Scientific Series

A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. In this talk I describe recent work showing that there are 6 new electronic topological insulators that have no non-interacting counterpart. Combined with the previously known band-insulators, these produce a total of 8 topologically distinct phases. Two of the new topological insulators have a simple physical description as Mott insulators in which the electron spins form spin analogs of the familiar topological band-insulator. The remaining are obtained as combinations of these two `topological paramagnets' and the topological band insulator. These 8 phases form a complete list of all possible interacting topological insulators, and are classified by a $\mathbb{Z}_2^3$ group-structure. As a necessary part of the talk I will also review progress in the theory of bosonic Symmetry Protected Topological phases in 3d.

We
employ the effective field theory approach for multi-field inflation which is a
generalization of Weinberg's work. In this method the first correction terms in
addition to standard terms in the Lagrangian have been considered. These terms
contain up to the fourth derivative of the fields including the scalar field
and the metric. The results show the possible shapes of the interaction terms
resulting eventually in non-Gaussianity in a general formalism. In addition
generally the speed of sound is different but almost unity. Since in this
method the adiabatic mode is not discriminated initially so we define the
adiabatic as well as entropy modes for a specific two-field model. It has been
shown that the non-Gaussianity of the adiabatic mode and the entropy mode are
correlated in shape and amplitude. It is shown that even for speed close to
unity large non-Gaussianities are possible in multi-field case. The amount of
the non-Gaussianity depends on the curvature of the classical path in the
phase-space in the Hubble unit such that it is large for the large curvature.
In addition it is emphasized that the time derivative of adiabatic and entropy
perturbations do not transform due to the shift symmetry as well as the
original perturbations. Though two specific combinations of them are invariant
under such a symmetry and these combinations should be employed to construct an
effective field theory of multi-field inflation.

We consider the production of strongly interacting, heavy SUSY pairs at the LHC. When the centre of mass energy is close to the production threshold of the pair, the corresponding cross sections receive large higher-loop QCD corrections. These corrections are classified as the so-called soft logarithms and Coulomb singularities and they lead to a break down of the usual perturbation expansion. In this talk I review the origin of these large corrections and explain how they can be resummed by using Effective Field theories. Finally, I will present some resummed results for the pair production cross sections of heavy squarks and gluinos. Based on: arXiv:1202.2260 and 1211.3408.

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.