Time: 2:00 pm
Venue: LeConte 402
Title: Criticality and universality of Floquet topological phase transitions
Abstract: Periodic driving has recently emerged as an extremely versatile tool to engineer and tune exotic topological states of matter in a controlled
way. For example, periodic driving generates a cascade of Majorana edge
modes beyond the static limitation of one per edge in the Kitaev chain,
resulting in a hierarchy of associated topological phase transitions
(TPT’s). Understanding the critical behavior of such out-of-equilibrium
TPT’s is therefore an important step in the quest to harness the unique
properties of Floquet systems.
In this talk, I will compare the nature of the topological phase
transitions in various static and periodically driven systems by means
of a renormalization group procedure on the curvature functions used to
construct topological invariants. I will demonstrate how this very
transparent and powerful method can identify the topological phase
boundaries and assess the nature of their criticality in terms of
universality classes. This procedure works even for topological phases
hosting anomalous edge modes, i.e. phases where the Floquet band Chern
number does not correspond to the number of edge states. Finally, I will
also show how the method can be effectively extended to explicitly
time-dependent curvature functions to capture the critical behavior as a
function of time.
Time/Venue: Wednesday, December 19 at 11:00 am, LeConte 325
Title: Tensor networks, geometry and AdS/CFT
Abstract: The multiscale entanglement renormalization ansatz (MERA) is a d+1 dimensional tensor network that describes the ground state of a d-dimensional critical quantum spin system. In 2009, Swingle argued that MERA is a lattice realization of the AdS/CFT correspondence, with the tensor network representing a time slice of AdS, namely hyperbolic space H2. Other authors have since then argued that, instead, MERA represents de Sitter spacetime dS2. I will introduce a criterion, based on CFT path integrals, to unambiguously attach a geometry to a tensor network and then conclude that MERA is neither H2 or dS2, but actually a light cone L2. Finally, I will introduce two new tensor networks, euclidean MERA and lorentzian MERA, corresponding to H2 and dS2 and discuss the implications of these results for holography and the study of quantum field theory in curved spacetime.
Title: Topological states in nano punctured graphene
Abstract: Artificially designed topological states attracts much attention recently, especially in systems beyond conventional electronic systems, such as photonic or phononic crystals. A widely applied scheme is to prepare artificially designed pseudospins, and use them to realize a state mimicking a quantum spin Hall state. Here, the idea of the pseudospin based topological states is reimported to an electronic system, graphene with regular arrays of holes, or graphene nanomesh. Inducing a gap in graphene by regular hole arrays itself is a known issue, but now we predict that topologically distinct states can be obtained by changing the hole arrangement, say from triangular hole arrays to honeycomb hole arrays. The topological nontriviality is shown as interface states with pseudospin current, which nicely mimic helical edge states in a quantum spin Hall state. We also show that the nanomesh can be characterized in a view point of a topological crystalline insulator.
Old LeConte 402
Title: A Black Hole as a Particle
Abstract: We study the quantum effects of Near-Extremal black holes near their horizons. The gravitational dynamics in such backgrounds are closely connected to a particle in 𝐴𝑑𝑆2 with constant electric field. We use this picture to solve the theory exactly. We will give a formula to calculate all correlation functions with quantum gravity backreactions as well as the exact Wheeler-DeWitt wavefunction. Using the WdW wavefunction, we investigate the complexity growth in quantum gravity.
2:00 pm, LeConte 402
Title: Thermal quantum Hall effect in a spin liquid: the role of phonons
Abstract: The recent observation of a half-integer quantized thermal Hall effect in α -RuCl3 is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity is never exactly quantized in bulk materials.. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge-picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue, that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The coupling of phonons to the spin liquid imprints a Berry phase onto the phonon system, which gives, however only a small correction to the quantized Hall effect.
Host: Ehud Altman
Title: Minimal Models and Spectral Statistics of Many-Body Quantum Chaotic Systems
Abstract: I will present two minimal models for many-body quantum chaotic systems. Each model has a q-dimensional Hilbert space at each site, and has a time evolution that is random in space but periodic in time (Floquet). I evaluate the spectral statistics of the Floquet operator and the dynamical behaviour of these models via diagrammatic techniques in the large-q limit. Using a mapping to classical statistical model, I explore the universal behaviour in the spectral correlations of many-body quantum chaotic systems that goes beyond the random matrix theory.
Title: Entanglement in mixed states of fermions
Abstract: Deciding whether a bipartite mixed state is separable (unentangled) or not is a computationally intractable (NP-hard) problem. In the case of qubits, the partial transpose of density matrices is known as a good candidate to diagnose separable states. In particular, it can be used to define an entanglement measure called the (logarithmic) negativity. Surprisingly, the extension of the partial transpose (and so the negativity) to fermionic systems remained intractable even for the non-interacting Gaussian states. In this talk, I will introduce partial time-reversal transformation as an analog of partial transpose for fermionic density matrices. This definition naturally arises from the spacetime picture of density matrices in which partial transpose is equivalent to reversing the arrow of time for one subsystem relative to the other subsystem. I will show that the partial time-reversal of density matrix can be computed efficiently for fermionic Gaussian states and its norm satisfies the necessary quantum information theoretic properties to qualify as an entanglement measure. Hence, we call it the fermionic negativity.
Time/Venue: Friday, November 16 at 1:00 pm, LeConte 375
Title: Solvable models of metals with interactions and disorder, and their transport properties
Abstract: Despite much theoretical effort, there is no complete theory of the “strange” metal phase of the high temperature superconductors, and its linear-in-temperature resistivity. This phase is believed to be a strongly-interacting metallic phase of matter without fermionic quasiparticles, and is virtually impossible to model accurately using traditional perturbative field-theoretic techniques. Recently, progress has been made using large-N techniques based on the solvable Sachdev-Ye-Kitaev (SYK) model, which do not involve expanding about any weakly-coupled limit. I will describe constructions of solvable models of strange metals based on SYK-like large-Nlimits, which can reproduce some of the experimentally observed features of strange metals and adjoining phases. These models, and further extensions, could possibly pave the way to developing a controlled theoretical understanding of the essential building blocks of the electronic state in correlated-electron superconductors near optimal doping.
Wednesday, November 14, 2:00 pm, LeConte 402
Title: “Topology and Quantum Criticality: edge modes in symmetry-enriched CFTs”
Abstract: Around 30 years ago, the spin-1 Heisenberg chain was realized to host edge modes protected by spin rotation symmetry and the Haldane gap—the first instance of a symmetry-protected topological phase. We show that the same model continues to surprise: tuning to criticality, a piece of the edge mode remains exponentially localized. It is clarified how this is a general phenomenon which can be stabilized by symmetry properties of the low-energy theory alone, related to a topological twist in a symmetry-enriched conformal field theory.
2:00 pm, LeConte 324
Title: Geometry and dynamics in the fractional quantum Hall effect
Abstract: One of the major efforts in current investigations of the fractional quantum Hall (FQH) effect is understanding the connections between topological order, geometry and symmetry breaking. Incompressible FQH fluids are now understood to possess a collective degree of freedom that can be viewed as a “quantum geometry”, which is the key to describing their properties beyond the remit of topological quantum field theory. In the first part of this talk, I will review these developments and show how geometric aspects of FQH states can be studied microscopically using the formalism of generalized Haldane pseudopotentials . In the second part, I will discuss how bulk dynamics of FQH states can be probed in experiment using a “geometric quench” . One of the physical consequences of geometric quenches in gapped FQH states is that they expose coherent oscillations of the emergent geometric degree of freedom, which can be viewed as the condensed matter analogue of the “graviton” particle. The geometric quench is a tool that allows analytical and numerical studies of new types of many-body quantum dynamics in strongly-correlated topological systems away from the zero temperature limit.
 Bo Yang, Zi-Xiang Hu, Ching Hua Lee, and Z. Papic, Phys. Rev. Lett. 118, 146403 (2017).
 Zhao Liu, Andrey Gromov, and Zlatko Papic, Phys. Rev. B 98, 155140 (2018).