Time: 2:00 pm, Wednesday, April 24

Venue: Old LeConte 402

Title: Supersymmetry and free fermions from interacting Majorana fermions

Abstract: Perturbing a quantum spin/Majorana chain with a self-dual four-fermi terms leads to tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. I explain how supersymmetry is not only an emergent property of the scaling limit, but give an example where explicit lattice expressions for the supersymmetry generators and currents can be found. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. At the strongly interacting pure four-fermi point, the model can be solved using free-fermion raising and lowering operators, giving a gapless system with dynamical critical exponent z=3/2. I will also explain how a parafermionic generalization yields interesting multicritical points along with an AKLT phase. At the AKLT point, a map to the ordered dual model makes it straightforward to find some exact excited states as well as the ground state.

## QM Seminar Speaker Paul Fendley (Oxford) Wednesday, April 24

## QM Seminar Speaker Constantin Schrade (MIT) Wednesday, May 15

Time: 2:00 pm, Wednesday, May 15

Venue: LeConte 402

Title: Twisted bilayer graphene and topological superconductors

Abstract: forthcoming

## Chern-Simons Lectures: Jean-Bernard Zuber (Laboratoire de Physique Théorique et Hautes Energies, Sorbonne Université, Paris) Tuesday, April 2-Thursday, April 4

**Lecture 1. Counting curves and knots and links***Tuesday April 2, 11:00-12.30 am, Le Conte 402*

This talk will be devoted to the problem of counting curves, knots and links, a classical mathematical problem in which physics may bring new ideas and methods. After reviewing how matrix integrals enable one to count planar “maps” and alternating links, I turn to the more difficult problem of counting and listing curves and knots, i.e. objects with a single component. **Lecture 2. Revisiting Horn’s problem***Wednesday April 3, 2:00-3.30 pm, Le Conte 402*

Horn’s problem deals with the following question: what can be said about the spectrum of eigenvalues of the sum C=A+B of two Hermitian matrices of given spectrum? The support of the spectrum of C is well understood, after a long series of works from Weyl (1912) to Horn (1952) to Klyachko (1998) and Knutson and Tao (1999). In this talk, after a short review of the problem, I show how to compute the probability distribution function of the eigenvalues of C, when A and B are independently and uniformly distributed on their orbit under the action of the unitary group. Comparison with the similar problem for real symmetric matrices and the action of the orthogonal group reveals unexpected differences…

**Lecture 3. Horn’s problem and representation theory***Thursday April 4, 11:00-12.30 am, Le Conte 402*

Horn’s problem has also amazing connections with group theory and the decomposition of tensor product of representations. Recent progress in that direction will be discussed in that third lecture.

## QM Seminar Speaker Antti Niemi (Nordita) Thursday, March 28

Time: Thursday, March 28, 11:00 am

Venue: LeConte 325

Title: Hamiltonian time crystals

Abstract: Time crystal is presumed to be a state of matter that cannot be isolated from its environment. A time crystal is supposed to be an open, non-equilibrium system. In this talk we show that there are also energy conserving, autonomous time crystals. For this we construct examples of Hamiltonian systems that are time crystals, and we propose their actual material realizations.

## QM Seminar Speaker Oles Shtanko (MIT) Wednesday, Friday, March 22

Time: 11:00 am

Venue: LeConte 325

Title: Quasi-viscous effects in open quantum systems

Abstract: In quantum transport problems, the thermal environment is responsible for crossover between coherent and diffusive propagation. We demonstrate that additionally to suppressing the transport due to dephasing, the environment is able to induce new dynamic effects absent in an isolated system. In particular, non-interacting particles in the presence of the stochastic environment may exhibit formation of vortices and Poiseuille flow, the effects similar to commonly considered signatures of hydrodynamic behavior. We provide a detailed analysis of the phenomenon and derive the equations for quasi-viscous flow. The environmentally induced quasi-viscosity suggests new possible transport regimes accessible in various mesoscopic solid state devices, cold atomic systems, and photonic quantum simulators.

## QM Seminar Speaker Christoph Fleckenstein (Institute of Theoretical Physics and Astrophysics, University of Würzburg, Germany) Wednesday, March 13

Time: 2:00 pm

Venue: LeConte 402

Title: Quantum Constrictions In Interacting Quantum Spin Hall Systems

Abstract: Quantum spin Hall insulators give rise to time-reversal protected

helical edge modes that provide a rich platform to test an extend

theories usually assigned to high energy physics. In particular, this

becomes even more exciting when quantum constrictions are considered,

such that the helical edge states of each edge interact with each

other. Then, the effective low energy theory can be gapped without

breaking time-reversal symmetry. For present superconducting order,

this gives rise to Majorana Kramers pairs. Interestingly, when the

system is gapped by Coulomb interactions, the nature of these

bound-states changes to parafermions, which are generalizations of

Majorana modes with richer braiding properties. Here, they can coexist

with Majorana modes and, in contrast to many former proposals, they

survive even in the weakly interacting regime. Remarkably, very recent

experiments done on quantum constrictions based on HgTe/HgCdTe quantum

wells not only imply the existence of interactions at the helical

edge, but also indicate the presence of two-particle scattering terms,

necessary for those parafermions.

## QM Seminar Speaker Chandra Varma (UC Berkeley Visiting Researcher) Wednesday, February 27

Time: 2:00 pm

Venue: LeConte 402

Title: Discovery of Chiral Spin Order in Some Compounds

Abstract: Examination of the magnetic torque measurements in some iridates and in RuCl(3) suggests that they have chiral spin-order of the form

< Si · (Sj × Sk > .

Given an anisotropy so that two of the three spins in the order parameter lie in the plane, a cusp is expected in the energy when a magnetic ﬁeld B is applied in a direction approaching the normal to the plane. This leads to a discontinuity in Torque with a magnitude ∝ |B|3. This prediction has been tested in experiments.

Relation of the connection of chiral order to spin-liquids, to topological eﬀects expected, and to the nature of the ground state and excitations for deviations from a spin per site, will also be discussed.

## QM Seminar Speaker Paolo Molignini (ETH Zurich) Wednesday, January 23

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.

## QM Seminar Speaker Guifre Vidal (Perimeter Institute) Wednesday, December 19

**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.

* *

## QM Seminar Speaker Toshikaze Kariyado (Harvard, NIMS/Japan) Wednesday, December 19

2 pm

LeConte 402

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.