Scientific Series

We present a set of models which realize interacting topological phases. The models are constructed in 2 dimensions for a system with U(1)xU(1) symmetry. We demonstrate that the models are topological by measuring their Hall conductivity, and demonstrating that they have gapless edge modes. We have also studied the models numerically.

Physical theories ought to be built up from colloquial notions such as ’long bodies’, ’energetic sources’ etc. in terms of which one can define pre-theoretic ordering relations such as ’longer than’, ’more energetic than’. One of the questions addressed in previous work is how to make the transition from these pre-theoretic notions to quantification, such as making the transition from the ordering relation of ’longer than’ (if one body covers the other) to the notion of how much longer. In similar way we introduce dynamical notions ’more impulse’ (if in a collision one object overruns the other) and ’more energetic’ (if the effect of one source exceeds the effect of the other). In a physical model - built by coupling congruent standard actions - those basic pre-theoretic notions become measurable. We derive all (classical and relativistic) equations between basic physical quantities of Energy,  Momentum and Inertial Mass and ultimately the principle of least action.

Weak values were introduced by Aharonov, Albert, and Vaidman 25 years ago, but it is only in the last 10 years that they have begun to enter into mainstream physics. I will introduce weak values as done by AAV, but then give them a modern definition in terms of generalized measurements. I will discuss their properties and their uses in experiment. Finally I will talk about what they have to contribute to quantum foundations. 

In this talk, I will present recent work aimed at tackling two cornerstone problems in the field of strongly correlated electrons---(1) conducting non-Fermi liquid electronic fluids and (2) the continuous Mott metal-insulator transition---via controlled numerical and analytical studies of concrete electronic models in quasi-one-dimension.  The former is motivated strongly by the enigmatic "strange metal" central to the cuprates, while the latter is pertinent to, e.g., the spin-liquid candidate 2D triangular
lattice organic materials \kappa-(BEDT-TTF)_{2}Cu_{2}(CN)_{3} and EtMe_{3}Sb[Pd(dmit)_{2}]_{2}.  In the first part of the talk, I will focus on point (1) and discuss our realization on the two-leg ladder of a novel non-Fermi liquid quantum phase---the "d-wave metal"---which we construct by placing the charge sector of the electronic system into a "Bose metal" with strong d-wave correlations.  Importantly, this phase is non-perturbative in that it cannot be accessed starting from free electrons and slowly turning on interactions.  Remarkably, we are able to realize this strange metal as the ground state of reasonable microscopic Hamiltonian by augmenting the t-J model with a simple, local four-site ring-exchange interaction.  In the second half of the talk, I will discuss recent work on various half-filled electronic models on the two-leg triangular strip in which we have identified a continuous Mott transition between a metal and "spin Bose metal", where the latter is a novel
Mott-insulating spin-liquid phase obtained from the former by gapping out only the overall charge mode at strong coupling. Our Mott transition is shown to be in the XY universality class and thus
constitutes a clear and direct quasi-1D analog of the elegant higher-dimensional scenario recently proposed by Senthil [1].  Finally, I will touch on the potential relevance of these studies to the actual 2D materials which inspired them:  the cuprates and the organics.

[1]  T. Senthil, PRB 78, 045109 (2008).

"A well constructed theory is in some respects undoubtedly an artistic production." - Sir Ernest Rutherford

"Design is the synthesis of form and content."-Paul Rand

On the surface, the scientific method (primarily analytic) and design methodologies (primarily synthetic) seem to be quite different processes but there is considerable overlap and communicating science involves a blend of both. Scientists tend to use a scientific approach when
communicating science but there are benefits to using a designer's approach. Communicating science always requires finding solutions to difficult, ill-defined problems but employing design frameworks can help. 

One such framework is "design thinking", a powerful approach to problem solving that is rarely explicitly used in science or science communication. Design thinking consists of a set of analytic and
synthetic steps, although not a purely linear sequence, involving various modes of thought and processes. Design thinking is user-centered, collaborative, experimental, and has a bias toward action. This colloquium will present a design-thinking framework that can be useful in communicating science and examine how it differs from a typical scientific approach to problem solving.

Although the colloquium will focus primarily on outreach-type communication, we shall also consider applying the framework to writing scientific papers. In the end we'll find that scientists are designers
too, but that reframing the intellectual toolkits on hand can be useful for scientists when  communicating science.

We introduce two relative entropy quantities called the min- and max-relative 
entropies and discuss their properties and operational meanings.

These relative entropies act as parent quantities for tasks such as data compression, information
transmission and entanglement manipulation in one-shot information theory. Moreover, they lead us to define entanglement monotones which have interesting operational interpretations.

In the past few years, optical cooling and manipulating of macroscopic objects, such as micro-mirrors and cantilevers has developed into an active field of research. In mechanical systems, the oscillator is attached to its suspension, a thermal contact that limits the motion isolation. On the other hand, when these small objects are levitated using the radiation pressure force of lasers, the excellent thermal isolation even at room temperatures helps produce very sensitive force detectors, and eventually quantum transducers for quantum computation purposes. These new techniques may have a variety of applications for fundamental physics such as short distance tests of gravity and gravitational wave detection at high frequencies. In addition, there are several proposals suggesting that optically levitated dielectrics can be cooled to the ground state of the center of mass motion,
opening the exciting possibility of creating macroscopic matter-wave interferometers.

Recently powerful techniques have emerged for performing multi-loop computations of scattering amplitudes in quantum gravity and  supergravity.  These techniques include generalized unitarity and the double-copy property, related to color-kinematics duality in gauge theory.  Using these  techniques, the ultraviolet divergence structure of N=8 supergravity, and more recently pure N=4 supergravity, have been assessed, not only in four space-time dimensions but also in higher dimensions.  The results can be compared to expectations based on potential counterterms that can be constructed using (conjectured) superspace formalisms or nonlinear symmetry constraints.  Interestingly, the critical ultraviolet dimension in which N=8 supergravity first diverges is equal to that for N=4 super-Yang-Mills theory through four loops.  If this statement were to hold to all loop orders, then N=8 supergravity would represent a perturbatively finite, point-like theory of quantum gravity in four dimensions.  In this talk, I will review all of this recent progress.

I describe recent work with with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamic stability is equivalent to the positivity of the canonical energy, $\mathcal E$, on a subspace of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon.  We further show that $\mathcal E$ is related to the second order variations of mass, angular momentum, and horizon area by $\mathcal E = \delta^2 M - \sum_i \Omega_i \delta^2 J_i - (\kappa/8\pi) \delta^2 A$, thereby establishing a close connection between dynamic stability and thermodynamic stability.

Thermodynamic instability of a family of black holes need not imply dynamic instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that all black branes corresponding to
thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of $\mathcal E$ is equivalent to the satisfaction of a ``local Penrose inequality,'' thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.

When a large number of quantum mechanical particles are put together and allowed to interact, various condensed matter phases emerge with macroscopic quantum properties. While conventional quantum phases like superfluids or quantum magnets can be understood as a simple collection of
single particle quantum states, recent discoveries of fractional quantum Hall or spin liquids states contain intrinsic entanglement among all the particles. To understand such unconventional phases requires unconventional methods. In this talk, I will discuss how the quantum information insights about many-body entanglement gives us a unique perspective and a powerful tool to study these
unconventional phases. In particular, starting from simple entanglement building blocks, we are able to construct new gapped quantum phases, classify all possible gapped phases in certain cases and obtain a better understanding of the structure of the phase diagram. With these progress, we expect the many-body entanglement point of view to play an important role in our effort to map the full quantum phase diagram, leading to breakthroughs in our understanding of gapless phases and phase transitions and in the development of numerical tools to simulate such systems.

Shor's algorithm can be a meaningful test for experimental quantum processing systems, when suitably realized.  I present results from a  recent implemenation of quantum factoring using trapped ion qubits, demonstrating feed-forward control, use of quantum memory during computation, and cascaded three-qubit gates.  Such capabilities are necessary ingredients for a future large-scale,
fault-tolerant quantum computing system.

Hexagon functions are a class of iterated integrals, depending on three variables (dual conformal cross ratios) which have the correct branch cut structure and other properties to describe the scattering of six gluons in planar N=4 super-Yang-Mills theory. We classify all hexagon
functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations.  As an example, the three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined
previously.

The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematics limits, including the near-collinear and multi-Regge
limits.  These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann-Zeta-valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability.  The multi-Regge limits agree with a factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one.  For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.