VIEWPOINT by the exponential of the classical action divided by ħ. In general, such an integral Quantum connections is not a well-defined mathematical object, because of the uncontrollably large number Sean Hartnoll, Subir Sachdev , Tadashi Takayanagi, Xie Chen, Eva Silverstein of possible configurations. However, in the low- temperature limit of charged and Julian Sonner black holes, it can be evaluated in the Theoretical high- energy and condensed- matter physics share various ideas and near- horizon region, where the classical tools. New connections between the two have been established through quantum theory shows that the spacetime becomes 1 + 1 dimensional. And the path integral information, providing exciting prospects for theoretical advances and even over these 1 + 1- dimensional spacetimes potential experimental studies. Six scientists discuss different directions of and electromagnetic fields maps exactly as research in this inter-disciplinary field. a hologram onto the low-temperature path integral of the 0 + 1- dimensional SYK model. New connections Quantum matter without quasiparticles In recent work, extensions of such mappings have led to advances in our understanding Sean Hartnoll. High- energy and Subir Sachdev. The study of compressible of the quantum behaviour of Einsteinian condensed- matter physics are organized states of electronic matter without theories of gravity, and insights into the around common fundamental concepts quasiparticle excitations began in the black- hole information paradox. such as symmetry breaking and the early 1980s, motivated by observations of renormalization group, and share core the ‘strange metal’ in copper-oxide- based Gravity and entanglement mathematical machinery including superconductors, and by the quantum Feynman diagrams and topology. This Hall state in the half-filled Landau level of Tadashi Takayanagi. The wavefunctions has led to a historically fruitful interface semiconductors in a strong magnetic field. of quantum many- body systems are between the two fields. In the last couple When quasiparticles are present, a quantum typically complicated from an algebraic of decades, two new points of connection many- body system will relax to equilibrium point of view. However, it is often possible have emerged. in response to an external perturbation in to extract a simple geometrical structure First, holographic duality has a time of the order of the mean collision from a wavefunction, namely quantum established that the classical evolution time between the quasiparticles. Without entanglement. In other words, the ‘skeleton’ of black-hole horizons precisely captures quasiparticles, equilibration proceeds of a many-body state is given by a network of the dissipative dynamics of a strongly more rapidly and in a time as short as quantum entanglement. quantum phase of matter. In recent the ‘Planckian time’ ħ/(kTB ), where Quantum entanglement also appears years, this connection has moved beyond T is the temperature of the final state. as a fundamental degree of freedom in simple correlation functions (that Remarkably, there is a solvable model of quantum gravity. The amount of quantum describe the approach to coarse-grained non- quasiparticle quantum dynamics, the entanglement is measured by a quantity thermal equilibrium) to more nuanced SYK model of electrons with all-to- all and called entanglement entropy. With observables that can probe signatures random interactions. This model displays the framework of holographic duality, of many-body quantum chaos. Tied up Planckian time relaxation and also describes entanglement entropies in conformal field with this shift has been the emergence some other aspects of the physics of the theories (CFTs) turn out to be equal to areas of the Sachdev–Ye–Kitaev (SYK) model. copper oxide superconductors. of minimal surfaces in an anti-de- Sitter This model shares many of the features A distinct physical system that also space. This holographic entanglement (and limitations) of fully fledged holographic displays Planckian time relaxation is a entropy formula was recently generalized theories, but is both microscopically closer to black hole, and this becomes clear from into CFTs coupled to a dynamical gravity, conventional condensed-matter Hamiltonians the quantum temperature of a black hole providing a remarkable explanation for the and under greater technical control. computed by Stephen Hawking in 1974. black hole information paradox. Second, many- body quantum In this case, there is a remarkable and Surprisingly, the above two observations entanglement has simultaneously emerged surprisingly close connection between in two different subjects suggest the as an organizing principle in both fields. the SYK model and black holes with a fascinating prospect that gravitational It appears that quantum states supporting net electric charge, the latter described by spacetime can emerge from quantum holographically emergent gravity have quantizing Einstein’s classical theory of entanglement. This idea has been used an entanglement structure that may gravity and Maxwell’s classical theory successfully over the past several years be analogous to that of topologically of electromagnetism. The quantization within the conventional holography non- trivial phases of matter. Fleshing out is described by a path integral over for a special class of spacetime whose this connection promises to be a source different configurations of spacetime and cosmological constant is negative. I expect of future progress. electromagnetic fields, each weighted this approach will also be crucial when NATURE REVIEWS | PHYSICS 0123456789();: VIEWPOINT trying to tackle holography for general to be possible. All these features suggest that spacetimes, including de Sitter spaces. these models cannot be properly described using a continuous field theory, at least not String theory Fracton models in the usual way. Progress has been made on many Xie Chen. In the past few years, a new aspects, including the discovery of new class of quantum many- body models, models, connecting some of the features to Quantum Quantum Black-hole called the ‘fracton’ models, has captured systems we are familiar with, and exploring information matter physics the imagination of theorists from the new conceptual ideas to properly capture condensed- matter and the high- energy the underlying order (for a review, see communities alike. These models, many REFS1,2). Yet we are only scratching the of which were discovered as quantum error surface. The exotic physics of the fracton Condensed- correction codes, host a number of exotic model may fundamentally change and matter properties never seen before. They contain extend the way we approach quantum physics point excitations that cannot move on their many- body systems, while bringing the own, the ground- state degeneracy grows quantum- information, condensed- matter Fig. 1 | Quantum connections. The study of exponentially with system size, and the usual and high- energy communities closer quantum matter lies at the intersection of four renormalization group transformation does together (Fig. 1). areas of fundamental physics, providing a fertile not apply. ground for the exchange of ideas and tools. Figure Fracton models challenge both A new notion of universality adapted with permission from REF.6, Cambridge condensed- matter and high-energy theory. University Press. The immobility of the point excitations Eva Silverstein. A classic connection results in slow and non-thermal dynamics between high- energy and condensed- matter that needs to be better understood and physics concerns the renormalization irrelevant’ phenomena that become characterized. The growing ground-state group and the related notion of universality. important in the presence of long times degeneracy indicates an order that is not The details of the microscopic theory do not or large fields. only beyond the symmetry-breaking affect the outcome of experiments involving Reversing this flow is generally paradigm but also beyond the conventional low- energy probes of a system, enabling fraught with ambiguity, since one cannot topological paradigm. The renormalization a principled focus on a small number of determine the microscopic physics from group transformation needs to be relevant terms in the Lagrangian of the a few relevant terms at low energy. But augmented with non-trivial resource states theory. There is an exception: ‘dangerously in a new development3–5, certain irrelevant deformations are solvable and universal in a new sense. These deformations are The contributors specified via a differential equation, through Sean Hartnoll is Associate Professor of Physics at Stanford University. He received his PhD from a step- by- step procedure. At each step, Cambridge University in 2005 and did postdocs at Cambridge, KITP Santa Barbara and Harvard. the Lagrangian of the theory is deformed by He won the New Horizons prize in 2015. He has co- authored a book on ‘Holographic Quantum a certain bilinear of the stress energy tensor Matter’ and works on a range of topics in high energy, gravitational and condensed matter physics. known as TT ; the effect of this tensor on the Subir Sachdev is Herchel Smith Professor of Physics at Harvard University. He was educated energy spectrum is calculable. Joining this at the Indian Institute of Technology, the Massachusetts Institute of Technology and Harvard. to a trajectory including the addition of a His honours include the Dirac Medal and the Onsager