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A concept -- quantum order -- is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize universality classes of quantum states (described by {\em complex}…

In a large number of rare-earth and actinide systems, Kondo effect tends to suppress magnetic order by making the spin singlet between localized and conduction electron spins. In the presence of orbital degrees of freedom, however, there…

Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…

A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…

Higher order time-correlators of spontaneous spin fluctuations reveal the information about spin interactions. We argue that in a broad class of spin systems one can justify a phenomenological approach to explore such correlators. Thus, we…

In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…

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…

Using analytic and numerical methods, we study a $2d$ Hamiltonian model of interacting particles carrying ferro-magnetically coupled continuous spins which are also locally coupled to their own velocities. This model has been characterised…

Quantum materials are epitomized by the influence of collective modes upon their macroscopic properties. Relatively few examples exist, however, whereby coherence of the ground-state wavefunction directly contributes to the conductivity.…

It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these…

A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…

Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…

In this paper, we found a new type of insulator - composite spin liquid which can be regarded as a short range B-type topological spin-density-wave. Composite spin liquid is topological ordered state beyond the classification of traditional…

Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are…

Pair spin-orbit interaction can emerge in strongly-interacting systems characterized by a large spin-orbit coupling. Here we study the role of this interaction in stabilizing ordered and unconventional superconducting phases. We find that,…

We describe a mechanism for order fractionalization in a two-dimensional Kondo lattice model, in which electrons interact with a gapless spin liquid of Majorana fermions described by the Yao-Lee (YL) model. When the Kondo coupling to the…

Topological order in strongly correlated systems, including quantum spin liquids, quantum Hall states in lattices and topological superconductivity is treated. Various metallic non-Fermi-liquid states are discussed, including fractionalized…

Electronic states localized at domain walls between ferromagnetically ordered phases in two-dimensional electron systems are generated by moderate spin-orbit coupling. The spin carried by these states depends on the slope of the magnetic…

In this article we show that the phase-ordering scaling state for binary fluids is not necessarily unique and that local correlations in the initial conditions can be responsible for selecting the scaling state. We describe a new scaling…