Quantum solitons and the Haldane phase in antiferromagnetic spin chains

Tianci Zhou, Michael Stone

Hans-Jürgen Mikeska, Paola Verrucchi

We study the structure and properties of the ground state of an antiferromagnetic S=1 spin chain with single-ion anisotropy energy d and exchange anisotropy energy \ensuremath{\epsilon}. We apply the nonlocal unitary transformation of Kennedy and Tasaki to take into account the essential correlations and restrict our study to the subspace of spin-zero defects (solitons). We investigate the quantum phase transitions in the (\ensuremath{\epsilon},d) plane in a cluster approximation which takes into account correlations between spins at 3 neighboring sites in the unitarily transformed representation. We obtain quantitative results for the phase diagram, for the values of the hidden order parameter, and for amplitudes that describe the transition from the N\'eel to the Haldane phase in terms of the dissociation of soliton pairs.

H.-J. Mikeska, Seiji Miyashita, Gerald H. Ristow

Hans‐Benjamin Braun, J. Kulda, B. Roessli +4 more

Rajiv R. P. Singh

We calculate the excitation spectra for the 1D Heisenberg-Ising antiferromagnets by expansions around the Ising limit. For S=1/2, the calculated expansion coefficients for the spinon spectra agree term by term with the solution of Johnson and McCoy. For S=1, the solitons become gapless before the Heisenberg limit is reached, signaling a transition to the Haldane phase. By applying a staggered field we calculate the one-magnon spectra for the S=1 Heisenberg chain. For S=3/2 the quantum renormalization of the spin-wave spectra is calculated to be approximately 1.16. \textcopyright{} 1996 The American Physical Society.

Keola Wierschem, Pinaki Sengupta

We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional (Q1D) geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean-field universality of the critical coupling times the coordination number of the lattice. Inspired by recent developments in the characterization of symmetry protected topological (SPT) states, of which the Haldane phase of the spin-1 Heisenberg antiferromagnetic chain is a preeminent example, we provide direct evidence that the Q1D Haldane phase is indeed a nontrivial SPT state.