UEDA GROUP
Department of Physics, The University of Tokyo
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2017年度 / Academic Year 2017

ご興味ある方の参加、歓迎します。研究室メンバーによるレギュラー・セミナーは下記要領で行います。 事前の連絡なく参加頂けますが、 夏学期の論文紹介ゼミについては発表者に連絡頂けましたら発表資料を必要分印刷します。
他研究室、他機関からのゲスト・スピーカーの方のセミナーも度々開催しています。

冬学期 / Winter semester (October 2017-Janurary 2018)

木曜日13:00から理学部1号館201a号室で行います(普段と場所or時間の異なる場合は赤字で示します)。
Every seminar starts from 13:00, Thursday @ #201a, Faculty of Science Bldg. 1 (unless otherwise indicated).
Oct. 2-3 Tokyo-Beijing Workshop on Ultracold Atoms
Oct. 5 Sho Higashikawa / Shuhei M. Yoshida
Oct. 12 Tomohiro Shitara / Ryusuke Hamazaki
Oct. 17-19 (Intensive lecture by Prof. Masatoshi Sato)
Oct. 26 Yuto Murashita / Kohei Kawabata
Nov. 2 Takumi Yoshino / Kazuya Fujimoto
Nov. 9 Zongping Gong / Shunsuke Furukawa (@201b)
Nov. 15-16 (Todai-ENS Workshop)
Nov. 21-22 (Topological Science Symposium @ Keio Univ.)
Nov. 23 (National Holiday)
Nov. 30 Emi Yukawa / Shun Uchino
Dec. 7 (No Seminar)
Dec. 14 Yuto Ashida / Naoto Tsuji
Dec. 21 Naoto Kura / Masaya Nakagawa
Jan. 11 Akihito Yoneyama / Zhikang Wang (tentative)
Jan. 18 (No Seminar)

2017/10/5(Thu.)
speaker Sho Higahsikawa
title Topological pump of Weyl fermion and Floquet chiral magnetic effect
abstract The periodicity of Brillouin zones imposes strong topological constraints on realizable band structures. For example, in a three-dimensional lattice system, left- and right-handed Weyl fermions must appear in pairs and hence it is impossible to realize a single Weyl fermion (Nielsen-Ninomiya theorem [1]). However, in periodically driven systems, topology of quasi-energy band structures of Floquet states is richer than static systems due to the time-periodic structure of Hamiltonians [2].
In this talk, we present a model which realizes a single Weyl fermion on a periodically driven three-dimensional lattice [3]. Our model is a three-dimensional analog of the topological Thouless pump. Reflecting the spin-momentum-locking nature of a Weyl fermion, a spin-polarized wave packet moves parallel to its spin direction in this pump. Furthermore, we show that, under this pump with a magnetic field, a wave packet moves parallel to the applied magnetic field, which is a Floquet analog of the chiral magnetic effect.
[1] H. B. Nielsen and M. Ninomiya, Phys. Lett. B 105, 219 (1981).
[2] T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82, 235114 (2010).
[3] S. Higashikawa, M. Nakagawa, and M. Ueda, in preparation.

speaker Shuhei M. Yoshida
title Universality of an Impurity in a Bose-Einstein Condensate
abstract Physicists aspire to find universality, where comlex phenomena are described by a small number of parameters. The unitary Fermi gas is a prime example, whose ground-state thermodynamics is completely determined by its density and the Bertsch parameter. The strongly correlated Bose gases, on the other hand, always have the three-body parameter, which emerges due to the Efimov effect and characterizes the three-body physics. One may ask, is the three-body parameter enough, or do we need other details to characterize a Bose gas? We address this question for a Bose polaron, which is a single impurity immersed in a Bose gas. We calculate the ground-state energy of a Bose polaron using two different models of interactions. By comparing their results and also the results of another model in the previous study [2], we show that the ground-state energy is a model-independent function of the three-body parameter if the background Bose gas is not too dense.
[1] S. M. Yoshida, S. Endo, J. Levinsen, and M. M. Parish, arXiv:1710.02968.
[2] L. A. P. Ardila, and S. Giorgini, Phys. Rev. A 92, 033612 (2015).

2017/10/12 (Thu.)
speaker Tomohiro Shitara
title Evaluating excess work in thermodynamic control
abstract One of difficulties in analyzing nonequilibrium processes is that physical quantities at a certain time generally depend on the history of the system. In particular, we consider excess work in nonequilibrium processes where the system is controlled by a time-dependent Hamiltonian or external potential. When the control is slow, the average excess work can be approximately evaluated based on the thermodynamic metric on the control parameter space, in which the work performed into the system at a certain time depends only on the velocity of the control parameter at that time.
In this seminar, we extend this thermodynamic metric formalism in two directions. First, we systematically expand the average excess work in terms of the slowness of the control in a phenomenological manner, where the most leading term coincides with the thermodynamic metric. Second, we formulate a method to determine higher order cumulants in overdamped Langevin systems.

speaker Ryusuke Hamazaki
title Atypicality of most few-body observables
abstract Understanding how isolated quantum systems thermalize has recently gathered renewed interest among theorists, thanks to the experimental realizations of such systems. If the eigenstate thermalization hypothesis (ETH) holds true, the microcanonical ensemble is justified as a steady-state ensemble [1]. The ETH states that diagonal matrix elements of an observable for the energy eigenstates are almost the same within a small energy shell. One possible explanations of the ETH has been the typicality argument, which predicts the exponentially small variation of diagonal matrix elements with the size of the system [2]. In this seminar, however, we show that the argument does not apply to most few-body observables for few-body Hamiltonians unless the width of the energy shell decreases exponentially with increasing the size of the system [3].
[1] M. Rigol, V. Dunjko, and M. Olshanii, Nature 452, 854 (2008).
[2] P. Reimann, Phys. Rev. Lett. 115, 010403 (2015).
[3] R. Hamazaki and M. Ueda, arXiv:1708.04772 (2017).

2017/10/26 (Thu.)
speaker Yûto Murashita
title Transient fractality as a mechanism of emergent irreversibility in chaotic Hamiltonian dynamics
abstract The Loschmidt paradox claims that one cannot obtain macroscopic irreversible behavior from microscopic reversible dynamics since there exists one-to-one correspondence between a trajectory and its time-reversed one. Boltzmann refuted this claim by arguing that trajectories with a positive entropy production are realized much more frequently than those with a negative entropy production despite this one-to-one correspondence. His idea was later elucidated in chaotic systems ruled by dissipative reversible equations of motion [1]. In their discussion, fractality in phase space plays a key role to account for emergent irreversibility. In this talk, we address the question of whether this picture applies to chaotic systems with conservative reversible equations of motion. Although the Liouville theorem prohibits fractality in the long time limit, we find that a fractal structure emerges in an intermediate timescale in a dynamical billiard. This transient fractality can be quantitatively evaluated by means of the time-reversal test and the Rényi divergence. Moreover, this emergent irreversibility has an intimate relation to a singular class of irreversibility called absolute irreversibility in the context of the fluctuation theorem. We suggest that the fractality is a universal mechanism to generate irreversibility from reversible equations of motion.
[1] B. L. Holian, W. G. Hoover and H. A. Posch, Phys. Rev. Lett. 59, 10 (1987).

speaker Kohei Kawabata
title Parity-time-symmetry-induced edge modes in the Majorana chain
abstract Non-Hermitian systems with parity-time (PT) symmetry have attracted growing interest over the past two decades [1]. Such systems exhibit unconventional spontaneous symmetry breaking that has no analogue in equilibrium systems, and recent experimental realizations [2-4] in classical systems have sparked diverse studies of phenomena unique to PT-symmetric systems. In the quantum regime, various aspects of PT-symmetric systems have been studied, such as critical phenomena [5] and quantum information [6]. However, much remains to be explored concerning the interplay between PT symmetry and topology. In this talk, we study a one-dimensional topological superconductor with PT symmetry [7]. We discover that PT symmetry breaking occurs as the emergence of new edge modes. We also find that anomalous current localized at edges is generated, which is induced by the combination of PT symmetry and topology.
[1] C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
[2] C. E. Rüter et al., Nat. Phys. 6, 192 (2010).
[3] A. Regensburger et al., Nature 488, 167 (2012).
[4] B. Peng et al., Nat. Phys. 10, 394 (2014).
[5] Y. Ashida, S. Furukawa, and M. Ueda, Nat. Commun. 8, 15791 (2017).
[6] K. Kawabata, Y. Ashida, and M. Ueda, arXiv: 1705.04628 (to appear in Phys. Rev. Lett.).
[7] K. Kawabata, Y. Ashida, H. Katsura, and M. Ueda, in preparation.

2017/11/2 (Thu.)
speaker Takumi Yoshino
title Collective modes of vortex lattices in two-component Bose-Einstein condensates
abstract A synthetic magnetic field can be induced in neutral atoms by rotating the gas or by optically dressing atoms. For scalar Bose-Einstein condensates (BEC), a synthetic magnetic field creates quantized vortices, which form Abrikosov’s triangular lattice owing to their mutual repulsion. In the case of rotating two-component BECs, mutually parallel magnetic fields are induced in the two components, and give rise to a variety of vortex lattice structures which are controlled by the ratio of the intercomponent interaction g↑↓to the intracomponent one g [1,2]. It can be shown within the Gross-Pitaevskii mean-field theory that two component BECs in antiparallel fields, which can be created by an optical dressing technique, exhibit exactly the same vortex lattice phase diagram [3].
We study collective modes of vortex lattices in two-component BECs by utilizing Bogoliubov theory and an effective theory. We numerically obtain excitation bands for each vortex lattice phase, and find the emergence of two modes with linear and quadratic dispersion relations at low energies for all phases in both the cases of parallel and antiparallel fields. We also derive dispersion relations for both the cases by using effective theory, and checked the consistency of our numerical results with the effective theory prediction.
[1] E. J. Mueller and T.-L. Ho, Phys. Rev. Lett 88, 180403 (2002).
[2] K. Kasamatsu, M. Tsubota, and M. Ueda, Phys. Rev. Lett. 91, 150406 (2003).
[3] S. Furukawa and M. Ueda, Phys. Rev. A 90, 033602 (2014).

speaker Kazuya fujimoto
title Isolated coarsening dynamics in a one-dimensional antiferromagnetic spinor Bose gas
abstract Coarsening dynamics is a ubiquitous relaxation phenomenon appearing after a sudden quench of system’s parameters across a phase transition point. Originally, this kind of relaxation has been intensively studied in various open dissipative systems such as a metal alloy and a binary liquid, and is found to be classified to some universality classes [1]. Recently, we study a one-dimensional (1D) coarsening dynamics in an isolated ferromagnetic spinor Bose gas, analytically and numerically discovering a new universality class unique to isolated systems [2]. Then, this study poses one question: “Is this the only universality class unique to isolated systems?”. In this talk, we discuss this issue, focusing on a 1D coarsening dynamics in an antiferromagnetic spinor Bose gas. We will show numerical results based on the truncated Wigner approximation.
[1] A. J. Bray, Adv. Phys. 43, 357 (1994).
[2] K. Fujimoto, R. Hamazaki, and M. Ueda, arXiv:1707.03615.

2017/11/9 (Thu.) @201b
speaker Zongping Gong
title Discrete time-crystalline order in cavity and circuit QED systems
abstract Discrete time crystals are a recently proposed [1-3] and experimentally observed [4,5] dynamical phase of out-of-equilibrium Floquet systems, where the stroboscopic evolution of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model [6], which can be implemented by cavity [7] and circuit QED systems [8]. In the thermodynamic limit, we employ semiclassical approaches and find unexpectedly rich dynamical phases in addition to the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a general phenomenology of dissipative discrete time crystals by generalizing the celebrating Landau theory of phase transitions to Floquet open systems.
[1] V. Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 116, 250401 (2016).
[2] D. V. Else, B. Bauer, and C. Nayak, Phys. Rev. Lett. 117, 090402 (2016).
[3] N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Phys. Rev. Lett. 118, 030401 (2017).
[4] J. Zhang et al., Nature 543, 217 (2017).
[5] S. Choi et al., Nature 543, 221 (2017).
[6] Z. Gong, R. Hamazaki, and M. Ueda, arXiv:1708.01472.
[7] K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Nature 464, 1301 (2010).
[8] F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Nat. Phys. 13, 39 (2017).

speaker Shunsuke Furukawa
title Magnetic properties of volborthite determined by a coupled-trimer model
abstract The natural mineral volborthite hosts layers of spin-1/2 moments forming a kagome lattice. While this material was initially considered as a candidate of a spin-1/2 kagome antiferromagnet, it exhibits rich magnetic behavior which is in many respects distinct from the known features of a kagome antiferromagnet. In particular, recent single-crystal experiments have revealed a wide 1/3 magnetization plateau starting at H = 26 T, an incommensurate spin-density-wave phase below H = 23 T, and the novel ``N'' phase inbetween them.
To explain these rich field-induced phenomena, we have performed microscopic modeling of volborthite by means of density functional theory (DFT) with the single-crystal structural data as a starting point. Using DFT+U, we find four leading magnetic exchanges: antiferromagnetic J and J2, as well as ferromagnetic J ' and J1 with a remarkable hierarchy J > |J1| > J2, |J '|. Due to the dominance of J, the magnetic planes break up into magnetic trimers. The 1/3-plateau state can be naturally interpreted as a product of polarized trimers, and a wide plateau extending to H = 225 T is predicted. Furthermore, we derive an effective pseudospin-1/2 model by restricting ourselves to the lowest-energy doublet on each trimer and treating the inter-trimer couplings perturbatively. This model shows a tendency towards condensation of magnon bound states preceding the plateau, providing a scenario for the observed ``N'' phase.
We are currently analyzing the effects of Dzyaloshinskii-Moriya interactions, which may be responsible for a low-field magnetic phase for H < 4 T and thermal Hall effect observed in recent experiments. The seminar will include a brief progress report in this direction.
Reference: O. Janson, S. Furukawa, T. Momoi, P. Sindzingre, J. Richter, and K. Held, Phys. Rev. Lett. 117, 037206 (2016).


夏学期 / Summer semester (April-August 2017)

木曜日13時から理学部1号館913号室で行います(普段と場所or時間の異なる場合は赤字で示します)。
Every seminar starts from 13:00, Thursday @ #913, Faculty of Science Bldg. 1 (unless otherwise indicated).
<Schedule>
July 4 Prof. Adolfo del Campo
July 24 Prof. Haruki Watanabe
August 24 Flore K. Kunst & Dr. Emil J. Bergholtz

April 13 (Thu) Zongping Gong
    "Coherence in Spontaneous Radiation Processes"
    R. H. Dicke, Phys. Rev. 93, 99 (1954)
    "Chaos and the quantum phase transition in the Dicke model"
    C. Emary and T. Brandes, Phys. Rev. E 67, 066203 (2003)
    "Dicke quantum phase transition with a superfluid gas in an optical cavity"
    K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Nature 464, 1301 (2010)

April 20 (Thu) Yuto Ashida
    "Matrix product states represent ground states faithfully"
    F. Verstraete and J. I. Cirac, Phys. Rev. B 73, 094423 (2006)
    "Solving the quantum many-body problem with artificial neural networks"
    G. Carleo and M. Troyer, Science 355, 602 (2017)
    "Neural network representation of tensor network and chiral states"
    Y. Huang and J. E. Moore, arXiv:1701.06246

April 27 (Thu) Sho Higashikawa
    "Absence of neutrinos on a lattice: (I). Proof by homotopy theory"
    H. B. Nielsen and M. Ninomiya, Nucl. Phys. B185, 20 (1981)
    "Absence of neutrinos on a lattice: (II). Intuitive topological proof"
    H. B. Nielsen and M. Ninomiya, Nucl. Phys. B193, 173 (1981)

May 4 (Thu) (National Holiday)

May 11 (Thu) (TMS International Conference)

May 18 (Thu) Ryusuke Hamazaki
    "A bound on chaos"
    J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 106

May 25 (Thu) Tomohiro Shitara
    "The large deviation approach to statistical mechanics"
    H. Touchette, Phys. Rep. 478, 1 (2009)

June 1 (Thu) (No Seminar)

June 8 (Thu) Yuto Murashita
    "Controlling chaos"
    E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)

June 15 (Thu) Shuhei M. Yoshida
    "Exponential expressivity in deep neural networks through transient chaos"
    B. Poole, S. Lahiri, M. Raghu, J. Sohl-Dickstein, and S. Ganguli, in Advances in Neural Information Processing Systems 29

June 22 (Thu) Naoto Kura
    "String-net condensation: A physical mechanism for topological phases"
    M. A. Levin and X.-G. Wen, Phys. Rev. B 71, 045110 (2005)

June 29 (Thu) Takumi Yoshino
    "Colloquium: Artificial gauge potentials for neutral atoms"
    J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011)

2017/7/4 (Tue.) 15:00- @ #201b
speaker Prof. Adolfo del Campo (UMass Boston)
title Engineering Quantum Thermal Machines
abstract Quantum thermodynamics has emerged as an interdisciplinary research field in quantum science and technology with widespread applications. Yet, the identification of scenarios characterized by quantum supremacy - a performance without match in the classical world - remains challenging. In this talk I shall review recent advances in the engineering and optimization of quantum thermal machines. I will show that nonadiabatic many-particle effects can give rise to quantum supremacy in finite-time thermodynamics [1].
Tailoring such nonadiabatic effects by making use of shortcuts to adiabaticity, quantum heat engines can be operated at maximum efficiency and arbitrarily high output power [2]. A thermodynamic cost of these shortcuts will be elucidated by analyzing the full work distribution function and introducing a novel kind of work-energy uncertainty relation [3]. I shall close by discussing the identification of scenarios with a quantum-enhanced performance in thermal machines run over many cycles [4].
[1] J. Jaramillo, M. Beau, and A. del Campo, New J. Phys. 18, 075019 (2016).
[2] M. Beau, J. Jaramillo, and A. del Campo, Entropy 18, 168 (2016).
[3] K. Funo, J.-N. Zhang, C. Chatou, K. Kim, M. Ueda, and A. del Campo, Phys. Rev. Lett. 118, 100602 (2017).
[4] G. Watanabe, B. P. Venkatesh, P. Talkner, and A. del Campo, Phys. Rev. Lett. 118, 050601 (2017).

July 6 (Thu) Kohei Kawabata
    "Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation"
    C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952)
    "Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model"
    T. D. Lee and C. N. Yang, Phys. Rev. 87, 410 (1952)

July 13 (Thu) Taisuke Matsuda
    "Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I"
    Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961)
    "Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II"
    Y. Nambu and G. Jona-Lasinio, Phys. Rev. 124, 246 (1961)

July 20 (Thu) Norifumi Matsumoto
    "Quantized Hall Conductance in a Two-Dimensional Periodic Potential"
    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982)
    "Topological invariant and the quantization of the Hall conductance"
    M. Kohmoto, Ann. Phys. 160, 343 (1985)

2017/7/24 (Mon.) 13:00-14:30 @ #1220(Faculty of Science Bldg. #4)
speaker Prof. Haruki Watanabe (UTokyo)
title 空間群の対称性に基づいた量子相の一般的な理解
abstract 量子多体系の基底状態や低エネルギー励起状態といった巨視的な(IRの)性質を、系の対称性や粒子数密度という微視的な(UVの)情報だけから、どこまで一般的に理解・予言できるだろうか。本講演の前半では、Lieb-Schultz-Mattis (Oshikawa-Hastings)定理を(磁気)空間群の仮定のもとに改良し、与えられた対称性・粒子数密度に対してどのような基底状態・低エネルギー励起が可能であるかを制限し、量子スピン液体を含むトポロジカル秩序相への応用を議論する[1]。
後半では特に自由粒子系のバンド構造に焦点を絞り、空間群の対称性やその表現に基づいてバンド構造のトポロジカルな性質を一般的にどのように理解できるかを議論する[2]。よく知られているように、Z2トポロジカル絶縁体の指標はもともとPfaffianをk空間で積分したもので与えられるが、系が反転対称性を有する場合にはこの煩雑な計算を実行する必要はなく、TRIMにおける占有軌道のパリティを掛け合わせればよい。この「反転対称性のパリティに基づくトポロジカル絶縁体の指標」を1651個の磁気空間群それぞれに拡張した「空間群の表現に基づくトポロジカル結晶絶縁体・トポロジカル半金属の指標」について説明し、興味深い具体例をいくつか議論する。
[1] H. Watanabe, H. C. Po, A. Vishwanath, and M. P. Zaletel, Proc. Natl. Acad. Sci. U.S.A. 112, 14551 (2015); H. C. Po, H. Watanabe, C.-M. Jian, and M. P. Zaletel, arXiv:1703.06882. 日本物理学会誌 2017年1月号に解説あり。
[2] H. Watanabe, H. C. Po, M. P. Zaletel, and A. Vishwanath, Phys. Rev. Lett. 117, 096404 (2016); H. C. Po, H. Watanabe, M. P. Zaletel, and A. Vishwanath, Sci. Adv. 2, e1501782 (2016); H. C. Po, A. Vishwanath, and H. Watanabe, Nat. Commun. 8, 50 (2017); H. Watanabe, H. C. Po, and A. Vishwanath, arXiv:1707.01903.

2017/8/24 (Thu.) 13:00-15:00 @ #201a
speaker Flore K. Kunst (Stockholm University / Freie Universitat Berlin)
title Anatomy of Topological Flat and Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices
abstract The main feature of topological phases is the presence of robust boundary states, which appear for example in the form of chiral edge states in Chern insulators and open Fermi arcs on the surfaces of Weyl semimetals. Even though, non-interacting, topological systems can be straightforwardly described in fully periodic systems, the detail of the corresponding boundary states has mainly relied on numerical studies. In our work, we present a general method on how to find exact, analytical solutions for topological as well as trivial boundary states using a generic tight-binding model on a large class of geometrically frustrated lattices without the necessity of having to fine-tune hopping amplitudes. Our method is inspired by a similar approach that has been used in the past to construct, topologically-trivial, flat band models from local constraints on ‘line graphs’, in which case fine-tuning is required in the sense that hopping is strictly local. We expand on this work by considering a larger class of lattices, finding solutions for both topologically trivial and non-trivial bands, and going beyond the need for fine-tuning. In this sense, it is likely that our work will contribute to both the research fields of flat-band physics and that of topological matter, as well as advance the cross-fertilization between them. In my talk, I will present a number of examples to illustrate our discoveries, some of which are experimentally relevant such as the derivation of exact solutions for Fermi arcs in the recently synthesized slabs of pyrochlore iridates.

speaker Dr. Emil J. Bergholtz (Stockholm University / Freie Universitat Berlin)
title Fractional Chern insulators: From higher Chern number phases to non-Abelian twist defects
abstract In this talk I will discuss fractional Chern insulators with emphasis on the analogy with more conventional continuum Landau level physics — and on aspects that are qualitatively new in the lattice setting such as Berry curvature fluctuations, competing instabilities and novel collective states of matter emerging in bands with higher Chern number. I will also explain how the lattice setting naturally allows for exotic extrinsic wormhole-like twist defects (aka “genons”) that effectively increase the genus of space.