Hidden Orders Research Articles

Composite quadrupole order in ferroic and multiferroic materials.

The formalism of composite and intertwined orders has been remarkably successful in discussing the complex phase diagrams of strongly correlated materials and high-$T_c$ superconductors. Here, we propose that composite orders are also realized in ferroelectric and ferromagnetic materials when lattice anisotropy is taken into account. This composite order emerges above the ferroic phase transition, and its type is determined by the easy axis of magnetization or polarization, respectively. In multiferroic materials, where polarization and magnetization are coupled, composites of both orders are possible. This formalism of composite orders naturally accounts for magnetoelectric monopole, toroidal, and quadrupole orders. More broadly, composite orders may explain precursor phenomena in incipient (multi)ferroic materials, arising at temperatures above the ferroic phase transition and potentially contributing to the characterization of currently hidden orders.

Odd-frequency superfluidity from a particle-number-conserving perspective

We investigate odd-in-time—or —pairing of fermions in equilibrium systems within the particle-number-conserving framework of Penrose, Onsager, and Yang, where superfluid order is defined by macroscopic eigenvalues of reduced density matrices. We show that odd-frequency pair correlations are synonymous with even fermion-exchange symmetry in a time-dependent correlation function that generalises the two-body reduced density matrix. Macroscopic even-under-fermion-exchange pairing is found to emerge from conventional Penrose-Onsager-Yang condensation in two-body or higher-order reduced density matrices through the symmetry-mixing properties of the Hamiltonian. We identify and characterize a matrix responsible for producing macroscopic even fermion-exchange correlations that coexist with a conventional Cooper-pair condensate, while a matrix is shown to be responsible for creating macroscopic even fermion-exchange correlations from hidden orders such as a multiparticle condensate. The transformer scenario is illustrated using the spin-balanced s-wave superfluid with Zeeman splitting as an example. The generator scenario is demonstrated by the composite-boson condensate arising for itinerant electrons coupled to magnetic excitations. Structural analysis of the transformer and generator matrices is shown to provide general conditions for odd-frequency pairing order to arise in a given system. Our formalism facilitates a fully general derivation of the Meissner effect for odd-frequency superconductors that holds also beyond the regime of validity for mean-field theory. Published by the American Physical Society 2024

Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice

Quantum loop and dimer models are prototypical correlated systems with local constraints, which are not only intimately connected to lattice gauge theories and topological orders but are also widely applicable to the broad research areas of quantum materials and quantum simulation. Employing our sweeping cluster quantum Monte Carlo algorithm, we reveal the complete phase diagram of the triangular-lattice fully packed quantum loop model. Apart from the known lattice nematic (LN) solid and the even Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} quantum spin liquid (QSL) phases, we discover a hidden vison plaquette (VP) phase, which had been overlooked and misinterpreted as a QSL for more than a decade. Moreover, the VP-to-QSL continuous transition belongs to the (2 + 1)D cubic* universality class, which offers a lattice realization of the (fractionalized) cubic fixed point that had long been considered as irrelevant towards the O(3) symmetry until corrected recently by conformal bootstrap calculations. Our results are therefore of relevance to recent developments in both experiments and theory, and facilitate further investigations of hidden phases and transitions.

Hidden Order of Boolean Networks.

It is a common belief that the order of a Boolean network is mainly determined by its attractors, including fixed points and cycles. Using the semi-tensor product (STP) of matrices and the algebraic state-space representation (ASSR) of the Boolean networks, this article reveals that in addition to this explicit order, there is a certain implicit or hidden order, which is determined by the fixed points and limit cycles of their dual networks. The structure and certain properties of dual networks are investigated. Instead of a trajectory, which describes the evolution of a state, the hidden order provides a global horizon to describe the evolution of the overall network. We conjecture that the order of networks is mainly determined by the dual attractors via their corresponding hidden orders. Then these results about the Boolean networks are further extended to the k -valued case.

Signatures of a surface spin–orbital chiral metal

The relation between crystal symmetries, electron correlations and electronic structure steers the formation of a large array of unconventional phases of matter, including magneto-electric loop currents and chiral magnetism1–6. The detection of such hidden orders is an important goal in condensed-matter physics. However, until now, non-standard forms of magnetism with chiral electronic ordering have been difficult to detect experimentally7. Here we develop a theory for symmetry-broken chiral ground states and propose a methodology based on circularly polarized, spin-selective, angular-resolved photoelectron spectroscopy to study them. We use the archetypal quantum material Sr2RuO4 and reveal spectroscopic signatures that, despite being subtle, can be reconciled with the formation of spin–orbital chiral currents at the surface of the material8–10. As we shed light on these chiral regimes, our findings pave the way for a deeper understanding of ordering phenomena and unconventional magnetism.

Unveiling multipole physics and frustration of icosahedral magnetic quasicrystals

Multipolar physics and their hidden orders have been widely discussed in the context of heavy fermions and frustrated magnets. However, despite extensive research, there are few examples of purely multipolar systems in the absence of magnetic dipoles. Here, we show the magnetic behavior of an icosahedral quasicrystal is generally described by multipoles, and in a specific case by pure magnetic octupoles, resulting from the interplay of spin-orbit coupling and crystal field splitting. Importantly, we emphasize that non-crystallographic symmetries of quasicrystals result in multipolar degrees of freedom, in contrast to the conventional crystals. We first classify the characteristics of multipoles and derive the effective spin Hamiltonian. We then explore how frustration and quantum fluctuations induce entangled quantum phases. Our study presents the magnetic icosahedral quasicrystal as a platform for investigating the exotic multipolar physics.

Shades of trade: Dark trading and price efficiency

Using a comprehensive approach, we investigate how various forms of non-displayed order flow such as hidden orders on exchanges, brokerage internalizations, and orders submitted to off-exchange venues affects price efficiency. By considering the multiple forms of dark trading available to traders, we are able to better understand the nuances of dark trading, its impacts on price efficiency, and mitigate the unobserved variable problems present in studies that examine only one aspect of dark trading. We find that hidden orders on exchange have a deleterious impact on price efficiency. The impacts of other types of pre-trade, non-displayed orders on price efficiency is more nuanced.

Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca5Ir3O12

Cluster multipole orderings composed of atomic high-rank multipole moments are theoretically investigated with a 5$d$-electron compound Ca$_5$Ir$_3$O$_{12}$ in mind. Ca$_5$Ir$_3$O$_{12}$ exhibits two hidden orders: One is an intermediate-temperature phase with time-reversal symmetry and the other is a low-temperature phase without time-reversal symmetry. By performing the symmetry and augmented multipole analyses for a $d$-orbital model under the hexagonal point group $D_{\rm 3h}$, we find that the 120$^{\circ}$-type ordering of the electric quadrupole corresponds to cluster electric toroidal dipole ordering with the electric ferroaxial moment, which can become the microscopic origin of the intermediate-temperature phase in Ca$_5$Ir$_3$O$_{12}$. Furthermore, based on ${}^{193}$Ir synchrotron-radiation-based M\"{o}ssbauer spectroscopy, we propose that the low-temperature phase in Ca$_5$Ir$_3$O$_{12}$ is regarded as a coexisting state with cluster electric toroidal dipole and cluster magnetic toroidal quadrupole, the latter of which is formed by the 120$^{\circ}$-type ordering of the magnetic octupole and accompanies a small uniform magnetization as a secondary effect. Our results provide a clue to two hidden phases in Ca$_5$Ir$_3$O$_{12}$.

Hidden k-Space Magnetoelectric Multipoles in Nonmagnetic Ferroelectrics.

In condensed matter systems, the electronic degrees of freedom are often entangled to form complex composites, known as hidden orders, which give rise to unusual properties, while escaping detection in conventional experiments. Here we demonstrate the existence of hidden k-space magnetoelectric multipoles in nonmagnetic systems with broken space-inversion symmetry. These k-space magnetoelectric multipoles are reciprocal to the real-space charge dipoles associated with the broken inversion symmetry. Using the prototypical ferroelectric PbTiO_{3} as an example, we show that their origin is a spin asymmetry in momentum space resulting from the broken space inversion symmetry associated with the ferroelectric polarization. In PbTiO_{3}, the k-space spin asymmetry corresponds to a pure k-space magnetoelectric toroidal moment, which can be detected using magnetic Compton scattering, an established tool for probing magnetism in ferromagnets or ferrimagnets with a net spin polarization, which has not been exploited to date for nonmagnetic systems. In particular, the k-space magnetoelectric toroidal moment combined with the spin-orbit interaction manifest in an antisymmetric magnetic Compton profile that can be reversed using an electric field. Our work suggests an experimental route to directly measuring and tuning hidden k-space magnetoelectric multipoles via specially designed magnetic Compton scattering measurements.

Efficient Method for Prediction of Metastable or Ground Multipolar Ordered States and Its Application in Monolayer α-RuX_{3} (X=Cl, I).

Exotic high-rank multipolar order parameters have been found to be unexpectedly active in more and more correlated materials in recent years. Such multipoles are usually dubbed "hidden orders" since they are insensitive to common experimental probes. Theoretically, it is also difficult to predict multipolar orders via abinitio calculations in real materials. Here, we present an efficient method to predict possible multipoles in materials based on linear response theory under random phase approximation. Using this method, we successfully predict two pure metastable magnetic octupolar states in monolayer α-RuCl_{3}, which is confirmed by self-consistent unrestricted Hartree-Fock calculations. We then demonstrate that these octupolar states can be stabilized in monolayer α-RuI_{3}, one of which becomes the octupolar ground state. Furthermore, we also predict a fingerprint of an orthogonal magnetization pattern produced by the octupole moment that can be easily detected by experiment. The method and the example presented in this Letter serve as a guide for searching multipolar order parameters in other correlated materials.

Two shades of opacity: Hidden orders and dark trading

Regulators are concerned that large volumes of trading outside lit venues (i.e., dark trading) harms the functioning of financial markets. In contrast, regulators are neutral about hidden-order trading as these occur on lit venues and are associated with positive effects on market quality. An unanswered economic question concerns the interrelation between these two types of opaque trading, i.e., hidden orders and dark trading. Employing two different empirical methodologies we find that dark and hidden-order trading are substitutes. We also show that both types of opaque trading increase when markets are volatile and fewer algorithmic trading occurs. Smart order routing increases dark trading but reduces hidden-order activity.

Hidden order and multipolar exchange striction in a correlated f-electron system

The nature of order in low-temperature phases of some materials is not directly seen by experiment. Such "hidden orders" (HOs) may inspire decades of research to identify the mechanism underlying those exotic states of matter. In insulators, HO phases originate in degenerate many-electron states on localized f or d shells that may harbor high-rank multipole moments. Coupled by intersite exchange, those moments form a vast space of competing order parameters. Here, we show how the ground-state order and magnetic excitations of a prototypical HO system, neptunium dioxide NpO2, can be fully described by a low-energy Hamiltonian derived by a many-body ab initio force theorem method. Superexchange interactions between the lowest crystal-field quadruplet of Np4+ ions induce a primary noncollinear order of time-odd rank 5 (triakontadipolar) moments with a secondary quadrupole order preserving the cubic symmetry of NpO2 Our study also reveals an unconventional multipolar exchange striction mechanism behind the anomalous volume contraction of the NpO2 HO phase.

Hidden Orders and Preserving Tools of Heritage Fabric

Heritage cities are suffering from many and varied problems that they were unable to meet the current requirements, which made them an unfit environment for contemporary housing, causing a change in its residential functional structure, with the desertion of part of its indigenous population, and threatening the social and historical value of its urban fabric. There is great importance in preserving the urban heritage fabric in general. The research objectives are concerned with the heritage fabric in Al-Shawaka- Al-Karkh / BAGHDAD- IRAQ, in particular. This can be said to be the area of origin before the construction of the round city of Baghdad, and it has preserved its residential function through the ages; this makes it a special area for preservation and rehabilitation of the urban fabric in it. The research problem: The hidden orders and its relations to the preservation of architectural and urban. The research hypothesis: Each urban fabric has its own Orders. There are apparent Orders at the level of the urban fabric, at the same time, there are hidden Orders. It is necessary to study the hidden Orders of the heritage urban fabric, and understand them, which leads to find new tools in the way it is preserved, rehabilitated, and linked to the contemporary fabric .The research also deals with the difference between architectural preservation and urban preservation at the fabric level. When moving between alleys of Al- Shawaka, there is a neglected legacy on the large and small levels, the researchers analyzed these alleys to find hidden order. The methodology: studying the specificities of heritage urban fabric context historically and morphologically. The research aims to find Hidden Orders as well as the phenomenon Orders in the region and it aims to arrive at general indicators to preserve and rehabilitate them.

Optimal Execution with Hidden Orders Under Self-Exciting Dynamics

Optimal Execution with Hidden Orders Under Self-Exciting Dynamics

‘opened out […] like an oyster shell': the Roach bed Portland stone cladding of the Smithsons’ Economist Building

Alison & Peter Smithson's Economist Building in London (1960–1964) has been much written about, but one of its most distinctive features – the Roach bed Portland stone cladding – has been relatively little discussed. Although there have been various retrospective explanations for the choice of this previously unused stone, whose surface is marked by cavities of now vanished shells, no direct evidence from the time fully accounts for the decision. Reliance upon inference, and upon retrospective statements, mean that no definitive explanation for the choice is now possible. Some new evidence from archives and interviews, and a re-examination of the contemporary concerns of the Smithsons, and of their artist friends Eduardo Paolozzi and Nigel Henderson, fellow members of the Independent Group during the 1950s, however, suggest a plausible, though speculative, interpretation. When considered in light of the Smithsons' and their friends' interests in pattern, in hidden orders, and in the problems of ‘human association’, the choice of Roach bed Portland stone seems less surprising. More than just ‘pretty’, as Peter Smithson was later to describe the material, it can be seen to connect with a fascination with underlying, non-human, systems of order, while at the same time providing a particularly expressive form of protection for human identity in the modern city.

Transparency in Fragmented Markets: Experimental Evidence

We experimentally examine pre-trade transparency in fragmented limit-order markets. Allowing traders to hide their orders encourages limit order usage. This improves measures of liquidity by increasing depth and narrowing spreads. However, because some of this depth is not displayed, market fragmentation may limit traders’ ability to capitalize on the improved liquidity. This happens when traders execute against displayed orders at worse prices than hidden orders in another market, often referred to as ‘trade-throughs.’ In our laboratory setting, increased trade-throughs due to a dark market impose costs of similar magnitude to the benefits of increases in depth leaving effective liquidity unchanged.

Multipole fluctuation theory for heavy fermion systems: Application to multipole orders in CeB6

In heavy fermion systems, multipole degrees of freedom make possible the emergence of rich phenomena, such as hidden orders and superconductivities. However, many of them remain unsolved since the origin of higher-rank multipole interaction is not well understood. Among these issues, we focus on the quadrupole order in CeB$_6$, which is a famous multipolar heavy fermion system actively studied for decades. We analyze the multiorbital periodic Anderson model for CeB$_6$, and find that both magnetic, quadrupole, and octupole fluctuations develop cooperatively due to the strong inter-multipole coupling given by higher-order many-body effects, called the vertex corrections. It is found that the antiferro-quadrupole order in CeB$_6$ is driven by the interference between magnetic-multipole fluctuations. The discovered inter-multipole coupling mechanism is a potential origin of various hidden orders in various heavy fermion systems.

Unveiling hidden multipolar orders with magnetostriction

Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as “hidden orders” due to the formidable task of detecting them with conventional probes. In this work, we theoretically propose that magnetostriction provides a powerful and novel tool to directly detect higher-order multipolar symmetry breaking—such as the elusive octupolar order—by examining scaling behaviour of length change with respect to an applied magnetic field h. Employing a symmetry-based Landau theory, we focus on the family of Pr-based cage compounds with strongly correlated f-electrons, Pr(Ti,V,Ir)2(Al,Zn)20, whose low energy degrees of freedom are purely higher-order multipoles: quadrupoles {cal{O}}_{20,22} and octupole {cal{T}}_{xyz}. We demonstrate that a magnetic field along the [111] direction induces a distinct linear-in-h length change below the octupolar ordering temperature. The resulting “magnetostriction coefficient” is directly proportional to the octupolar order parameter, thus providing clear access to such subtle order parameters.

Detecting competing orders through the edge states in the heterostructures with high- Tc superconductors

Considering a $d$-wave superconductor being in proximity to a two-dimensional Weyl model, a topological superconductor with gapless edge states may be realized. We here demonstrate that the system can become topologically trivial when an additional d-density-wave order is also included. The edge states become gapped and may be detected in experiments. For this, the d-density-wave order can be detected experimentally, so that different scenarios for the pseudogap in high-T$_c$ superconductors may be distinguished. Moreover, this method may be used to detect various hidden orders through putting high-T$_c$ superconductors being in proximity to various topological nontrivial materials.

Hidden Charge Orders in Low-Dimensional Mott Insulators

The opening of a charge gap driven by interaction is a fingerprint of the transition to a Mott insulating phase. In strongly correlated low-dimensional quantum systems, it can be associated to the ordering of hidden non-local operators. For Fermionic 1D models, in the presence of spin–charge separation and short-ranged interaction, a bosonization analysis proves that such operators are the parity and/or string charge operators. In fact, a finite fractional non-local parity charge order is also capable of characterizing some two-dimensional Mott insulators, in both the Fermionic and the bosonic cases. When string charge order takes place in 1D, degenerate edge modes with fractional charge appear, peculiar of a topological insulator. In this article, we review the above framework, and we test it to investigate through density-matrix-renormalization-group (DMRG) numerical analysis the robustness of both hidden orders at half-filling in the 1D Fermionic Hubbard model extended with long range density-density interaction. The preliminary results obtained at finite size including several neighbors in the case of dipolar, screened and unscreened repulsive Coulomb interactions, confirm the phase diagram of the standard extended Hubbard model. Besides the trivial Mott phase, the bond ordered and charge density wave insulating phases are also not destroyed by longer ranged interaction, and still manifest hidden non-local orders.