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Register a new userDynamical properties of the Haldane chain with bond disorder
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By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the $S=1$ antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at $delta_{Delta}sim 0.5$ with more and more low-energy excitations coming out. After the critical disorder strength $delta_csim 1$, the system reaches a random-singlet phase with prominent sharp peak at $omega=0$ and broad continuum at $omega>0$ of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These spins can form the weakly coupled long-range singlets due to quantum fluctuation which contribute to the sharp peak at $omega=0$.
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The Haldane phase represents one of the most important symmetry protected states in modern physics. This state can be realized using spin-1 and spin-${1over 2}$ Heisenberg models and bosonic particles. Here we explore the emergent Haldane phase in an alternating bond $mathbb{Z}_3$ parafermion chain, which is different from the previous proposals from fundamental statistics and symmetries. We show that this emergent phase can also be characterized by a modified long-range string order, as well as four-fold degeneracy in the ground state energies and entanglement spectra. This phase is protected by both the charge conjugate and parity symmetry, and the edge modes are shown to satisfy parafermionic statistics, in which braiding of the two edge modes yields a ${2pi over 3}$ phase. This model also supports rich phases, including topological ferromagnetic parafermion (FP) phase, trivial paramagnetic parafermion phase, classical dimer phase and gapless phase. The boundaries of the FP phase are shown to be gapless and critical with central charge $c = 4/5$. Even in the topological FP phase, it is also characterized by the long-range string order, thus we observe a drop of string order across the phase boundary between the FP phase and Haldane phase. These phenomena are quite general and this work opens a new way for finding exotic topological phases in $mathbb{Z}_k$ parafermion models.
Thermodynamic properties of the S=1/2 Heisenberg chain in transverse staggered magnetic field H^y_s and uniform magnetic field H^x perpendicular to the staggered field is studied by the finite-temperature density-matrix renormalization-group method. The uniform and staggered magnetization and specific heat are calculated from zero temperature to high temperatures up to T/J=4 under various strength of magnetic fields from H^y_s/J, H^x/J=0 to 2.4. The specific heat and magnetization of the effective Hamiltonian of the Yb_4As_3 are also presented, and field induced gap formation and diverging magnetic susceptibility at low temperature are shown.
Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].
The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix method.
We investigate the ground-state phase diagram of the spinless Haldane-Hubbard model in the presence of quenched disorder, contrasting results obtained from both exact diagonalization as well as density matrix renormalization group, applied to a honeycomb cylinder. The interplay of disorder, interactions and topology gives rise to a rich phase diagram, and in particular highlights the possibility of a disorder-driven trivial-to-topological transition in the presence of finite interactions. That is, the topological Anderson insulator, demonstrated in non-interacting settings, is shown to be stable to the presence of sufficiently small interactions before a charge density wave Mott insulator sets in. We further perform a finite-size analysis of the transition to the ordered state in the presence of disorder, finding a mixed character of first and second order transitions in finite lattices, tied to specific conditions of disorder realizations and boundary conditions used.
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