Exotic Order Research Articles

Exotic magnetic orderings in the kagome Kondo-lattice model

We consider the Kondo-lattice model on the kagome lattice and study its weak-coupling instabilities at band filling fractions for which the Fermi surface has singularities. These singularites include Dirac points, quadratic Fermi points in contact with a flat band, and Van Hove saddle points. By combining a controlled analytical approach with large-scale numerical simulations, we demonstrate that the weak-coupling instabilities of the Kondo-lattice model lead to exotic magnetic orderings. In particular, some of these magnetic orderings produce a spontaneous quantum anomalous Hall state.

Ultracold Fermi gases with emergent SU(N) symmetry

We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern–Gerlach effect, (3) the realization of a Mott insulator of 173Yb atoms, (4) the creation of various kinds of Fermi–Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.

Competing phases, phase separation, and coexistence in the extended one-dimensional bosonic Hubbard model

We study the phase diagram of the one-dimensional bosonic Hubbard model with contact $(U)$ and near neighbor $(V)$ interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime $(U,V$, and $\ensuremath{\mu})$ where this phase exists and how it competes with other phases, such as the supersolid (SS) phase, is incompletely understood. We use the stochastic Green function quantum Monte Carlo algorithm as well as the density matrix renormalization group to map out the phase diagram. Our main conclusions are that the HI exists only at $\ensuremath{\rho}=1$, the SS phase exists for a very wide range of parameters (including commensurate fillings), and displays power law decay in the one-body Green function. In addition, we show that at fixed integer density, the system exhibits phase separation in the $(U,V)$ plane.

Competing orders in a three-orbital model of cuprates: Is there a loop-current order?

Apart from the prominent d-wave superconductivity in cuprates, there are competing phases that are believed to be responsible for the pseudogap normal state. Proposals range from spin and charge density waves (SDW and CDW) at finite momentum to the more exotic loop-current order (LCO) at zero momentum. The latter is however beyond the scope of the effective single-orbital Zhang–Rice model. Aiming at treating all possible orderings in a unified framework, here we use a three-orbital model in terms of the copper dx2-y2 orbital and the oxygen px and py orbitals, and perform functional renormalization group calculations for the effect of electron correlations. We find that in the parameter regime relevant to experiments, antiferromagnetic SDW and d-wave superconductivity are the main ordering tendencies, with dominant contents from the copperdx2-y2-orbital, suggesting that the Zhang–Rice model is sufficient to capture the essential physics. If the Coulomb interaction between nearest copper and oxygen is hypothetically strong, an intra-unitcell CDW describing charge imbalance between copper and oxygen sites is realized. The long-sort LCO is too weak even in the three-orbital model, and should be irrelevant in cuprates.

Superconductivity from fractionalized excitations inURu2Si2

An unconventional pairing mechanism in the heavy-fermion material $\mathrm{URu_{2}Si_{2}}$ is studied. We propose a mixed singlet-triplet $d$-density wave to be the hidden-order state in $\mathrm{URu_{2}Si_{2}}$. The exotic order is topologically nontrivial and supports a charge $2e$ skyrmionic spin texture, which is assumed to fractionalize into merons and antimerons at the deconfined quantum critical point. The interaction between these fractional particles results in a (pseudo)spin-singlet chiral $d$-wave superconducting state, which breaks time reversal symmetry. Therefore, it is highly likely to produce a nonzero signal of the polar Kerr effect at the onset of the superconductivity, consistent with recent experiments. In addition, the nodal structures of the possible pairing functions in our model are consistent with the thermodynamic experiments in $\mathrm{URu_{2}Si_{2}}$.

Multifunctionalities driven by ferroic domains

Considerable attention has been paid to ferroic systems in pursuit of advanced applications in past decades. Most recently, the emergence and development of multiferroics, which exhibit the coexistence of different ferroic natures, has offered a new route to create functionalities in the system. In this manuscript, we step from domain engineering to explore a roadmap for discovering intriguing phenomena and multifunctionalities driven by periodic domain patters. As-grown periodic domains, offering exotic order parameters, periodic local perturbations and the capability of tailoring local spin, charge, orbital and lattice degrees of freedom, are introduced as modeling templates for fundamental studies and novel applications. We discuss related significant findings on ferroic domain, nanoscopic domain walls, and conjunct heterostructures based on the well-organized domain patterns, and end with future prospects and challenges in the field.

Toroidal order in metals without local inversion symmetry

The hallmark of the toroidal order $\mathbf{T}$ in solids is the presence of the cross-coupling term $\mathbf{T}\ensuremath{\cdot}(\mathbf{H}\ifmmode\times\else\texttimes\fi{}\mathbf{E})$ in the free energy of the system that leads to antisymmetric magneto-electric effect. In the last several years toroidal order has attracted interest in connection with multiferroic insulating materials. The authors of this manuscript show that such an exotic order can occur even in metallic systems on lattice structures where the spatial-inversion symmetry is preserved globally but broken intrinsically at each magnetic site. They suggest a uranium compound UNi${}_{4}$B as a candidate material where such a state can be realized.

Erratum: Realization of 2D spin-orbit interaction and exotic topological orders in cold atoms [Phys. Rev. Lett.112, 086401 (2014)

Erratum: Realization of 2D spin-orbit interaction and exotic topological orders in cold atoms [Phys. Rev. Lett.<b>112</b>, 086401 (2014)

Exotic Spin Order due to Orbital Fluctuations

We investigate the phase diagrams of the spin-orbital $d^9$ Kugel-Khomskii model for increasing system dimensionality: from the square lattice monolayer, via the bilayer to the cubic lattice. In each case we find strong competition between different types of spin and orbital order, with entangled spin-orbital phases at the crossover from antiferromagnetic to ferromagnetic correlations in the intermediate regime of Hund's exchange. These phases have various types of exotic spin order and are stabilized by effective interactions of longer range which follow from enhanced spin-orbital fluctuations. We find that orbital order is in general more robust and spin order melts first under increasing temperature, as observed in several experiments for spin-orbital systems.

Two-step pressure-induced collapse of magnetic order in the MnGe chiral magnet

Cubic helimagnets such as MnSi and FeGe have provided paradigmatic cases of pressure-induced collapse of band ferromagnetism in metals, accompanied with exotic partial order and chiral spin textures. Isostructural MnGe stands out owing to its much shorter helix pitch and high magnetic moment. By combining resistivity, ac susceptibility, and neutron diffraction measurements under very high pressure, we show that the helical order in MnGe transforms around 6 GPa from a high-spin to a low-spin state, recalling the weak ferromagnetism of MnSi at ambient pressure. Helical order collapses only above 10 GPa. The spin-state transition is supported by ab initio calculations.

Exotic Magnetic Order in the Orbital-Selective Mott Regime of Multiorbital Systems

The orbital-selective Mott phase of multiorbital Hubbard models has been extensively analyzed before using static and dynamical mean-field approximations. In parallel, the properties of block states (antiferromagnetically coupled ferromagnetic spin clusters) in Fe-based superconductors have also been much discussed. The present effort uses numerically exact techniques in one-dimensional systems to report the observation of block states within the orbital-selective Mott phase regime, connecting two seemingly independent areas of research, and providing analogies with the physics of double-exchange models.

A Quantum Critical Point Lying Beneath the Superconducting Dome in Iron Pnictides

Whether a quantum critical point (QCP) lies beneath the superconducting dome has been a long-standing issue that remains unresolved in many classes of unconventional superconductors, notably cuprates, heavy fermions, and, most recently, iron pnictides. The existence of a QCP may offer a route to understanding the origin of unconventional superconductors’ anomalous non-Fermi liquid properties, the microscopic coexistence between unconventional superconductivity and magnetic or some other exotic order, and, ultimately, the mechanism of superconductivity itself. The isovalent substituted iron pnictide BaFe2(As1−xPx)2 offers a new platform for the study of quantum criticality, providing a unique opportunity to study the evolution of the electronic properties in a wide range of the phase diagram. Recent experiments in BaFe2(As1−xPx)2 have provided the first clear and unambiguous evidence of a second-order quantum phase transition lying beneath the superconducting dome.

Realization of 2D Spin-Orbit Interaction and Exotic Topological Orders in Cold Atoms

Majorana zero bound mode exists in the vortex core of a chiral $p+ip$ superconductor or superfluid, which can be driven from an s-wave pairing state by two-dimensional (2D) spin-orbit (SO) coupling. We propose here a novel scheme based on realistic cold atom platforms to generate 2D SO interactions in a blue-detuned square optical lattice, and predict both the quantum anomalous Hall effect and chiral topological superfluid phase in the experimentally accessible parameter regimes. This work opens a new direction with experimental feasibility to observe non-Abelian topological orders in cold atom systems.

Exotic topological order in fractal spin liquids

We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of string-like extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly-fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.

Competing Supersolid and Haldane Insulator Phases in the Extended One-Dimensional Bosonic Hubbard Model

The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum MonteCarlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.

Correlated topological phases and exotic magnetism with ultracold fermions

Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter–Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin–orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interaction-induced transition from a normal to a topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spin–orbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.

Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice.

Ever since the experiments which founded the field of highly frustrated magnetism, the kagome Heisenberg antiferromagnet has been the archetypical setting for the study of fluctuation induced exotic ordering. To this day the nature of its classical low-temperature state has remained a mystery: the nonlinear nature of the fluctuations around the exponentially numerous harmonically degenerate ground states has not permitted a controlled theory, while its complex energy landscape has precluded numerical simulations at low temperature, T. Here we present an efficient MonteCarlo algorithm which removes the latter obstacle. Our simulations detect a low-temperature regime in which correlations asymptote to a remarkably small value as T→0. Feeding these results into an effective model and analyzing the results in the framework of an appropriate field theory implies the presence of long-range dipolar spin order with a tripled unit cell.

Exotic spin orders driven by orbital fluctuations in the Kugel-Khomskii model

We study zero temperature phase diagram of the three-dimensional Kugel-Khomskii model on a cubic lattice using the cluster mean field theory and different perturbative expansions in the orbital sector. The phase diagram is rich, goes beyond the single-site mean field theory due to spin-orbital entanglement. In addition to the antiferromagnetic (AF) and ferromagnetic (FM) phases, one finds also a plaquette valence-bond phase with singlets ordered either on horizontal or vertical bonds. More importantly, for increasing Hund's exchange we identify three phases with exotic magnetic order stabilized by orbital fluctuations in between the AF and FM order: (i) an AF phase with two mutually orthogonal antiferromagnets on two sublattices in each $ab$ plane and AF order along the c axis (ortho-$G$-type phase), (ii) a canted-$A$-type AF phase with a non-trivial canting angle between nearest neighbor FM layers along the c axis, and (iii) a striped-AF phase with anisotropic AF order in the $ab$ planes. We elucidate the mechanism responsible for each of the above phases by deriving effective spin models which involve second and third neighbor Heisenberg interactions as well as four-site spin interactions going beyond Heisenberg physics, and explain how the entangled nearest neighbor spin-orbital superexchange generates spin interactions between more distant spins.

Noncollinear Magnetic Order Stabilized by Entangled Spin-Orbital Fluctuations

Quantum phase transitions in the two-dimensional Kugel-Khomskii model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization Ansatz. When 3z(2)-r(2) orbitals are favored by the crystal field and Hund's exchange is finite, both methods give a noncollinear exotic magnetic order that consists of four sublattices with mutually orthogonal nearest-neighbor and antiferromagnetic second-neighbor spins. We derive an effective frustrated spin model with second- and third-neighbor spin interactions which stabilize this phase and follow from spin-orbital quantum fluctuations involving spin singlets entangled with orbital excitations.

Bose-Hubbard Models with Synthetic Spin-Orbit Coupling: Mott Insulators, Spin Textures, and Superfluidity

Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose-Hubbard model in a non-Abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean-field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from the MI and display, in addition, unusual modulated current patterns. We present a slave-boson theory which gives insight into such intertwined spin-charge orders in the SF, and discuss signatures of these orders in Bragg scattering, in situ microscopy, and dynamic quench experiments.