### 今後の予定

日時：2024年7月3日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：濱田 雄大（場の量子論・素粒子論研究室）

題目：Fermion on the lattice

概要：When defining fermion fields on lattice spaces, a challenge known as the doubling problem arises. In this issue, taking the continuous limit of the fermion action on the lattice results in two fermionic degrees of freedom for each dimension. This is undesirable from the perspective of the physical properties of low-energy systems, such as asymptotic freedom. Moreover, according to the Nielsen-Ninomiya theorem, the fundamental properties of lattice fermion actions lead to a strong constraint that the doubling problem is necessarily unavoidable. In this presentation, we will explore lattice field theory and gauge invariance on the lattice. We will then examine Wilson fermions, which are commonly used to address the doubling problem, as well as domain-wall fermions, discussing their relationship with topological insulators.

日時：2024年7月10日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：宮井 誠一郎（量子多体）

題目：TBA

概要：TBA

日時：2024年7月24日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：武上 響生（京都大学）

題目：Spin Green’s function approach to the Kitaev model

概要：The Kitaev model is a quantum spin system defined on a honeycomb lattice whose ground state has been shown to be a strictly spin liquid state [1,2]. Furthermore, the existence of fractionalized Majorana fermion excitations has been suggested. Although Majorana fermions are essential for obtaining the exact ground state, their physical interpretation in terms of spin operators remains unclear. In this study, we employ the Green’s function equation of motion approach for the analysis of the spin correlations in the isotropic Kitaev model while preserving SU(2) symmetry [3]. In this method, the temperature dependence of the spin-spin correlation function is obtained based on the short-range spin correlations. The spin Green's functions describe the propagation of the Z2 flux defined at each hexagonal plaquette. This approach aligns with the high-temperature expansion in the high-temperature regime. We present the temperature dependence of the nearest neighbor spin-spin correlation function, and show that its value is very close to the exact value at zero temperature. We also present some exact results for the spin-spin correlation function.

### 過去のセミナー

日時：2024年4月17日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：植田 健太 （量子多体）

題目：Anomalous tunneling of collective excitations in a Rydberg atomic system

概要：We study tunneling properties of low-energy excitations through a potential barrier in a spin-1/2 ferromagnetic XY model with dipole-dipole interactions, which has been realized with Rydberg atoms in an optical tweezer array [1]. In a system with spontaneous breaking of U(1) symmetry and short-range interaction, it is known that low-energy excitations exhibit anomalous tunneling behavior, in which the transmission probability increases with decreasing the excitation energy and the barrier is completely transparent at the zero-energy limit [2]. We aim to elucidate how the long-range nature of the dipole-dipole interaction affects such tunneling properties of the low-energy excitations. Specifically, within a mean field theory, we numerically calculate the transmission probability. As a result, we find that anomalous tunneling indeed occurs. We also discuss physical properties unique to the systems with long-range interactions.

[1] C. Chen et al., Nature, 616, 691 (2023).

[2] Yu. Kagan et al., Phys. Rev. Lett. 90, 130402 (2003).

日時：2024年5月8日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：Rammohan, Sidharth（量子多体）

題目：Studying quantum phases in dipolar Bosons in planar array using cluster mean-field

概要：Dipolar bosons in optical lattices have emerged as a promising candidate for the quantum simulation of the condensed matter systems. These systems have been widely employed to study phase transitions in spin models because of their tunability with regard to the interaction strengths. These prospects now motivate scientists even more to explore for interesting phases in these kinds of systems, such Luttinger liquids. A theoretical study conducted in 2008 employed dipolar bosons in planar arrays to investigate the formation of the "sliding Luttinger liquid" (SLL) phase [1]. Since it is difficult to observe the SLL phase experimentally, the main objective of this work was to propose one such platform that would allow for the observation of the SLL phase utilizing dipolar bosons.

Despite the usual challenges associated with experimental advancements, experimental research has recently accelerated, and dipolar bosons can already be realized in optical lattices in laboratories. In 2023, Griener's group investigated the formation of dipolar quantum solids in a Hubbard quantum simulator [2]. Given the current status of the research field, we think that adopting a different approach, like a cluster mean-field method, to the problem will help to develop a computationally efficient solution and open the door to studying the real-time dynamics of the systems. We believe that the cluster mean field strategy introduced in [3] will work nicely for this.

While [3] studies the phase transition in a hardcore Bose-Hubbard model, this method can also be effectively applied to the dipolar boson in planar array case.Thus, in my talk, I will be talking about this proposal, focusing mostly on the concepts of the cluster mean-field approach from [3] and the current state of the exploration of phase transition in dipole bosons in planar array. Finally, I will provide a quick summary of the cluster mean-field approach's potential for this purpose at the end of my session.

[1] C. Kollath *et.al.*, PRL **100, **130403 (2008).

[2] Lin Su *et.al.*, Nature **622** (2023).

[3] D. Yamamoto *et.al., *PRB **86**, 054516 (2012).

日時：2024年5月15日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：段下 一平（量子多体）

題目：Creating Ising model with sign-inverted next-nearest-neighbor interaction by using Rydberg atoms:

Application to studies of surface criticality

概要：We propose a way to realize a system quantitatively described by a mixed-field Ising model, in which the sign of the next-nearest-neighbor (NNN) interaction is opposite to that of nearest-neighbor one [1], with use of Rydberg atoms in an optical-tweezer array. We theoretically show that the proposed system is suited to studying surface criticality associated with discontinuous quantum phase transitions [2,3]. Specifically, we derive the Ginzburg-Landau (GL) equation of the Ising model with the sign-inverted NNN interaction, which provides us with analytical insights of the surface criticality. By presenting numerical calculations based on a mean-field theory, we confirm the validity of the GL equation near the quantum tricritical point (QTCP). We also find that the logarithmic divergence behavior, which is a characteristic of the surface criticality, persists even away from the QTCP.

[1] Y. Kato and T. Misawa, Phys. Rev. B 92, 174419 (2015).

[2] R. Lipowsky, Phys. Rev. Lett. 49, 1575 (1982).

[3] I. Danshita, D. Yamamoto, and Y. Kato, Phys. Rev. A 91, 013603 (2015).

日時：2024年5月22日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：百合 巧（大阪大学）

題目：Construction of Many-Body Quantum Simulators Using Phonons in Trapped Ions

概要：Quantum simulation, which uses a well-controlled quantum system to simulate another quantum system [1], is gaining attention as a new method for exploring the properties of matter, and research in this area is becoming increasingly active. Arrays of ions trapped by electromagnetic fields in a vacuum are a promising choice for quantum simulation due to their high coherence and controllability. In quantum information processing using ions, both qubits (internal states) and phonons (vibrational quantum states of ions) play important roles. The internal states of cooled ions can be controlled with high precision, making them ideal quantum bits. Experiments using ion arrays, from a few to many ions, have primarily focused on the internal states [2~4]. On the other hand, the phonon degrees of freedom have more energy levels and can handle more information. However, due to the difficulty of controlling phonons, experiments focusing on phonons have so far only been reported with a few ions [5~8]. This research aims to conduct experimental studies of quantum many-body systems described by the Jaynes-Cummings- Hubbard (JCH) model using phonons in ion arrays. In this talk, as preparation for observing quantum phase transitions in the JCH model, I will present results from measurements of Rabi oscillations and sideband cooling with ten ions using a macroscopic light addressing beam, as well as results from Rabi oscillations and sideband cooling with 20 ions. I will also discuss plans for future research.

[1] R. P. Feynman, Intl. J. Theor. Phys. 21, 467(1982).

[2] B. P. Lanyon et. al., Science 334, 57 (2011).

[3] Q.-X. Nei et. al., PRL 128, 100504 (2022).

[4] M.-W. Li et. al., PRL 129, 140501(2022).

[5] E. K. Irish et. al., PRA 77, 033811(2008).

[6] K. Toyoda et. al., PRL 111, 160501(2013).

[7] R. Ohira et. al., PRA 100, 06031(R) (2019).

[8] S. Muralidharan et. al., PRA 104, 062410(2021).

日時：2024年5月29日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：小久保 治哉 （物性理論）

題目：Size Dependence of the critical velocity of the superfluid wake

概要：Wake is a flow that occurs behind an obstacle moving through fluids, the dynamics of which is determined by the size and velocity of the obstacle, and is associated with various fluid phenomena such as vortex formation and turbulent transition. Wake in superfluid has been studied both experimentally and theoretically in weakly interacting Bose systems, and it has been shown that the critical velocity depends on the shape of the obstacle. In numerical simulations, Gaussian potentials are often used to simulate an optical laser obstacle. However, it is difficult to measure the dependence of the critical velocity on the shape of the obstacle due to the unclear effects of the tail in the Gaussian potential. In this work, we consider the wake with a plate-shaped obstacle to evaluate the dependence of the critical velocity on the size of the obstacle. In this talk, we describe the size dependence of the critical velocity by numerical simulations for a 2-dimensional Bose-Einstein condensate and present a method for quantitative evaluation of the critical velocity using the complex potential flow.

日時：2024年6月5日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：安藤 京介（物性理論）

題目：Machine learning analysis of Fully Frustrated XY Model (FFXY) in two-dimensional square lattice

概要：The recent remarkable development of artificial neural networks in image recognition, image classification, and natural language processing has influenced many scientific fields, and the search for new discoveries by applying this technology to any problem has begun. In the field of classical statistical physics, machine learning algorithms were introduced to identify symmetry-broken phase [1-3], and in some of these cases neural networks were shown to be able to learn order parameters and other thermodynamic parameters [1,3]. Having been able to apply machine learning techniques to conventional phase transitions, it is natural to ask whether the algorithm can be applied to unconventional phase transitions. As an example of such a system, we focus on the 2D Fully Frustrated XY Model (FFXY) [4]. The FFXY model has an Ising model-like transition and an XY model-like transition.

The purpose of this study is to see if machine learning algorithms trained by the XY and Ising models can detect phase transitions for the two-dimensional square lattice FFXY model. The two neural networks used were trained from the spin configuration of the Ising model and the vortex configuration of the XY model. The FFXY model detects vortices from spin configurations obtained from Monte Carlo simulations, and inputs them to the learning model. Also introduce the graph-convolutional network (GCN) method for learning phase transitions.

[1] J. Carrasquilla and R. G. Melko, Nat. Phys. 13, 431 (2017).

[2] E. P. L. van Nieuwenburg, Y.-H. Liu, and S. D. Huber, Nat. Phys.13, 435 (2017).

[3] S. J. Wetzel and M. Scherzer, Phys. Rev. B 96, 184410 (2017).

[4] Stephen Teitel, 40 Years of Berezinskii–Kosterlitz–Thouless Theory (World Scientific), pp. 201-235 (2013).

日時：2024年6月12日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：笠松 健一（物性理論）

題目：Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates

概要：We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through a Gaussian stirring potential. When the condensates have unequal intracomponent coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasiequilibrium state, of like-signed vortices with an extended size of the vortex core. The time of formation of this state is shortened when the parameter asymmetry of the intracomponent couplings or the trap frequencies is enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a k^{-3} power law around the range of the wave number determined by the spin healing length (the size of the extended vortex core) and (ii) a flat region around the range of the wave number determined by the density healing length. The latter is associated with the small scale phase fluctuation relegated outside the Thomas-Fermi radius and is more prominent as the strength of intercomponent interaction approaches the strength of intracomponent interaction. We also study the impact of the intercomponent interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the intercomponent coupling gives rise to the decay of the clustered configuration.Reference

Thudiyangal Mithun, Kenichi Kasamatsu, Bishwajyoti Dey, and Panayotis G. Kevrekidis, Phys. Rev. A 103, 023301 (2021)

日時：2024年6月19日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：近藤 康（量子制御）

題目：Artificial Relaxation in NMR Experiment

概要：Environmental noises cause quantum systems to relax, which can significantly impact the precision of operations. Grasping the relaxation mechanism caused by environmental noises is a crucial step in the development of quantum technologies. Relaxations can be viewed as a process of information dissipation from the system into an environment with infinite degrees of freedom (DoF). This concept has led to the proposal and demonstration of a model of artificial relaxation in NMR experiments. While the current model has successfully captured the central idea of relaxation, we have observed recursive behavior due to the limited DoF of the ``artificial environment''. This limitation hampers its ability to describe relaxation accurately. This paper aims to overcome this limitation by extending the approach and studying the relaxation-like behavior through manipulating DoF. Our study promises to provide a more comprehensive understanding of the concept of relaxation.

日時：2024年6月26日10:45-

教室： 31号館3階シミュレーション実験室 + Zoomでのオンライン配信

発表者：手塚 真樹（京都大学）

題目：Quantum error correction and spectral statistics in Sachdev-Ye-Kitaev-type long-range interacting models

概要：The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model with maximally chaotic behavior at low temperatures. The model contains N fermions with random, all-to-all interactions and can be solved in the large-N limit. Since its proposal in 2015, the model has received significant attention due to its simplicity and the potential to study quantum gravity via the holographic principle. Numerous variants of the SYK model have been proposed, including a sparse version where only O(N) couplings are nonzero.

In this talk, we discuss our results [1] on the scrambling feature of SYK-type models including the binary-coupling sparse version [2], obtained by estimating the decoding error for the Hayden-Preskill protocol, where quantum information is embedded in a larger quantum system undergoing unitary dynamics. We also briefly introduce our

proposal for a further simplified model [3] that employs spin operators instead of Majorana fermions, presenting numerical results such as eigenenergy statistics and discussing the potential for quantum simulations.

[1] Y. Nakata and M. Tezuka, Phys. Rev. Research 6, L022021 (2024).

[2] M. Tezuka, O. Oktay, E. Rinaldi, M. Hanada, and F. Nori, Phys. Rev. B. 107, L081103 (2023).

[3] M. Hanada, A. Jevicki, X. Liu, E. Rinaldi, and M. Tezuka, J. High Energ. Phys. 05(2024)280.