Talks

The average quantum physicist on the street believes that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian $H=p^2+ix^3$, which is obviously not Dirac Hermitian, has a real positive discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While $H=p^2+ix^3$ is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined space reflection P and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. Some of these properties have recently been verified in laboratory experiments. If one generalizes classical mechanics into the complex domain, the resulting theories have equally remarkable properties.

The second law of thermodynamics tells that physics imposes a fundamental constraint on the efficiency of all thermal machines. Here I will address the question of whether size imposes further constraints upon thermal machines, namely whether there is a minimum size below which no machine can run, and whether when they are small if they can still be efficient? I will present a simple model which shows that there is no size limitation and no limit on the efficiency of thermal machine and that this leads to a unified view of small refrigerators, pumps and engines.

We discuss the coupling of fermions to holographic superconductors in 3+1 and 4+1 (bulk) dimensions. We do so from a top-down perspective, by considering the reduction of the fermionic sector in recently found consistent truncations of type IIB and D=11 supergravity on squashed Sasaki-Einstein manifolds, which notably retain a finite number of charged (massive) modes. The truncations in question also include the string/M-theory embeddings of various models which have been proposed to describe systems with non-relativistic scale invariance via holography. We show that the lower-dimensional effective action for the fermion modes includes certain interactions that had been discussed in bottom-up constructions, as well as a variety of new couplings that may be relevant for applications of holographic techniques to the study of condensed matter systems

The idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT is developed. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, I consider the anomalous dimensions, gamma(n,l), of the double-trace operators of the form O (del^2)^n (del)^l O. Purely from the CFT, perturbative unitarity places a bound on these dimensions; non-renormalizable AdS interactions lead to violations of the bound at large values of n. I also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. The presence of the heavy field "unitarizes" the growth in the anomalous dimensions, and leads to a resonance-like behavior in gamma(n,l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, I demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flat-space S-matrix elements in d+1 dimensions

Entanglement renormalization is a coarse-graining transformation for quantum lattice systems. It produces the multi-scale entanglement renormalization ansatz, a tensor network state used to represent ground states of strongly correlated systems in one and two spatial dimensions. In 1D, the MERA is known to reproduce the logarithmic violation of the boundary law for entanglement entropy, S(L)~log L, characteristic of critical ground states. In contrast, in 2D the MERA strictly obeys the entropic boundary law, S(L)~L, characteristic of gapped systems and a class of critical systems. Therefore a number of highly entangled 2D systems, such as free fermions with a 1D Fermi surface, Fermi liquids and spin Bose metals, which display a logarithmic violation of the boundary law, S(L)~L log L, cannot be described by a regular 2D MERA. It is well-known that at low energies, a many-body system may decouple into two or more independent degrees of freedom (e.g. spin-charge separation in 1D systems of electrons). In this talk I will explain how, in systems where low energy decoupling occurs, entanglement renormalization can be used to obtain an explicit decoupled description. The resulting tensor network state, the branching MERA, can reproduce a logarithmic violation of the boundary law in 2D and, as additional numeric evidence also suggests, might be a good ansatz for the highly entangled systems with a 1D Fermi (or Bose) surface mentioned above. In addition, after recalling that the MERA can be regarded as a specific (discrete) realization of the holographic principle, we will see that the branching MERA leads to exotic holographic geometries.