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Floquet topological phases in correlated electron systems


Norio Kawakami (Kyoto Univ.)


We here discuss two topics on Floquet topological phases induced by laser irradiation in correlated electron systems. We first propose a possible way to realize topological superconductivity with application of laser light to superconducting cuprate thin films. Applying Floquet theory to a model of d-wave superconductors with Rashba spin-orbit coupling, we derive an effective model and discuss its topological nature. Interplay of the Rashba spin-orbit coupling and the laser light effect induces the synthetic magnetic fields, thus making the system gapped. Then the system acquires the topologically non-trivial nature which is characterized by Chern numbers. The effective magnetic fields do not create the vortices in superconductors, and thus the proposed scheme provides a promising way to dynamically realize a topological superconductor in cuprates. We further study the nature of laser-irradiated Kondo insulators. Applying Floquet theory to a periodic Anderson model, we find two generic effects induced by laser light. One is the dynamical localization, which suppresses hopping and hybridization and the other is the laser-induced hopping and hybridization, which can be interpreted as a synthetic spin-orbit coupling or magnetic field. In topological Kondo insulators, linearly polarized laser light realizes phase transitions between trivial, weak topological, and strong topological Kondo insulators, whereas circularly polarized laser light breaks time-reversal symmetry and induces Weyl semimetallic phases.


Generalized Compatibility Relation: Atiyah-Hirzebruch Spectral Sequence in Band Topology


Ken Shiozaki (RIKEN)


We study the Atiyah-Hirzebruch spectral sequence (AHSS) for equivariant K-theory in the context of band theory. The AHSS is known to be a mathematical tool to compute a cohomology theory. We found that the AHSS is a natural framework to study the band topology: it gives us a systematic description of bulk gapless phases and approximates the K-group. The AHSS can be considered as the suitable generalization of the compatibility relation. Using the AHSS, we got the complete classification of topological invariants for 230 space groups in class A and AIII. Some new topological invariants we discovered will be presented.


EMUS-QMC: Elective Momentum Ultra-Size Quantum Monte Carlo Method


Yang Qi (Fudan Univ.)


One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice model of interacting fermions, the best methodology at hand still scales with βN^3 where β is the inverse temperature and N is the system size. Such scaling behavior has greatly hampered the accessibility of the universal infrared (IR) physics of many interesting correlated electron models at (2+1)D, let alone (3+1)D. To reduce the computational complexity, we develop a new QMC method with inhomogeneous momentum-space mesh, dubbed elective momentum ultra-size quantum Monte Carlo (EQMC). In this method, the fermion determinant is written in momentum-space, where more attention is paid towards the k-points associated with the IR physics (in this case, the so-called hot-spots), such that the computational complexity is reduced to Nf^33 where Nf is the volume of momentum patches around hot-spots. Speedup, to the level of 10^3, can be easily achieved in EQMC as it is easy to have N/Nf ∼ 10. We demonstrate the power of this method with a model of antiferromagnetic itinerant quantum critical point, realized in frustrated transverse-field triangle lattice Ising model coupled to Fermi surface. The system size of 48 × 48 × 48 (L × L × β, more than 5 times larger than the previous investigations) are comfortably accessed with EQMC. Spin fluctuations introduce effective interactions among fermions and the fermions in return render the bare bosonic critical point into a different universality with Hertz-Mills type exponents. With much larger system sizes, the antiferromagnetic itinerant quantum critical scaling is unveiled with unprecedingly high accuracy.


Symmetry based indicator of band topology


Haruki Watanabe (Univ. Of Tokyo)


Symmetry does not only protect topological phases but also helps us diagnosing the topological properties of the system.  In this talk, we will discuss how the symmetry representations of band insulators are related to their topology and surface states.


Spin and Thermal Excitations in Kitaev-type Frustrated Magnets


Youhei Yamaji (Univ. Of Tokyo)


Topological states of matters in strongly correlated electron systems are characterized by emergence of fractionalized quasiparticles. The Majorana fermions are examples of the fractionalized excitations, which have recently attracted much attention as ingredients of topological quantum computations. Intensive studies on a possible realization of the Majorana fermions in crystalline solids have been triggered by the pioneering finding of the spin liquid ground state in the Kitaev model and theoretical proposal on the realization of the Kitaev model in iridium oxides. Recently, a ruthenium chloride, α-RuCl3, has been an important Majorana hunting field. As the simplest effective Hamiltonian of α-RuCl3, the Kitaev-Γ model has been studied and shown that the ground state is non magnetic and adiabatically connected to the ground state of the Kitaev model. We further found the plateau in temperature dependence of entropy and spin excitation continuum at finite temperatures, which show a significant crossover from the Kitaev limit to the Γ limit.


Lieb-Schultz-Mattis Theorem and Topological Phase


Gil Young Cho (POSTECH)


The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this talk, we will compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that, they can be both described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it is a local symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly, which is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gapless-ness local in the parameter space. We will conclude the talk with a few future research topics stemming from the discussed topics.