This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

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Doping a Mott insulator: Physics of high-temperature superconductivity

Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

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Wetting and Spreading

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.

http://www.physics.udel.edu/~bnikolic/QTTG/NOTES/DMRG/SCHOLLWOCK=RMP_dmrg.pdf

The density-matrix renormalization group

We report on transport measurements in the mixed state of YBa[sub 2]Cu[sub 3]O[sub 7] single crystals using the dc flux transformer geometry. In the vortex fluid regime we have observed the onset of a nonlocal conductivity. At lower temperatures, close to but above the phase transition temperature the vortices become effectively three dimensional in character. This is in sharp contrast to recent flux transformer experiments on Bi[sub 2]Sr[sub 2]CaCu[sub 2]O which have failed to see a nonlocal conductivity, confirming the two-dimensional character at high temperatures of the vortices in that system. These observations suggest that in a finite temperature interval, the vortex state in YBa[sub 2]Cu[sub 3]O[sub 7] is a line liquid.

Observation of a nonlocal conductivity in the mixed state of YBa2Cu3O7- delta : Experimental evidence for a vortex line liquid.

The residual energy, $\ensuremath{\epsilon}(\ensuremath{\tau})$, left after cooling to zero temperature in a finite time $\ensuremath{\tau}$ is analyzed for various disordered systems, including spin-glasses and random-field magnets. We argue that the generic behavior for such frustrated systems is $\ensuremath{\epsilon}(\ensuremath{\tau})\ensuremath{\sim}{(\mathrm{ln}\ensuremath{\tau})}^{\ensuremath{-}\ensuremath{\zeta}}$ for large $\ensuremath{\tau}$, with the exponent $\ensuremath{\zeta}$ depending on the system. This result is dominated in some cases by a distribution of classical two-level systems with low excitation energies, and in other cases by large-scale nonequilibrium effects.

Residual energies after slow cooling of disordered systems.

A systematic method for developing high-order, zero-temperature perturbation expansions for quantum many-body systems is presented. The models discussed explicitly are spin models with a variety of interactions, in one and two dimensions. The wide applicability of the method is illustrated by expansions around Hamiltonians with ordered and disordered ground states, namely Ising and dimerized models. Computer implementation of this method is discussed in great detail. Some previously unpublished series are tabulated.

Perturbation expansions for quantum many-body systems

We have developed a general scheme for carrying out systematic perturbation expansions for groundstate properties of quantum lattice models. As an application, we study the onset of spontaneous N\'eel order in $S=\frac{1}{2}$ Heisenberg antiferromagnets by expanding around dimerized Hamiltonians. In one dimension (1D) we recover accurately the known exact results. On the square lattice we find novel critical points separating N\'eel ordered and disordered phases; the estimated critical exponents are consistent with those of the 3D classical Heisenberg model.

Ground states of low-dimensional quantum antiferromagnets.

We examine, with Monte Carlo simulations, the off-diagonal long-range correlations in a highly simplified model of a three-dimensional disordered superconductor in a magnetic field. Comparisons are made to the three-dimensional Ising and {ital XY} Edwards-Anderson spin-glass models. Somewhat surprisingly, the model superconductor behaves very much like the Ising spin glass, suggesting that it too may have a spin-glass-like ordered phase at nonzero temperature, namely the vortex-glass phase.

David A. Huse

Papers

Observation of a nonlocal conductivity in the mixed state of YBa2Cu3O7- delta : Experimental evidence for a vortex line liquid.

Residual energies after slow cooling of disordered systems.

Perturbation expansions for quantum many-body systems

Ground states of low-dimensional quantum antiferromagnets.

Possible vortex-glass transition in a model random superconductor