Hidden Order in URu2Si2URu_2Si_2

We review current attempts to characterize the underlying nature of the hidden order in $URu_2Si_2$. A wide variety of experiments point to the existence of two order parameters: a large primary order parameter of unknown character which co-exists with secondary antiferromagnetic order. Current theories can be divided into two groups determined by whether or not the primary order parameter breaks time-reversal symmetry. We propose a series of experiments designed to test the time-reversal nature of the underlying primary order in $URu_2Si_2$ and to characterize its local single-ion physics

Hidden Order in the Cuprates

We propose that the enigmatic pseudogap phase of cuprate superconductors is characterized by a hidden broken symmetry of d(x^2-y^2)-type. The transition to this state is rounded by disorder, but in the limit that the disorder is made sufficiently small, the pseudogap crossover should reveal itself to be such a transition. The ordered state breaks time-reversal, translational, and rotational symmetries, but it is invariant under the combination of any two. We discuss these ideas in the context of ten specific experimental properties of the cuprates, and make several predictions, including the existence of an as-yet undetected metal-metal transition under the superconducting dome.Comment: 12 pages of RevTeX, 9 eps figure

Hidden Order Behaviour in URu2Si2 (A Critical Review of the Status of Hidden Order in 2014)

Throughout the past three decades the hidden order (HO) problem in URu$_2$Si$_2$ has remained a "hot topic" in the physics of strongly correlated electron systems with well over 600 publications related to this subject. Presently in 2014 there has been significant progress in combining various experimental results embedded within electronic structure calculations using density functional theory (DFT) to give a consistent description of the itinerant behaviour of the HO transition and its low temperature state. Here we review six different experiments: ARPES, quantum oscillations, neutron scattering, RXD, optical spectroscopy and STM/STS. We then establish the consistencies among these experiments when viewed through the Fermi-surface nesting, folding and gapping framework as predicted by DFT. We also discuss a group of other experiments (torque, cyclotron resonance, NMR and XRD) that are more controversial and are presently in a "transition" state regarding their interpretation as rotational symmetry breaking and dotriacontapole formation. There are also a series of recent "exotic" experiments (Raman scattering, polar Kerr effect and ultrasonics) that require verification, yet they offer new insights into the HO symmetry breaking and order parameter. We conclude with some constraining comments on the microscopic models that rely on localised $5f$-U states and strong Ising anisotropy {for explaining} the HO transition, and with an examination of different models in the light of recent experiments.Comment: 21 pages, 12 figures; to appear in Phil. Ma

Second-Order Belief Hidden Markov Models

Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief functions such that Bayesian probabilities were replaced with mass functions. In this paper, we present a second-order Hidden Markov Model using belief functions. Previous works in belief HMMs have been focused on the first-order HMMs. We extend them to the second-order model

Itinerancy and Hidden Order in URu2Si2URu_2Si_2

We argue that key characteristics of the enigmatic transition at $T_0= 17.5K$ in $URu_2Si_2$ indicate that the hidden order is a density wave formed within a band of composite quasiparticles, whose detailed structure is determined by local physics. We expand on our proposal (with J.A. Mydosh) of the hidden order as incommnesurate orbital antiferromagnetism and present experimental predictions to test our ideas. We then turn towards a microscopic description of orbital antiferromagnetism, exploring possible particle-hole pairings within the context of a simple one-band model. We end with a discussion of recent high-field and thermal transport experiment, and discuss their implications for the nature of the hidden order.Comment: 18 pages, 7 figures. v2 contains added referenc