Sho Yaida

Viscosity bound violation in higher derivative gravity

Motivated by the vast string landscape, we consider the shear viscosity to entropy density ratio in conformal field theories dual to Einstein gravity with curvature square corrections. After field redefinitions these theories reduce to Gauss-Bonnet gravity, which has special properties that allow us to compute the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning of the coupling, the value of the shear viscosity to entropy density ratio can be adjusted to any positive value from infinity down to zero, thus violating the conjectured viscosity bound. At linear order in the coupling, we also check consistency of four different methods to calculate the shear viscosity, and we find that all of them agree. We search for possible pathologies associated with this class of theories violating the viscosity bound.

Viscosity bound and causality violation.

In recent work we showed that, for a class of conformal field theories (CFT) with Gauss-Bonnet gravity dual, the shear viscosity to entropy density ratio, eta/s, could violate the conjectured Kovtun-Starinets-Son viscosity bound, eta/s > or = 1/4 pi. In this Letter we argue, in the context of the same model, that tuning eta/s below (16/25)(1/4 pi) induces microcausality violation in the CFT, rendering the theory inconsistent. This is a concrete example in which inconsistency of a theory and a lower bound on viscosity are correlated, supporting the idea of a possible universal lower bound on eta/s for all consistent theories.

Holographic Lattices, Dimers, and Glasses

We holographically engineer a periodic lattice of localized fermionic impurities within a plasma medium by putting an array of probe D5-branes in the background produced by N D3-branes. Thermodynamic quantities are computed in the large N limit via the holographic dictionary. We then dope the lattice by replacing some of the D5-branes by anti-D5-branes. In the large N limit, we determine the critical temperature below which the system dimerizes with bond ordering. Finally, we argue that for the special case of a square lattice our system is glassy at large but finite N, with the low temperature physics dominated by a huge collection of metastable dimerized configurations without long-range order, connected only through tunneling events.

Adventures in Holographic Dimer Models

We abstract the essential features of holographic dimer models, and develop several new applications of these models. Firstly, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Secondly, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.

Disordered holographic systems: Functional renormalization

We study quenched disorder in strongly correlated systems via holography, focusing on the thermodynamic effects of mild electric disorder. Disorder is introduced through a random potential which is assumed to self-average on macroscopic scales. Studying the flow of this distribution with energy scale leads us to develop a holographic functional renormalization scheme. We test this scheme by computing thermodynamic quantities and confirming that the Harris criterion for relevance, irrelevance or marginality of quenched disorder holds.

Disordered holographic systems: Marginal relevance of imperfection

We continue our study of quenched disorder in holographic systems, focusing on the effects of mild electric disorder. By studying the renormalization group evolution of the disorder distribution at subleading order in perturbations away from the clean fixed point, we show that electric disorder is marginally relevant in (2+1)-dimensional holographic conformal field theories.

Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling

Significance Computer simulations give precious insight into the microscopic behavior of disordered and amorphous materials, but the timescales they cover are orders of magnitude shorter than in experiments. For instance, simulations of glass-forming liquids cover at most 4–5 decades of viscous slowing down, which fall far short of the 12–13 decades commonly accessible in experimental studies. We here close this enormous gap for some realistic liquid models, and even equilibrate beyond experimental timescales by means of the swap Monte Carlo algorithm. We show that the approach to the glass phase is accompanied by a precipitous decrease of the configurational entropy as well as by growing spatial correlations, which we visualize in real space under experimentally relevant conditions. Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, because of the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally relevant timescales. In this work, we not only close the colossal gap between experiments and simulations but manage to create in silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

Point-to-set lengths, local structure, and glassiness.

The growing sluggishness of glass-forming liquids is thought to be accompanied by growing structural order. The nature of such order, however, remains hotly debated. A decade ago, point-to-set (PTS) correlation lengths were proposed as measures of amorphous order in glass formers, but recent results raise doubts as to their generality. Here, we extend the definition of PTS correlations to agnostically capture any type of growing order in liquids, be it local or amorphous. This advance enables the formulation of a clear distinction between slowing down due to conventional critical ordering and that due to glassiness, and provides a unified framework to assess the relative importance of specific local order and generic amorphous order in glass formation.

Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions.

The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon-the Gardner transition-has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_{u}=6. Here, we obtain evidence for the existence of these transitions in d<d_{u} using a two-loop calculation. Because the critical fixed point is found in the strong-coupling regime, we corroborate the result by resumming the perturbative series with inputs from a three-loop calculation and an analysis of its large-order behavior. Our study offers a resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.

Efficient measurement of point-to-set correlations and overlap fluctuations in glass-forming liquids

Cavity point-to-set correlations are real-space tools to detect the roughening of the free-energy landscape that accompanies the dynamical slowdown of glass-forming liquids. Measuring these correlations in model glass formers remains, however, a major computational challenge. Here, we develop a general parallel-tempering method that provides orders-of-magnitude improvement for sampling and equilibrating configurations within cavities. We apply this improved scheme to the canonical Kob-Andersen binary Lennard-Jones model for temperatures down to the mode-coupling theory crossover. Most significant improvements are noted for small cavities, which have thus far been the most difficult to study. This methodological advance also enables us to study a broader range of physical observables associated with thermodynamic fluctuations. We measure the probability distribution of overlap fluctuations in cavities, which displays a non-trivial temperature evolution. The corresponding overlap susceptibility is found to provide a robust quantitative estimate of the point-to-set length scale requiring no fitting. By resolving spatial fluctuations of the overlap in the cavity, we also obtain quantitative information about the geometry of overlap fluctuations. We can thus examine in detail how the penetration length as well as its fluctuations evolve with temperature and cavity size.