連絡先： 島田尚(shimadaあっと ap.t.u-tokyo.ac.jp)、 森貴司(moriあっと spin.phys.s.u-tokyo.ac.jp)

宮下研究室｜ 伊藤研究室 (セミナー)｜ 藤堂研究室｜ 羽田野研究室 (セミナー)｜ 桂研究室

日時 | 場所 | 講演者（敬称略） | 講演題目 |
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**日時：**12月20日17時より

**場所：**理学部1号館 447教室

**講演者：** 松井千尋

**講演タイトル：** Hidden supersymmetry in the Fateev-Zamolodchikov spin chain

**講演要旨：**

It is well known that the low-energy regime of a massless quantum spin chain is described by a quantum field theory (QFT) called the effective field theory. If the spin chain is integrable, its effective field theory is also integrable. These two models have the scattering matrices associated to the same solution of the Yang-Baxter equation.
What is interesting is the effective field theory of a non-supersymmetric spin chain with arbitrary spin possesses the supersymmetry (SUSY). This fact motivates us to study whether the SUSY arises as a result of the scaling limit or it already exists in the spin chain but just cannot be explicitly obtained.

Recently works by Fendley and Hagendorf [1,2] showed the discrete analog of the SUSY to the non-SUSY spin chains. Since the supercharges exchange a boson and a fermion, the original idea of this SUSY analog was introduced in such a way that the supercharges change the length of the spin chains [3].
In the talk, I discuss how the SUSY analog is connected to the original SUSY obtained in QFTs. As the simplest case, I show the SUSY analog of the integrable spin-1 (Fateev-Zamolodchikov; FZ) chain in the spinon basis and their relation to the SUSY of the SUSY sine-Gordon (SSG) model [4].

Reference:

[1] C. Hagendorf and P. Fendley, “ The eight-vertex model and lattice supersymmetry ”, J. Stat. Phys., 146:1122-1155, 2012.

[2] C. Hagendorf, “Spin chains with dynamical lattice supersymmetry”, J. Stat. Phys., 150:609-657, 2013.

[3] X. Yang and P. Fendley, “Non-local spacetime supersymmetry on the lattice”, J. Phys. A: Math. Gen., 37:8937-8948, 2004.

[4] C. Matsui, “Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry”, Nucl. Phys. B913:15-33, 2016.

**日時：**12月15日16時より

**場所：**理学部4号館 1320教室

**講演者：** Jorge Linares (Versailles Saint-Quentin-en-Yvelines University)

**講演タイトル：** Monte Carlo entropic sampling applied to Ising-like model for 2D Spin Crossover nanoparticles

**講演要旨：**

**日時：**12月13日15時より

**場所：**理学部1号館 447教室

**講演者：** 藤堂眞治

**講演タイトル：** Critical Decay Exponents of Ising Ferromagnet with Long-range Interactions

**講演要旨：**

We investigate the universality class of the finite-temperature phase
transition of the two-dimensional Ising model with the algebraically
decaying ferromagnetic long-range interaction, J_ij =
|r_i-r_j|^-(d+\sigma), where d (=2) is the dimension of the system and
\sigma the decay exponent, by means of the order-N cluster-algorithm
Monte Carlo method [1,2]. In particular, we focus on the upper and
lower critical decay exponents, the boundaries between the
mean-field-universality, intermediate, and short-range-universality
regimes. At the critical decay exponents, it is found that the
standard Binder ratio of magnetization at the critical temperature
exhibits the extremely slow convergence as a function of the system
size. We propose more effective physical quantities, the combined
Binder ratio and the self-combined Binder ratio, both of which cancel
the leading finite-size corrections of the conventional Binder
ratio. Utilizing these techniques, we clearly demonstrate that in two
dimensions the lower and upper critical decay exponents are \sigma = 1
and 7/4, respectively [3], contrary to the recent Monte Carlo and the
renormalization-group studies.

[1] K. Fukui, S. Todo, J. Comp. Phys. 228, 2629 (2009).

[2] S. Todo, H. Suwa, J. Phys.: Conf. Ser. 473, 012013 (2013).

[3] T. Horita, H. Suwa, S. Todo, arXiv:1605.09496.

**日時：**12月6日15時より

**場所：**理学部1号館 447教室

**講演者：** 溝口知成 (小形研）

**講演タイトル：** Effect of interaction between fractional charges on classical spin liquid on kagome lattice

**講演要旨：**

Fractionalization is a ubiquitous phenomenon in topological states of
matter. For example, in quantum spin liquids (QSLs), the spins are
separated into spinons and fluctuating gauge fields [1]. The fractional
charges reflect the nature of QSLs, and a full understanding of their
character is awaited. Nevertheless, the effects of interactions between
fractional charges have little been understood since they are usually
treated as free objects. To study the many-body effect of fractional
charges, classical spin liquids (CSLs) provide a good stage, which have
many in common with QSL’s. For instance, in classical spin ice,
interactions between fractional charges (or monopoles) give rise to their
recombination and alter their dynamical properties [2]. It is plausible to
expect similar nontrivial effects will be found in other CSLs.

In this seminar, I will show the equilibrium properties of the Ising
model on a kagome lattice, in which the second (J2) and the third (J3)
neighbor interactions are translated into the short-range interaction
between the fractional charges. I will report that the recombination of
charges leads to the new CSLs. In one of the new CSLs, the magnetic
structure factor shows a “half-moon” pattern instead of pinch points, which
may provides a clue to looking for this new CSL.

[1] L. Balents, Nature (London) **464**, 199 (2010).

[2] M. Udagawa, L. D. C. Jaubert, C. Castelnovo, and R. Moessner, Phys.
Rev. B **94**, 104416 (2016).

**日時：**11月29日15時より

**場所：**理学部1号館 447教室

**講演者：** 蘆田祐人 (上田研)

**講演タイトル：** Quantum critical phenomena influenced by measurement backaction

**講演要旨：**

Recent realization of quantum gas microscopy has offered the possibility of continuous monitoring of the dynamics of quantum many-body system at the single-particle level [1-3]. In this talk, we ask how the measurement backaction influences on quantum critical phenomena. By analyzing effective non-Hermitian Hamiltonians for interacting bosons in an optical lattice and continuum, we demonstrate that the backaction of quantum measurement shifts the quantum critical point and gives rise to a unique 1D critical phase beyond the conventional universality class [4]. We will also discuss unconventional quantum critical phenomena in parity-time symmetric many-body systems and their realization in ultracold atoms [5].

References:

[1] W. Bakr et al., Nature 462, 74 (2009).

[2] YA and M. Ueda, PRL 115, 095301 (2015).

[3] Y. S. Patil et al., PRL 115, 140402 (2015).

[4] YA, S. Furukawa, and M. Ueda, PRA 94, 053615 (2016).

[5] YA, S. Furukawa, and M. Ueda, arXiv:1611.00396 (2016).

**日時：**11月22日15時より

**場所：**理学部1号館 447教室

**講演者：** 大越孝洋

**講演タイトル：** Development of many-variable variational Monte Carlo method for electron-phonon coupled systems and its applications to the Hubbard models

**講演要旨：**

The electron-phonon interaction plays an important role in various
phenomena
of condensed matter such as conventional superconductor, charge density
wave,
and electric resistivity. Although its roles are well understood in
those phenomena,
they have not been fully understood in strongly-correlated electrons
such as high-Tc cuprates.
To study the interplay of strong electron-electron interactions and
electron-phonon interactions,
we have developed the many-variable variable Monte Carlo (mVMC)
method[1,2] for electron-phonon coupled systems[3].
In this talk, I will present details of our mVMC method and show our
recent applications to the
two-dimensional Hubbard model with electron-phonon interactions.

[1] D. Tahara and M. Imada, J. Phys. Soc. Jpn. 77, 114701 (2008)

[2] https://github.com/issp-center-dev/mVMC

[3] T. Ohgoe and M. Imada, Phys. Rev. B 89, 195139 (2014).

**日時：**11月8日15時より

**場所：**理学部1号館 447教室

**講演者：** 伊藤伸泰

**講演タイトル：** Simulation of quantum computer

**講演要旨：**

In quantum (gate) computer research, simulation using present "classical" computer has been achieved
bigger development than realization using physical quantum phemonema. Now we can simulate up to
46 q-bits using the K computer. In this seminary talk, the simulation and optimization algorithm
of quantum gate circuit is to be shown, which will be useful when one simulates quantum spin systems.

**日時：**11月1日15時より

**場所：**理学部1号館 447教室

**講演者：** Alexander Wietek (The University of Innsbruck)

**講演タイトル：** Chiral Spin Liquids in Frustrated Quantum Magnetism

**講演要旨：**

Topological states of matter are of of fundamental interest in contemporate condensed matter physics. The Fractional Quantum Hall effect is the main experimental system where this physics can be observed experimentally. The question remains whether also different systems might exhibit topological ordering. Candidate systems are certain frustrated quantum magnets. Chiral Spin Liquids are a lattice analogue of Fractional Quantum Hall Effect wave functions. These wavefunctions have been envisioned in 1987 but only very recently several simple local lattice models have been proposed realizing chiral spin liquid physics. In this talk I will introduce chiral spin liquids, discuss their relation to the Fractional Quantum Hall effect and present recent numerical studies that provide conclude evidence for the emergence of this exotic state of matter in frustrated extended Heisenberg models.

Literature:

[1] P. Nataf, M. Lajkó, A. Wietek, K. Penc, F. Mila, and A. M. Läuchli, Phys. Rev. Lett. 117 167202 (2016)

[2] A. Wietek, A. Sterdyniak, and A. M. Läuchli,
Phys. Rev. B 92 125122 (2015)

[3] A. Wietek and A. M. Läuchli, arXiv:1604.07829 [cond-mat]

**日時：**10月25日15時より

**場所：**理学部1号館 447教室

**講演者：** 白石直人 (清水研)

**講演タイトル：** 有限パワー熱機関のカルノー効率達成不可能性

**講演要旨：**

熱機関を特徴づける量として、効率とパワーという二つの量がある。効率の上限値はカルノー効率で与えられており、準静的極限で動かした熱機関がその上限値を達成することをカルノーは約200年前に示した。しかし準静的極限で動かす熱機関はパワーがゼロとなり実用的には無意味なため、「有限パワーの熱機関がカルノー効率に達成することはあるか」という問いが自然に出てくる。直感的にはこれは明らかに不可能なように思えるが、熱力学等の一般的枠組ではこの問題をうまく扱うことが出来ず、カルノー以来の未解決問題として残されてきた。特に近年、線形領域でも磁場を用いれば「有限パワーかつカルノー効率」は可能かもしれないという提案[1]がなされ、これをきっかけに具体的なモデルによる線形領域の解析が多数なされてきた[2-9]。ほとんどすべての研究は、具体的モデルの線形領域の範囲においては「有限パワーかつカルノー効率」は不可能だという結論を与えている[2-7]が、一部では「有限パワーかつカルノー効率」を実現するという（抽象的な）方法の提案もなされており[8,9]、未だに決定的な解決はなされてこなかった。

これに対し我々は、線形領域に限らず、またモデルにもよらない一般的な形で、「有限パワーかつカルノー効率」に対する禁止定理を導くことに成功したので、それについて発表する。我々は、系をマルコフ的な場合と非マルコフ的な場合に分け、それぞれに対して禁止定理を証明する。マルコフ的な場合には、熱流とエントロピー生成の不等式を経由することで、パワーと効率の間の一般的な不等式を導出し、そのコロラリーとして禁止定理を導く[10]。非マルコフ的な場合には、Lieb-Robinson限界を利用することで、効率に対する不等式を導出し、それによって禁止定理を示す[11]。我々の結果は、長い論争に終止符を打つものであると同時に、熱力学の枠内で取り扱えていなかった「操作速度」という概念を組み入れる方法を提示するものである。

[1] G. Benenti, K. Saito, and G. Casati, Phys. Rev. Lett. 106, 230602 (2011).

[2] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. Lett. 110, 070603 (2013).

[3] V. Balachandran, G. Benenti, and G. Casati, Phys. Rev. B 87, 165419 (2013).

[4] R. S. Whitney. Phys. Rev. Lett. 112, 130601 (2014).

[5] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. X 5, 031019 (2015).

[6] K. Proesmans and C. Van den Broeck, Phys. Rev. Lett. 115, 090601 (2015).

[7] K Yamamoto, O Entin-Wohlman, A Aharony, N Hatano, Phys. Rev. B 94,
121402 (2016).

[8] M. Campisi and R. Fazio, arXiv:1603.05024 (2016).

[9] M. Ponmurugan, arXiv:1604.01912 (2016).

[10] N. Shiraishi, K. Saito, and H. Tasaki, arXiv:1605.00356 (2016)
(to be published in PRL).

[11] N. Shiraishi, H. Tajima, and K. Saito, in preparation.

**日時：**10月18日15時より

**場所：**理学部1号館 447教室

**講演者：** 桂法称 (桂研)

**講演タイトル：** Supersymmetry breaking and Nambu-Goldstone fermions in lattice models

**講演要旨：**

Nambu-Goldstone (NG) bosons are gapless excitations associated with
spontaneously broken continuous symmetries. Recently, a classification of
NG bosons in non-relativistic systems has attracted much attention [1,2]. A
natural next step is to understand fermionic NG modes in non-relativistic
systems. To this end, we introduce and study a class of lattice fermion
models with manifest supersymmetry (SUSY). The model has one adjustable
parameter g, which interpolates between the Nicolai model (g=0) [3] and a
free-fermion model (infinite g). When g is sufficiently large, SUSY is
spontaneously broken in this model, in which case the existence of gapless
fermionic excitations is expected. In the talk, I will show that this is
indeed the case using a variety of analytical and numerical methods [4].

Reference:

[1] H. Watanabe and H. Murayama, Phys. Rev. Lett. 108, 251602 (2012).

[2] Y. Hidaka, Phys. Rev. Lett. 110, 091601 (2013).

[3] H. Nicolai, J. Phys. A: Math. Gen. 9, 1497 (1976).

[4] N. Sannomiya, H. Katsura, and Y. Nakayama, Phys. Rev. D 94, 045014
(2016).

**日時：**10月11日15時より

**場所：**理学部1号館 447教室

**講演者：** 宮下精二 (宮下研)

**講演タイトル：** Relaxation processes of metamagnetic state of ferromagnets and their dependence on field and size of the system

**講演要旨：**

Coercive force of magnets is determined by properties of relaxation of metastable states in ferromagnets, whose microscopic mechanism depends on the range of interaction and also on the spatial structure of the system. We study various types of dependence of the relaxation phenomena on the temperature, field, size of the system, and observation time. In particular, the magnetization reversal phenomena at the boundary region between ferromagnetic grains will be discussed.

**日時：**6月28日15時より

**場所：**理学部1号館 447教室

**講演者：** 森貴司 (宮下研)

**講演タイトル：** Ensemble equivalence in equilibrium statistical mechanics and beyond

**講演要旨：**

Ensemble equivalence is one of the important results of equilibrium statistical mechanics, and it has been extensively studied until now. When the microcanonical entropy and the canonical free energy are related with each other via the Legendre transformation, it is said that the microcanonical ensemble is thermodynamically equivalent to the canonical ensemble. The ensemble equivalence in this sense has been rigorously proven for a large class of physical systems.

More recently, deeper levels of the ensemble equivalence were proposed, which are called the "macrostate equivalence" and the "measure equivalence". The macrostate equivalence means that the two ensembles give an identical prediction for measurements of macroscopic quantities. The measure equivalence means that the relative entropy per particle between the two ensembles vanishes in the thermodynamic limit. As far as we consider the microcanonical, canonical, and grandcanonical ensembles, it has been recently proven by Touchette [1] that these three definitions of ensemble equivalence (thermodynamic, macrostate, and measure) are identical.

If we go beyond the equilibrium statistical mechanics, the non-thermal ensembles which are different from the above equilibrium ensembles appear. Therefore, the ensemble equivalence between two general ensembles is an important problem, although it has not been explored yet. In this talk, we discuss this problem, and it is shown that the vanishing specific relative entropy implies the macrostate (partial) equivalence [2].

[1] H. Touchette, J. Stat. Phys. 159, 987 (2015)

[2] T. Mori, arXiv:1602.06182

**日時：**6月21日15時より

**場所：**理学部1号館 447教室

**講演者：** 鈴木貴文 (宮下研)

**講演タイトル：** Detection scheme of non-Gaussian fluctuation in quantum conductors

**講演要旨：**

Nonequilibrium current fluctuation through mesoscopic devices has been intensively studied in both classical and quantum regimes [1]. It is experimentally possible, in the classical regime, to count the number of the electrons which pass through a conductor, and the histogram is used to characterize the nonequilibrium transport [2]. The fluctuation theorem is tested also in the quantm regime [3].
In general, it requires a sophisticated scheme to measure the current fluctuation compared with the conductance measurement.
Recent experiments utilize on-chip detectors to accurately measure the current fluctuation [2]. The detector of the current
distribution can be understood as a tracer particle driven by non-Gaussian noise [4,5].
In this talk, we study the detection scheme of the non-Gaussian fluctuation in quantum conductors. We consider the quantum p
oint point coupled to a detector LC circuit, which is a simple and generic setup.

[1] J. P. Pekola, Nat. Phys. 11, 118 (2015).

[2] B. Kueng et al., Phys. Rev. X 2, 011001 (2012).

[3] S. Nakamura et al., Phys. Rev. Lett. 104, 080602 (2010).

[4] Y. Utsumi et al., Phys. Rev. B 86, 075420 (2012).

[5] K. Kanazawa et al., Phys. Rev. Lett. 114, 090601 (2015).

**日時：**6月14日15時より

**場所：**理学部1号館 447教室

**講演者：**Cristian Enachescu (Alexandru Ioan Cuza University)

**講演タイトル：** Spin crossover micro and nanoparticles. Theoretical and experimental investigations

**講演要旨：**

Spin crossover molecular magnets[1] were extensively studied in recent years due to their potential applications in thermal and pressure sensors, optical displays, actuators or in data storage.
They are inorganic compounds, commutable between two states in thermodynamic competition: the low spin state (LS), stable at
low temperatures and the high spin state (HS), stable at high temperature. These two states have different optical, geometrical (volume), magnetic and vibrational properties. If the intermolecular interactions of elastic origin are higher than a threshold then the thermal switch between HS and LS states is accompanied by a thermal hysteresis; its width depends on the interaction strength while the transition temperatures are determined by the enthalpy vs. entropy ration in the HS and LS states. The LS and HS states commutation can also be triggered by irradiating the compound with an appropriate wavelength at low temperatures [2]. Under permanent light irradiation when temperature is changed back and forth, one is measuring the Light Induced Thermal Hysteresis (determined by the competition between the irradiation and the temperature dependent HS-LS nonradiative relaxation) [3]. These properties form the basis of
promising applications, such as memory devices, sensors or actuators.

In this communication we shall focus on some of the most recent experimental and theoretical investigations carried on spin crossover nanoparticles, such as thermal and relaxation properties in an environment [4] or the photoswitching at femtoseconds scale and subsequent studies on elastically driven cooperativity [5].

[1] M.A. Halcrow, Spin-crossover materials - properties and applications, in, John Wiley & Sons, Chichester, UK, 2013.

[2] S. Decurtins, P. Guetlich, C.P. Kohler, H. Spiering, A. Hauser, Light-induced excited spin state trapping in a transitio
n-metal complex: the hexa-1-propyltetrazole-iron (II) tetrafluoroborate spin-crossover system, Chem. Phys. Lett., 10 (1984)
1-4.

[3] C. Enachescu, R. Tanasa, A. Stancu, F. Varret, J. Linares, E. Codjovi, Phys. Rev. B, 72 (2005) 054413.

[4] R. Tanasa, J. Laisney, A. Stancu, M.L. Boillot, C. Enachescu, Hysteretic behavior of Fe(phen)(2)(NCS)(2) spin-transition
microparticles vs. the environment: A huge reversible component resolved by first order reversal curves, Appl. Phys. Lett.,
104 (2014).

[5] R. Bertoni, M. Lorenc, H. Cailleau, A. Tissot, J. Laisney, M.L. Boillot, L. Stoleriu, A. Stancu, C. Enachescu, E. Collet
, Elastically driven cooperative response of a molecular material impacted by a laser pulse, Nature Materials, 15 (2016) 606
-610.

**日時：**6月7日15時より

**場所：**理学部1号館 447教室

**講演者：**Per Arne Rikvold (Florida State University)

**講演タイトル：** Model Spin-crossover Material with Short-range Antiferromagnetic and Long-range Ferromagnetic Interactions: Wang-L andau Calculation of Free-energy Landscapes

**講演要旨：**

Spin-crossover materials present an interesting example of systems with competing interactions on different length scales. In these systems, the short-range interactions may be geometric or electronic in nature, while the long-range interactions are typically elastic.

Here I present a “toy model” of such a system: a square-lattice Ising model with nearest-neighbor antiferromagnetic and mean-field like long-range ferromagnetic interactions. Using standard importance sampling Monte Carlo (MC) methods, we have recently obtained rather complex phase diagrams for this model in several parameter regimes.

One question that cannot easily be answered by these methods, is that of the structure of the free-energy landscape in the space of the two macroscopic order parameters: magnetization and staggered magnetization. We have therefore developed a new method to directly obtain the density of states (DOS) of such a model, using the Wang-Landau MC (WLMC) method. I will give a brief introduction to the original WLMC method, and then describe the modifications we have made to obtain DOS constrained to specific values of the order parameters. I will show numerical free-energy landscapes for several parameter values and compare the results with phase diagrams previously obtained with importance sampling MC. The comparison raises some new questions about the nature of metastable phases in models with competing short-range and long-range interactions.

**日時：**5月31日15時より

**場所：**理学部1号館 447教室

**講演者：**赤城裕(桂研)

**講演タイトル：**Topological Excitations in Frustrated Magnets

**講演要旨：**

Topological defects play an important role in both conventional liquid crystals, such as nematic phase, and in the theory of two-dimensional quantum spin liquids [1]. However, relatively little is known about their role in spin version of nematic phase, namely quantum spin nematic phases which have no long-range dipole order and break only spin-rotational symmetry [2-5]. Moreover, most studies on such topological defects were analyzed in the continuum limit. Little is also known about the properties of topological defects on discrete lattice systems in microscopic models.

Then, we investigate such topological defects in these nontrivial states in a microscopic model. The model is the spin-1 bilinear biquadratic model in which such nontrivial states are stabilized on the triangular lattice [6-8]. Using homotopy analysis and numerical minimization of a variational wave function, we exhaustively examine what topological defects are in this model.

(1) We identify a new family of solitons at special SU(3) symmetric point. We also find that a soliton with higher topological charge spontaneously decays into “elementary” solitons with emergent interaction [9,10].

(2) In antiferro nematic phase with SU(2) symmetry [3-5], we find that \bar{C_0} type point defect spontaneously splits into two C_z type point defects, expanding the vortex core region [10].

(3) In antiferromagnetic 120°order, we clarify that the famous Z_2 vortex [11] has a preference of orientation in this model. As a nontrivial result, we also find the spin lengths are diminished near vortex core, depending on parameter region [10].

Reference:

[1] A. V. Chubukov, S. Sachdev, and T. Senthil, Nucl. Phys. B 426 [FS], 601 (1994).

[2] B. A. Ivanov, R. S. Khymyn, and A. K. Kolezhuk, Phys. Rev. Lett. 100, 047203 (2008).

[3] T. Grover and T. Senthil, Phys. Rev. Lett. 107, 077203 (2011).

[4] J. Takano and H. Tsunetsugu, J. Phys. Soc. Jpn. 80, 094707 (2011).

[5] C. Xu and A. W. W. Ludwig, Phys. Rev. Lett, 108, 047202 (2012).

[6] A. Lauchil, F. Mila, and K. Penc, Phys. Rev. Lett. 97, 087205 (2006).

[7] H. Tsunetsugu and M. Arikawa, J. Phys. Soc. Jpn. 75, 083701 (2006).

[8] A. Smerald and N. Shannon, Phys. Rev. B 88, 184430 (2013).

[9] H. T. Ueda, Y. Akagi, and N. Shannon, Phys. Rev. A. 93, 021606(R) (2016).

[10] Y. Akagi, H. T. Ueda, and N. Shannon, in preparation.

[11] H. Kawamura and S. Miyashita, J. Phys. Soc. Jpn. 53, 4138 (1984).

**日時：**5月24日15時より

**場所：**理学部1号館 447教室

**講演者：**島田尚氏（伊藤研）

**講演タイトル：**Multiple Gapless-Excitation Modes at Neel to Valence-Bond-Solid Transition

**講演要旨：**

A key and universal feature of various real complex systems such as ecosystems, reaction networks in living organisms, and s
ocial communities is its open and evolving nature. In those evolving open systems, their complexity emerges as a result of (
or at least persist) successive introductions of new elements. Therefore it is natural to ask how can a community or system,
which consists of lots of elements interacting each other, grow to more complex structure by adding new elements to it. To
tackle this general question, we have introduced a very simple graph dynamics model and found a novel type of mechanism of d
etermining the robustness of the system [1].

Comparing to the classical condition for dynamical systems based on the linear stability, which allow each element to have a
t most only one strong interaction [2], the growth condition in our different class of system is looser (each element can ha
ve more than 10 interactions). However, dynamical systems are often used for modeling complex systems so it is important to
consider the relevance of our framework to dynamical systems. I will first show the condition to have an extinction of an el
ement in a certain type of coupled dynamical system reduces to our graph model [3]. The only condition one should consider d
uring this mapping is to make the interactions mutual. Therefore I next show how the bidirectional interactions change the r
obustness of the system.

[1] T. Shimada, Scientific Reports 4, 4082 (2014).

[2] M. R. Gardner and W. R. Ashby, Nature 228, 784 (1970).

[3] T. Shimada, Y. Murase, and N. Ito, Proceedings of the International Conference on Social Modeling and Simulation, plus E
conophysics Colloquium 2014, p. 99-109 (2015).

**日時：**5月17日15時より

**場所：**理学部1号館 447教室

**講演者：**諏訪秀麿(藤堂研)

**講演タイトル：**Multiple Gapless-Excitation Modes at Neel to Valence-Bond-Solid Transition

**講演要旨：**

Most continuous phase transitions are described by the Landau-Ginzburg-Wilson (LGW) paradigm where the fluctuation of an order parameter diverges together with a spontaneous symmetry breaking at a critical point. For more than a decade, the deconfined criticality has caught a great deal of attention as a highly non-trivial phase-transition point breaking the LGW paradigm[1]. The low-energy (or long-length-scale) physics will be described not by the original degrees of freedom manifest in the model Hamiltonian but by internal degrees of freedom emerging as fractional excitation. The existence or the stability of such a deconfined critical point has been debated for the Neel to the valence-bond-solid transition in the two-dimensional quantum spin systems, the three-dimensional non-compact CP$^1$ action, the loop, and the dimer models. The Monte Carlo simulations, as reported in the previous researches, suffer from the anomalous finite-size effect and the breakdown of the conventional finite-size scaling. It was recently proposed that this enigma can be resolved by introducing a critical scaling form with two divergent length scales, the correlation length and the spinon-deconfinement length (or the domain-wall thickness)[2].

We have studied the excitation energy around the deconfined critical point between the Neel and the valence-bond-solid phases in the two-dimensional quantum spin system (J-Q model) by means of the unbiased worldline quantum Monte Carlo method. The energy gaps are estimated by the generalized moment method capturing the asymptotic behavior of the imaginary-time correlation[3]. The transition point is located by the level spectroscopy using the lowest gaps, and the duality between the singlet and triplet excitations is found. We have shown that the multiple gapless sectors appear both in the singlet and triplet excitations at the critical point and the unique velocity governs the linear dispersions. Our results strongly support the fundamental excitation consists of deconfined spinons as predicted by the deconfined critical theory[4].

References:

[1] T. Senthil, et al., Science 303, 1490 (2004).

[2] H. Shao, et al., Science 352, 213 (2016).

[3] H. Suwa and S. Todo Phys. Rev. Lett. 115, 080601 (2015).

[4] H. Suwa, A. Sen, and A. W. Sandvik, in preparation.

**日時：**4月19日15時より

**場所：**理学部1号館 447教室

**講演者：**渡辺悠樹(東大物理工学科)

**講演タイトル：**Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals

**講演要旨：**

In this talk, we will discuss our new guiding principle that is useful to identify candidate materials for quantum spin
liquids and topological Dirac/Weyl semimetals, based on the electron filling and space group symmetry. To that end, we will
extend the previous Oshikawa-Hastings-Lieb-Schultz-Mattis theorem in two ways: (i) we allow for arbitrary spin-orbit coupling
and (ii) fully utilize the space group symmetry, not only the lattice translation symmetry, and find stronger conditions
when the space group is nonsymmorphic. We will also discuss a new type of topological crystalline insulator, which we call
'filling-enforced quantum band insulators'.

References:

[1] HW, H.C. Po, A. Vishwanath, and M. Zaletel, PNAS (2015) (arXiv:1505.04193).

[2] H.C. Po, HW, M. Zaletel, and A. Vishwanath, Science Advances (2016), in press (arXiv:1506.03816).

[3] HW, H.C. Po, M. Zaletel, and A. Vishwanath, arXiv:1603.05646.