Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at half filling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p-band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2I+1) symmetry which depend only on the nuclear spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when I=1/2,5/2,9/2,..., which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I(=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2I+1)-symmetry

Magnetization plateaus in weakly coupled dimer spin system

I study a spin system consisting of strongly coupled dimers which are in turn weakly coupled in a plane by zigzag interactions. The model can be viewed as the strong-coupling limit of a two-dimensional zigzag chain structure typical, e.g., for the $(ac)$-planes of KCuCl_3. It is shown that the magnetization curve in this model has plateaus at 1/3 and 2/3 of the saturation magnetization, and an additional plateau at 1/2 can appear in a certain range of the model parameters; the critical fields are calculated perturbatively. It is argued that for the three-dimensional lattice structure of the KCuCl_3 family the plateaus at 1/4 and 3/4 of the saturation can be favored in a similar way, which might be relevant to the recent experiments on NH_4CuCl_3 by Shiramura et al., J. Phys. Soc. Jpn. {\bf 67}, 1548 (1998).Comment: serious changes in Sect. II,III, final version to appear in PR

Magnetization Curves of Antiferromagnetic Heisenberg Spin-1/2 Ladders

Magnetization processes of spin-1/2 Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus are ladders with 3 legs where plateaux with magnetization one third of the saturation value are shown to exist.Comment: 5 pages REVTeX, 4 PostScript figures included using psfig.sty; this is the final version to appear in Phys. Rev. Let

Low-lying excitations and magnetization process of coupled tetrahedral systems

We investigate low-lying singlet and triplet excitations and the magnetization process of quasi-1D spin systems composed of tetrahedral spin clusters. For a class of such models, we found various exact low-lying excitations; some of them are responsible for the first-order transition between two different ground states formed by local singlets. Moreover, we find that there are two different kinds of magnetization plateaus which are separated by a first-order transition.Comment: To appear in Phys.Rev.B (Issue 01 August 2002). A short comment is adde

Massive and Massless Behavior in Dimerized Spin Ladders

We investigate the conditions under which a gap vanishes in the spectrum of dimerized coupled spin-1/2 chains by means of Abelian bosonization and Lanczos diagonalization techniques. Although both interchain ($J'$) and dimerization ($\delta$) couplings favor a gapful phase, it is shown that a suitable choice of these interactions yields massless spin excitations. We also discuss the influence of different arrays of relative dimerization on the appearance of non-trivial magnetization plateaus.Comment: 5 pages, RevTex, 5 Postscript figure

Magnetization plateaus in antiferromagnetic-(ferromagnetic)_{n} polymerized S=1/2 XXZ chains

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)$_{n}$ polymerized $S=1/2$ XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for $4 \leq p \leq 13$ where $p(\equiv n+1)$ is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with $p$ for small $p$ but increases for larger enough $p$. It is also found that the plateau for large $p$ is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for $p = 3$ chains which are narrow for a wide range of exchange coupling even away from the critical point

String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states

We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and characterized by a set of nonlocal string order parameters. The Hamiltonian possesses a hidden $(Z_{2}\times Z_{2})^{n}$ topological symmetry. The breaking of this hidden symmetry leads to $4^{n}$ degenerate ground states with disentangled edge states in an open chain system. Such matrix product states can be regarded as cluster states, applicable to measurement-based quantum computation.Comment: 5 pages, 1 figur

Magnetization Plateaus in a Solvable 3-Leg Spin Ladder

We present a solvable ladder model which displays magnetization plateaus at fractional values of the total magnetization. Plateau signatures are also shown to exist along special lines. The model has isotropic Heisenberg interactions with additional many-body terms. The phase diagram can be calculated exactly for all values of the rung coupling and the magnetic field. We also derive the anomalous behaviour of the susceptibility near the plateau boundaries. There is good agreement with the phase diagram obtained recently for the pure Heisenberg ladders by numerical and perturbative techniques.Comment: 4 pages, revtex, 3 postscript figures, small changes to the text and references update

Series expansion analysis of a tetrahedral cluster spin chain

Using series expansion by continuous unitary transformations we study the magnetic properties of a frustrated tetrahedral spin-1/2 chain. Starting from the limit of isolated tetrahedra we analyze the evolution of the ground state energy and the elementary triplet dispersion as a function of the inter-tetrahedral coupling. The quantum phase diagram is evaluated and is shown to incorporate a singlet product, a dimer, and a Haldane phase. Comparison of our results with those from several other techniques, such as density matrix renormalization group, exact diagonalization and bond-operator theory are provided and convincing agreement is found.Comment: 6 pages, 5 figures, 1 tabl

A new family of models with exact ground states connecting smoothly the S=1/2 dimer and S=1 Haldane phases of 1D spin chains

We investigate the isotropic two-leg S=1/2 ladder with general bilinear and biquadratic exchange interactions between spins on neighboring rungs, and determine the Hamiltonians which have a matrix product wavefunction as exact ground state. We demonstrate that a smooth change of parameters leads one from the S=1/2 dimer and Majumdar-Ghosh chains to the S=1 chain with biquadratic exchange. This proves that these model systems are in the same phase. We also present a new set of models of frustrated S=1/2 spin chains (including only bilinear NN and NNN interactions) whose ground states can be found exactly.Comment: 4 pages, RevTeX, uses psfig.sty, submitted to Phys. Rev. Let