Quantum Matter Seminar

Introduction to Topological Insulators: The Ten-fold Classification of Topological Insulators and Superconductors

May 24 at 14:00 - 15:30, 2022

Dr. Ching-Kai Chiu (Senior Research Scientist, iTHEMS)

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: Topological Superconductors and Quantum Computing

May 9 at 14:00 - 15:30, 2022

Dr. Ching-Kai Chiu (Senior Research Scientist, iTHEMS)

Venue: via Zoom

Event Official Language: English

Local and global topology for Dirac points with multi-helicoid surface states

March 24 at 17:00 - 18:15, 2022

Dr. Tiantian Zhang (Specially Appointed Assistant Professor, School of Science, Tokyo Institute of Technology)

Though topological invariants defined for topological semimetals are usually local ones, they also have a global nature. For example, the Z type local monopole charge C for Weyl points, has a global nature, telling us its influence to the rest of the Brillouin zone, giving rise to bulk-surface correspondence associated with helical surface states. In Dirac systems, helical surface states are not guaranteed due to C=0. However, a new bulk-surface correspondence associated with double/quad-helicoid surface states (DHSSs/QHSSs) can be obtained for Dirac points with the protection of a Z2 type monopole charge Q, which is defined in terms of the time-reversal (T)-glide (G) symmetry (TG)2= -1. Here we study the topology of Q for Z2 Dirac points and establish its bulk-surface correspondence with strict proofs. We find that Q is equivalent to the G-protected Z2 invariant v mathematically and physically in Z2 Dirac systems. This result is counterintuitive, since v is always trivial in T-preserving gapped systems, and was thought to be ill-defined in gapless systems. We offer a gauge-invariant formula for Q, which is associated with DHSSs in both the spinless and spinful systems with single G. Q is formulated in a simpler form in spinless systems with two vertical G, associated with QHSSs, which is also entangled with filling-enforced topological band insulators in three space groups when a T-breaking perturbation is introduced. Since Q is ill-defined in spinful systems with two vertical G, QHSSs will not be held. Material candidate Li2B4O7 together with a list of possible space groups preserving QHSSs are also proposed for demonstration on our theory and further studies. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

How is turbulence born: Spatiotemporal complexity and phase transition of transitional fluids

February 24 at 17:00 - 18:15, 2022

Dr. Hong-Yan Shih (Assistant Research Fellow, Institute of Physics, Academia Sinica, Taiwan)

How a laminar flow becomes turbulence has been an unsolved problem for more than a century and is important in various industrial applications. Recently precise measurements in pipe flow experiments showed non-trivial spatiotemporal complexity at the onset of turbulence. Based on numerical evidence from the hydrodynamics equations, we discovered the surprising fact that the fluid behavior at the transition is governed by the emergent predator-prey dynamics of the important long-wavelength mode, leading to the mathematical prediction that the laminar-turbulent transition is analogous to an ecosystem on the edge of extinction. This prediction demonstrates that the laminar-turbulent transition is a non-equilibrium phase transition in the directed percolation universality class, and provides a unified picture of transition to turbulence emerging in systems ranging from turbulent convection to magnetohydrodynamics. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Bethe ansatz and quantum computing

January 26 at 22:00 - 23:15, 2022

Prof. Rafael I. Nepomechie (Professor, Physics Department, University of Miami, Florida, USA)

We begin with a brief review of the Heisenberg quantum spin chain and its remarkable solution found by Bethe. We then review a probabilistic algorithm for preparing exact eigenstates of this model on a quantum computer. An exact formula for the success probability is presented, and the computation of correlation functions is discussed. A generalization of the algorithm to open chains with boundaries is also noted.

Venue: via Zoom

Event Official Language: English

Topological exchange statistics in one dimension

November 17 at 17:00 - 18:15, 2021

Prof. Harshman Nathan (Department of Physics, American University, USA)

In two dimensions, the topological approach to exchange statistics predicts the existence of anyons obeying statistics given by the braid group. However, in one dimension the topological approach is ambiguous because particles cannot exchange without coincidence and scattering. I will review the topological approach and show how old controversies can be resolved using orbifolds (roughly, manifolds with symmetry) to describe configuration space for one-dimensional systems. Using orbifolds also predicts new topological physics, including possibilities for “traid group” statistics when there are three-body interactions in one dimension and non-abelian statistics for indistinguishable particles on a ring. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Nonlinear response in strongly correlated systems

October 20 at 17:00 - 18:15, 2021

Dr. Robert Peters (Lecturer, Department of Physics, Graduate School of Science, Kyoto University)

Nonlinear responses in condensed matter are intensively studied because they provide rich information about materials and hold the possibility of being applied in diodes or high-frequency optical devices [1-4]. While nonlinear responses in noninteracting models have been explored widely, the effect of strong correlations on the nonlinear response is still poorly understood. This talk will introduce a Green's function method to calculate nonlinear conductivities in strongly correlated materials [5-6]. Correlation effects are thereby included by the self-energy of the material. I will then use this method to study the nonlinear conductivities in noncentrosymmetric f-electron systems. The first system is a heavy Fermion system, where a nonreciprocal conductivity appears in the ferromagnetic phase. The nonreciprocal conductivity thereby always occurs perpendicular to the magnetization of the system and has a strong spin dependence, which might be advantageous for spintronic applications. The second system is a model corresponding to the Weyl-Kondo semimetal Ce3Bi4Pd3, in which a giant spontaneous Hall effect without time-reversal symmetry breaking has been observed [7]. This Hall effect can be explained as a nonlinear Hall effect in an inversion-symmetry broken Weyl-semimetal. It has been shown that the nonlinear Hall effect is related to the Berry curvature dipole [4]. Our study shows that the magnitude of the experimentally observed nonlinear Hall effect can be explained by the strong correlations inherent in this f-electron material [8]. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Symmetry-based analysis for unconventional superconductors: Diagnosis of topological and nodal superconductivity

October 12 at 16:00 - 17:15, 2021

Mr. Seishiro Ono (Department of Applied Physics, School of Engineering, The University of Tokyo)

The physics of unconventional superconductors has gained a new dimension in the past decade, thanks to the bloom in the understanding of topological quantum materials. Keeping in mind the success of the symmetry-based diagnosis in the large-scale discovery of topological insulator and semimetal candidates [1], it is natural to ask whether the approach can be generalized to superconducting systems. In this talk, I provide a unified way to diagnose topology and superconducting nodes in unconventional superconductors. First, I review symmetry-indicator theory for the topological insulators [2]. Also, I also discuss how to generalize the theory to superconductors [3,4,5]. Next, I show that the symmetry-based approach can extensively classify superconducting nodes pinned to high-symmetric momenta [6]. Finally, I show that these results enable us to derive the comprehensive correspondences between pairing symmetries and topological/nodal superconducting nature for each material [7].
 *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Wave function geometry and anomalous Landau levels of flat bands

October 7 at 16:00 - 17:15, 2021

Prof. Bohm-Jung Yang (Associate Professor, Department of Physics and Astronomy, Seoul National University, Republic of Korea)

Semiclassical quantization of electronic states under magnetic field describes not only the Landau level spectrum but also the geometric responses of metals under a magnetic field. However, it is unclear whether this semiclassical idea is valid in dispersionless flat-band systems, in which an infinite number of degenerate semiclassical orbits are allowed. In this talk, I am going to show that the semiclassical quantization rule breaks down for a class of flat bands including singular flat bands [1-5] and isolated flat bands [6]. The Landau levels of such a flat band develop in the empty region in which no electronic states exist in the absence of a magnetic field. The total energy spread of the Landau levels of flat bands is determined by the quantum geometry of the relevant Bloch states, which is characterized by their Hilbert–Schmidt quantum distance and fidelity tensors. The results indicate that flat band systems are promising platforms for the direct measurement of the quantum geometry of wavefunctions in condensed matter. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Extended and interacting bound states in elemental superconductors

September 1 at 16:00 - 17:15, 2021

Dr. Levente Rózsa (Condensed Matter Physics, University of Konstanz, Germany)

Combining magnetism with superconductivity leads to the emergence of localized states, including Majorana bound states predicted to be relevant for topological quantum computation. In this talk, I discuss how these bound states are influenced by the details of the electronic structure. It will be shown how the shape of the Fermi surface leads to a long-ranged anisotropic extension of Yu-Shiba-Rusinov states in the vicinity of magnetic impurities [1]. The same type of Fermi surface will be demonstrated to give rise to topologically trivial Caroli-de Gennes-Matricon bound states in vortex cores [2], with similar spatial profiles to those of topological Majorana bound states. The role of spin-orbit coupling will be discussed in the hybridization of Yu-Shiba-Rusinov bound states of dimers with ferromagnetic and antiferromagnetic spin alignments [3]. The general theoretical concepts will be illustrated by experimental realizations in specific materials. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Application of Machine Learning on Many-Body Problems

August 23 at 16:00 - 17:15, 2021

Prof. Daw-Wei Wang (Professor, Department of Physics, National Tsinghua University, Taiwan)

Time: 4pm ~ 5:15pm (JST); 9am ~ 10:15am (CET); 3pm ~ 4:15pm (Taiwan) In this talk, I will briefly introduce the application of machine learning methods on quantum many-body problems. It includes a self-supervised learning approach to decide the topological phase transition in the systems of ultracold atoms by using Time-of-Flight images only without knowing any priori knowledge [1]. We then develop the Random Sampling Neural Networks for the investigation of quantum many body ground state properties in the strong interacting regime by a model rtained in the weak interacting regime [2]. Finally, we provide an Quantum-Inspired-Recurrent Neural Network, which could give a precise long-time dynamics of a quantum many-body system, even the model is trained in the short-time regime. We hope to show the great possibility to use machine learning as a new tool to investigate the quantum many-body problems. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Theory of Anomalous Floquet Higher-Order Topology

May 26 at 22:00 - 23:15, 2021

Dr. Rui-Xing Zhang (University of Maryland, College Park, USA)

Periodically-driven or Floquet systems can realize anomalous topological phenomena that do not exist in any equilibrium states of matter, whose classification and characterization require new theoretical ideas that are beyond the well-established paradigm of static topological phases. In this work, we provide a general framework to understand anomalous Floquet higher-order topological insulators (AFHOTIs), the classification of which has remained a challenging open question. In two dimensions (2D), such AFHOTIs are defined by their robust, symmetry-protected corner modes pinned at special quasienergies, even though all their Floquet bands feature trivial band topology. The corner-mode physics of an AFHOTI is found to be generically indicated by 3D Dirac/Weyl-like topological singularities living in the phase spectrum of the bulk time-evolution operator. Physically, such a phase-band singularity is essentially a "footprint" of the topological quantum criticality, which separates an AFHOTI from a trivial phase adiabatically connected to a static limit. Strikingly, these singularities feature unconventional dispersion relations that cannot be achieved on any static lattice in 3D, which, nevertheless, resemble the surface physics of 4D topological crystalline insulators. We establish the above higher-order bulk-boundary correspondence through a dimensional reduction technique, which also allows for a systematic classification of 2D AFHOTIs protected by point group symmetries. We demonstrate applications of our theory to two concrete, experimentally feasible models of AFHOTIs protected by C2 and D4 symmetries, respectively. Our work paves the way for a unified theory for classifying and characterizing Floquet topological matters. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Aperiodic and amorphous topological phases

May 12 at 17:00 - 18:15, 2021

Prof. Christopher Bourne (Visiting Scientist, iTHEMS / Assistant Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

Key features of topological insulators and superconductors such as stable edge modes have been found in an increasingly broad class of materials and systems. In this talk, I will introduce a mathematical framework to study Hamiltonians and topological phases on a general class of (aperiodic/random) point atterns. Using techniques from noncommutative geometry, we then show how bulk topological invariants and the bulk-boundary correspondence can be rigorously established in such generic systems. This is based on joint work with Emil Prodan and Bram Mesland. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Unconventional Spin Transport in Quantum Materials

April 21 at 17:00 - 18:15, 2021

Dr. Se Kwon Kim (Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea)

Recent advancements in spintronic techniques originally developed for spin-based devices now enable us to study fundamental spin physics of various quantum materials with unprecedented spin-current control and measurement, opening a new area of theoretical and experimental investigation of quantum systems. In this talk, we will introduce this emerging research area of spin transport in quantum materials which is fueled by the global interest in quantum information science. As examples, we will discuss our discovery of magnonic topological insulators realized by 2D magnets [1-3], which shows how spintronic techniques can be used for probing elusive quantum materials, and our prediction of long-range spin transport mediated by a vortex liquid in superconductors [4], which shows that quantum materials can provide novel platforms for efficient spin-transport devices. We will conclude the talk by offering a future outlook on quantum spintronics. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

What "Holography" is and how to use it

April 14 at 17:00 - 18:15, 2021

Dr. Mario Flory (Instituto de Fisica Teorica, Universidad Autonoma de Madrid, Spain)

In this talk, I will give an introduction to the holographic principle and the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. I will also discuss the role that quantum entanglement plays in this correspondence via the Ryu-Takayanagi formula which maps the calculation of entanglement entropy to a geometric problem of extremal surfaces. Then, I will present a holographic model of a Kondo like effect as an example of how the AdS/CFT correspondence can be employed in practice. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Geometric nonlinear optical effects

March 16 at 17:00 - 18:15, 2021

Prof. Takahiro Morimoto (Associate Professor, Department of Applied Physics, The University of Tokyo)

Time: 5pm ~ 6:15pm (JST); 9am ~ 10:15am (CET) The responses of materials to high intensity light, i.e., nonlinear optical responses, constitute a vast field of physics and engineering. While geometry and topology has been playing a central role in recent studies of condensed matters, geometrical aspects of nonlinear optical effects have not been fully explored so far. In this talk, I will show a few examples of nonlinear optical effects that have geometrical origins. First, I present that the second-order nonlinear optical effects including the shift-current, a candidate mechanism for recently discovered solar cell action in perovskite materials, has a close relationship to the modern theory of polarization, and is described by the Berry connection of Bloch wave function [1]. I will also discuss how electron correlations can enhance/modify shift current response in inversion broken materials. Next, I show that another second-order nonlinear effect, circular photogalvanic effect (CPGE), is governed by Berry curvature and shows quantization in Weyl semimetals [2]. I will report a recent measurement on chiral multifold fermion RhSi that observed a plateau structure in CPGE which is consistent with the expected quantization [3].

Venue: via Zoom

Event Official Language: English

Exceptional Topology of Non-Hermitian Systems: from Theoretical Foundations to Novel Quantum Sensors

March 3 at 17:00 - 18:15, 2021

Prof. Jan Budich (Professor, Quantum Many-Body Physics, TU Dresden, Germany)

CET: 9:00a.m. - 10:15a.m. on March 3, 2021 JST: 5:00p.m. - 6:15p.m. on March 3, 2021 EST: 3:00a.m. - 4:15a.m. on March 3, 2021 In a broad variety of physical scenarios ranging from classical meta-materials to open quantum systems, non-Hermitian (NH) Hamiltonians have proven to be a powerful and conceptually simple tool for effectively describing dissipation. Motivated by recent experimental discoveries, investigating the topological properties of such NH systems has become a major focus of current research. In this talk, I give an introduction to this rapidly growing field, and present our latest results. Specifically, we discuss the occurrence of novel gapless topological phases unique to NH systems. There, the role of spectral degeneracies familiar from Hermitian systems such as Weyl semimetals is played by exceptional points at which the effective NH Hamiltonian becomes non-diagonalizable. Furthermore, we show how guiding principles of topological matter such as the bulk boundary correspondence are qualitatively changed in the NH realm. Finally, we demonstrate that the sensitivity of NH systems to small changes in the boundary conditions may be harnessed to devise novel high-precision sensors. *Detailed information about the seminar refer to the email.

Venue: via Zoom

Event Official Language: English

Mathematics of magic angles for bilayer graphene

February 3 at 20:00 - 21:15, 2021

Mr. Simon Becker (Ph.D. Student, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK)

20:00pm ~ 21:15pm on Feb. 03th, 2021 (JST) 11:00am ~ 12:15am on Feb. 03th, 2021 (UK) Magic angles are a hot topic in condensed matter physics: when two sheets of graphene are twisted by those angles the resulting material is superconducting. Please do not be scared by the physics though: I will present a very simple operator whose spectral properties are thought to determine which angles are magical. It comes from a recent PR Letter by Tarnopolsky–Kruchkov–Vishwanath. The mathematics behind this is an elementary blend of representation theory (of the Heisenberg group in characteristic three), Jacobi theta functions and spectral instability of non-self-adjoint operators (involving Hoermander’s bracket condition in a very simple setting). The results will be illustrated by colourful numerics which suggest some open problems. This is joint work with M. Embree, J. Wittsten, and M. Zworski.

Venue: via Zoom

Event Official Language: English

Time-dependent driven quantum critical systems in (1+1) dimension

January 18 at 10:00 - 11:15, 2021

Dr. Xueda Wen (Postdocs, Physics Department, Harvard University, USA)

10:00am ~ 11:15am on Jan. 18th, 2021 (JST) 8:00pm ~ 9:15pm on Jan. 17th, 2021 (EST) I will introduce an analytically solvable setup for time-dependent driven quantum critical systems in (1+1)D, whose low-energy physics are described by conformal field theories. In general, one may observe two different phases (heating and non-heating), where the correlation functions such as the entanglement entropy and energy-momentum density can be analytically solved. The dependence of phase diagrams on (i) the types of driving Hamiltonians and (ii) the types of driving sequences (such as periodic, quasi-periodic and random drivings) will be discussed.

Venue: via Zoom

Event Official Language: English