Three of the new SPT phases are tx,ty,tz,…
Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important…
We study the spin-1/2 two-leg Heisenberg ladder with four-spin ring exchanges under a magnetic field. We introduce an exact duality transformation which is an extension of the spin-chirality duality developed previously and yields a new…
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…