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We first argue that the covalent bond and the various closed-shell interactions can be thought of as symmetry brok
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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.
In quantum mechanics the deterministic property of classical physics is an emergent phenomenon appropriate only on macroscopic scales. Lee and Wick introduced Lorentz invariant quantum theories where causality is an emergent phenomenon appropriate for macroscopic time scales. In this paper we analyze a Lee-Wick version of the O(N) model. We argue that in the large N limit this theory has a unitary and Lorentz invariant S matrix and is therefore free of paradoxes in scattering experiments. We discuss some of its acausal properties.
A variety of emergent phenomena has been enabled by interface engineering in the complex oxides heterostructures. While extensive attention has been attracted to LaMnO3 (LMO) thin films for observing the control of functionalities at its interface with substrate, the nature of the magnetic phases in the thin film is, however,controversial. Here, it is reported that the ferromagnetism in 2 and 5 unit cells thick LMO films epitaxially deposited (001)-SrTiO3 substrates ferromagnetic/ferromagnetic coupling in 8 and 10-unit-cell ones, and a striking ferromagnetic/antiferromagnetic pinning effect with apparent positive exchange bias in 15 and 20-unit-cell ones are observed. This novel phenomenon in both 15 and 20-unit-cell films indicates a coexistence of three magnetic orderings in a single LMO film.The high-resolution scanning transmission electron microscopy suggests a P21/n to Pbnm symmetry transition from interface to surface, with the spatial stratification of MnO6 octahedral morphology, corresponding to different magnetic orderings. These results should shed some new lights on manipulating the functionality of oxides by interface engineering.
We examine the standard model of many-body localization (MBL), i.e., the disordered chain of interacting spinless fermions, by representing it as the network in the many-body (MB) basis of noninteracting localized Anderson states. By studying eigenstates of the full Hamiltonian, for strong disorders we find that the dynamics is confined up to very long times to disconnected MB clusters in the Fock space. By keeping only resonant contributions and simplifying the quantum problem to rate equations (REs) for MB states, in analogy with percolation problems, the MBL transition is located via the universal cluster distribution and the emergence of the macroscopic cluster. On the ergodic side, our approximate RE approach to the relaxation processes captures well the diffusion transport, as found for the full quantum model. In a broad transient regime, we find an anomalous, i.e., subdiffusivelike, transport, emerging from weak links between MB states.
We show that the liquid-to-crystal quantum phase transition in the Rokhsar--Kivelson dimer model on the two-dimensional triangular lattice occurs as a condensation of vortex-like excitations called ``visons. This conclusion is drawn from the numerical studies of the vison spectrum in the liquid phase by using the Greens function Monte Carlo method. We find that visons remain the lowest excitation throughout the liquid phase and that their gap decreases continuously to zero at the phase transition. The nature of the crystal phase and the second order of the phase transition are in agreement with the earlier prediction of Moessner and Sondhi [Phys. Rev. B 63, 224401 (2001)].
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