Related papers: Orientational order parameters for arbitrary quant…
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…
It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum…
Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems, since very few…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic…
A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the…
The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and…
The formation of new phases close to itinerant electron quantum critical points has been observed experimentally in many compounds. We present a unified analytical model that explains the emergence of new types of order around itinerant…
We consider a two-dimensional interacting Fermi system which displays a nematic phase within mean-field theory. The system is analyzed using a non-perturbative renormalization-group scheme. We find that order-parameter fluctuations can…
The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between…
We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the…
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}…
Equilibrium statistical ensembles impose stringent constraints on phases of quantum matter. For example, the Mermin-Wagner theorem prohibits long-range order in low-dimensional systems beyond the ground state. Here, we show that quantum…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
A new graph-based order parameter is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system, and is transferable to all structural geometries. Three sets of data are…
In strongly correlated multi-orbital systems, various ordered phases appear. In particular, the orbital order in iron-based superconductors attracts much attention since it is considered to be the origin of the nematic state. In order to…
By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the…
We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum…
We report the discovery of a mixed orientational structure in the quasi-one-dimensional fluid of hard non-spherical bodies with the exact calculation of the thermodynamic and structural quantities using the transfer operator method. The…
The characterization of quantum magnetism in a large spin ($\geq 1$) system naturally involves both spin-vectors and -tensors. While certain types of spin-vector (e.g., ferromagnetic, spiral) and spin-tensor (e.g., nematic in frustrated…