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arXiv:1401.6401 · Physical Review B

Topological order-by-disorder in orbitally degenerate dipolar bosons on a zigzag lattice

Gaoyong Sun, T. Vekua

Published Sep 19, 2014• 2 citations
arXivHTMLPDF

Abstract

Spinor bosons offer a conceptually simple picture of macroscopic quantum behavior of topological order-by-disorder: The paramagnetic state of two-component dipolar bosons in an orbitally degenerate zigzag lattice is unstable against infinitesimal quantum fluctuations of orbitals, $\ensuremath{\lambda}$, towards developing nonlocal hidden order. Adjacent to the topological state a locally correlated exact ground state with spontaneously a quadrupoled lattice constant is realized for the broad parameter regime. The topological order is extremely robust surviving the $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit where the ground state evolves into the Majumdar-Ghosh state of a frustrated spin-$\frac{1}{2}$ chain.

DOI
10.1103/physrevb.90.094414

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Spinor bosons offer a conceptually simple picture of macroscopic quantum behavior of topological order-by-disorder: The paramagnetic state of two-component dipolar bosons in an orbitally degenerate zigzag lattice is unstable against infinitesimal quantum fluctuations of orbitals, \ensuremathλ\ensuremath{\lambda}\ensuremathλ, towards developing nonlocal hidden order. Adjacent to the topological state a locally correlated exact ground state with spontaneously a quadrupoled lattice constant is realized for the broad parameter regime. The topological order is extremely robust surviving the \ensuremathλ\ensuremath→\ensuremath∞\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}\ensuremathλ\ensuremath→\ensuremath∞ limit where the ground state evolves into the Majumdar-Ghosh state of a frustrated spin-12\frac{1}{2}21​ chain.
The order from quantum disorder (OFQD) phenomenon was first discovered in quantum spin systems in geometric frustrated lattice. Similar phenomenon was also discovered in interacting bosonic systems or quantum spin systems with spin-orbit coupling in a bipartite lattice. Here we show that the OFQD also leads to a topological phase transition. We demonstrate this new connection in the experimentally realized weakly interacting Quantum Anomalous Hall system of spinor bosons in an optical lattice. There are two classes of topological phenomena: the first class is a perturbative one smoothly connected to the non-interacting limit. The second one is a non-perturbative one which has no analog in the non-interacting limit. Their experimental detections are also discussed.
In the first part we study O(N) spins on geometrically frustrated pyrochlore and planar pyrochlore lattices. For classical spins the strong frustration causes a lack of ordering for N 6= 2 at all temperatures. Nevertheless at low temperatures the system is strongly correlated. We find degrees of freedom that are relevant in this regime and find that the correlations are dipolar up to distance ∼ 1/√T and then decay exponentially. We use various approaches — most notably, we show that this holds to any order in the 1/N expansion. Then we look at spin evolution under precessional and Monte-Carlo dynamics and find that in both cases the dynamical correlations decay exponentially in time with a scale τ ∼ 1/T and that the long distance and long time correlations are described by the simple Langevin evolution of the degrees of freedom found in the static case. Finally we look at the effects of quantum fluctuations by studying the quantum rotor model on the pyrochlore lattice. Using quantum Monte-Carlo simulations and analytical arguments we find that for every N there is a region in quantum coupling—temperature plane with long range nematic order. In the second part we study stability of topological order in Kitaev’s model under arbitrary small local perturbations. Using the Fredenhagen-Marcu order parameter [13] we show in quantum perturbation theory that in two or more dimensions, the topologically ordered phase is distinct from more conventional phases. Further we show that this distinction survives to positive temperatures in three or more dimensions and that the topological phase is also distinct from the high temperature phase. We extend this result to odd Ising gauge theories and note that the relation between these and dimer models strongly suggests
Ultracold dipolar spinor fermions in zig-zag--type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled ddd levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.
We study the topological phases in spin-orbit-coupled dipolar bosons in a one-dimensional optical lattice. The magnetic dipolar interactions between atoms give rise to intersite interactions. In the Mott-insulating regime, this system can be described by the quantum XYZ spin model with Dzyaloshinskii-Moriya interactions in a transverse field. We focus on investigating the effect of dipolar interactions on the topological phase. The topological phase can be shown when spin-orbit coupling combines with the repulsive dipolar interaction. We find that the dipolar interaction can broaden the range of parameters of spin-orbit coupling and transverse field for exhibiting the topological phase. The sum of spin correlations between the two nearest-neighboring atoms can be used to indicate the topological phase. This may be useful for detecting topological phases in experiments.
Motivated by the experiment [St-Jean et al., Nat. Photonics 11, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless ppp-orbital fermions with local interorbital hoppings and repulsive interactions between px{p}_{x}px​ and py{p}_{y}py​ bands in zigzag optical lattices. We show that spinless ppp-band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state phases and quantum phase transitions of the model. This work provides a simple scheme to simulate topological phases and the quench dynamics of many-body systems in optical lattices.
Quantum paramagnets are strongly correlated phases of matter where competing interactions frustrate magnetic order down to zero temperature. In certain cases, quantum fluctuations instead induce topological order, supporting fractionalized quasiparticles. In this Letter, we investigate paradigmatic spin models and show how magnetic frustration can also give rise to higher-order topological properties. We first study the frustrated Heisenberg model in a square lattice, where a plaquette valence bond solid appears through the spontaneous breaking of translational invariance. Despite the amount of effort that has been devoted to study this phase, its topological nature has so far been overlooked. By means of tensor network simulations, we establish how such a state belongs to a higher-order symmetry-protected topological phase, where long-range plaquette order and nontrivial topology coexist. Through this interplay, we uncover excitations that would be absent otherwise, such as cornerlike bulk states bound to dynamical topological defects. Finally, we demonstrate how this higher-order topological quantum paramagnet is also induced by dipolar interactions, indicating the possibility to directly observe this phase using atomic quantum simulators.