Claudio Castelnovo

Magnetic Monopoles in Spin Ice

Electrically charged particles, such as the electron, are ubiquitous. In contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches (see ref. 1 for example). We pursue an alternative strategy, namely that of realizing them not as elementary but rather as emergent particles—that is, as manifestations of the correlations present in a strongly interacting many-body system. The most prominent examples of emergent quasiparticles are the ones with fractional electric charge e/3 in quantum Hall physics. Here we propose that magnetic monopoles emerge in a class of exotic magnets known collectively as spin ice: the dipole moment of the underlying electronic degrees of freedom fractionalises into monopoles. This would account for a mysterious phase transition observed experimentally in spin ice in a magnetic field, which is a liquid–gas transition of the magnetic monopoles. These monopoles can also be detected by other means, for example, in an experiment modelled after the Stanford magnetic monopole search.

Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7

Magnetic Monopoles Magnets come with a north and a south pole. Despite being predicted to exist, searches in astronomy and in high-energy particle physics experiments for magnetic monopoles (either north or south on their own) have defied observation. Theoretical work in condensed-matter systems has predicted that spin-ice structures may harbor such elusive particles (see the Perspective by Gingras). Fennell et al. (p. 415, published online 3 September) and Morris et al. (p. 411, published online 3 September) used polarized neutron scattering to probe the spin structure forming in two spin-ice compounds—Ho2Ti2O7 and Dy2Ti2O7—and present results in support of the presence of magnetic monopoles in both materials. Neutron scattering measurements on two spin-ice compounds show evidence for magnetic monopoles. Sources of magnetic fields—magnetic monopoles—have so far proven elusive as elementary particles. Condensed-matter physicists have recently proposed several scenarios of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes—classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. We demonstrated, by diffuse neutron scattering, the presence of such strings in the spin ice dysprosium titanate (Dy2Ti2O7). This is achieved by applying a symmetry-breaking magnetic field with which we can manipulate the density and orientation of the strings. In turn, heat capacity is described by a gas of magnetic monopoles interacting via a magnetic Coulomb interaction.

Spin Ice, Fractionalization, and Topological Order

The spin ice compounds Dy2Ti2O7 and Ho2Ti2O7 are highly unusual magnets that epitomize a set of concepts of great interest in modern condensed matter physics: Their low-energy physics exhibits an emergent gauge field and their excitations are magnetic monopoles that arise from the fractionalization of the microscopic magnetic spin degrees of freedom. In this review, we provide an elementary introduction to these concepts and we survey the thermodynamics, statics, and dynamics—in and out of equilibrium—of spin ice from these vantage points. Along the way, we touch on topics such as emergent Coulomb plasmas, observable Dirac strings, and irrational charges. We close with the outlook for these unique materials.

Thermal quenches in spin ice.

We study the diffusion-annihilation process which occurs when spin ice is quenched from a high temperature paramagnetic phase deep into the spin-ice regime, where the excitations--magnetic monopoles--are sparse. We find that due to the Coulomb interaction between the monopoles, a dynamical arrest occurs, in which nonuniversal lattice-scale constraints impede the complete decay of charge fluctuations. This phenomenon is outside the reach of conventional mean-field theory for a two-component Coulomb liquid. We identify the relevant time scales for the dynamical arrest and propose an experiment for detecting monopoles and their dynamics in spin ice based on this nonequilibrium phenomenon.

From quantum mechanics to classical statistical physics: Generalized Rokhsar–Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition

Abstract Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar–Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.

Topological order in a three-dimensional toric code at finite temperature

We study topological order in a toric code in three spatial dimensions or a

Cluster assembling of nanostructured carbon films

3+1\text{D}

Quantum topological phase transition at the microscopic level

{\mathbb{Z}}_{2}

Quantum mechanical and information theoretic view on classical glass transitions

gauge theory at finite temperature. We compute exactly the topological entropy of the system and show that it drops, for any infinitesimal temperature, to half its value at zero temperature. The remaining half of the entropy stays constant up to a critical temperature