Existence of Long-Range Order in One and Two Dimensions
TL;DR: In this paper, it was shown that a rigorous inequality first proved by Bogoliubov may be used to rule out the existence of quasi-averages (or long-range order) in Bose and Fermi systems for one and two dimensions.
Abstract: It is pointed out that a rigorous inequality first proved by Bogoliubov may be used to rule out the existence of quasi-averages (or long-range order) in Bose and Fermi systems for one and two dimensions and $T\ensuremath{
e}0$.
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TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
Abstract: This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.
6,601 citations
TL;DR: In this article, a new definition of order called topological order is proposed for two-dimensional systems in which no long-range order of the conventional type exists, and the possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation.
Abstract: A new definition of order called topological order is proposed for two-dimensional systems in which no long-range order of the conventional type exists. The possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation. The critical behaviour found in this model displays very weak singularities. The application of these ideas to the xy model of magnetism, the solid-liquid transition, and the neutral superfluid are discussed. This type of phase transition cannot occur in a superconductor nor in a Heisenberg ferromagnet.
6,371 citations
TL;DR: The renormalization group theory has been applied to a variety of dynamic critical phenomena, such as the phase separation of a symmetric binary fluid as mentioned in this paper, and it has been shown that it can explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions.
Abstract: An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.
4,980 citations
TL;DR: Two-dimensional heterostructures with extended range of functionalities yields a range of possible applications, and spectrum reconstruction in graphene interacting with hBN allowed several groups to study the Hofstadter butterfly effect and topological currents in such a system.
Abstract: BACKGROUND Materials by design is an appealing idea that is very hard to realize in practice. Combining the best of different ingredients in one ultimate material is a task for which we currently have no general solution. However, we do have some successful examples to draw upon: Composite materials and III-V heterostructures have revolutionized many aspects of our lives. Still, we need a general strategy to solve the problem of mixing and matching crystals with different properties, creating combinations with predetermined attributes and functionalities. ADVANCES Two-dimensional (2D) materials offer a platform that allows creation of heterostructures with a variety of properties. One-atom-thick crystals now comprise a large family of these materials, collectively covering a very broad range of properties. The first material to be included was graphene, a zero-overlap semimetal. The family of 2D crystals has grown to includes metals (e.g., NbSe 2 ), semiconductors (e.g., MoS 2 ), and insulators [e.g., hexagonal boron nitride (hBN)]. Many of these materials are stable at ambient conditions, and we have come up with strategies for handling those that are not. Surprisingly, the properties of such 2D materials are often very different from those of their 3D counterparts. Furthermore, even the study of familiar phenomena (like superconductivity or ferromagnetism) in the 2D case, where there is no long-range order, raises many thought-provoking questions. A plethora of opportunities appear when we start to combine several 2D crystals in one vertical stack. Held together by van der Waals forces (the same forces that hold layered materials together), such heterostructures allow a far greater number of combinations than any traditional growth method. As the family of 2D crystals is expanding day by day, so too is the complexity of the heterostructures that could be created with atomic precision. When stacking different crystals together, the synergetic effects become very important. In the first-order approximation, charge redistribution might occur between the neighboring (and even more distant) crystals in the stack. Neighboring crystals can also induce structural changes in each other. Furthermore, such changes can be controlled by adjusting the relative orientation between the individual elements. Such heterostructures have already led to the observation of numerous exciting physical phenomena. Thus, spectrum reconstruction in graphene interacting with hBN allowed several groups to study the Hofstadter butterfly effect and topological currents in such a system. The possibility of positioning crystals in very close (but controlled) proximity to one another allows for the study of tunneling and drag effects. The use of semiconducting monolayers leads to the creation of optically active heterostructures. The extended range of functionalities of such heterostructures yields a range of possible applications. Now the highest-mobility graphene transistors are achieved by encapsulating graphene with hBN. Photovoltaic and light-emitting devices have been demonstrated by combining optically active semiconducting layers and graphene as transparent electrodes. OUTLOOK Currently, most 2D heterostructures are composed by direct stacking of individual monolayer flakes of different materials. Although this method allows ultimate flexibility, it is slow and cumbersome. Thus, techniques involving transfer of large-area crystals grown by chemical vapor deposition (CVD), direct growth of heterostructures by CVD or physical epitaxy, or one-step growth in solution are being developed. Currently, we are at the same level as we were with graphene 10 years ago: plenty of interesting science and unclear prospects for mass production. Given the fast progress of graphene technology over the past few years, we can expect similar advances in the production of the heterostructures, making the science and applications more achievable.
4,851 citations
Cites background from "Existence of Long-Range Order in On..."
...For a system with a continuous order parameter, it is not possible to have true long-range order in less than three dimensions at any finite temperature T, implying that even minute thermal fluctuations can destroy order (23)....
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TL;DR: In this article, the authors reviewed the Bose-Einstein condensation of dilute gases in traps from a theoretical perspective and provided a framework to understand the main features of the condensation and role of interactions between particles.
Abstract: The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.
4,782 citations