2024 SeminarRecords | Fujimoto-Mizushima Lab

Seminar

1

Introduction and development of Monte Carlo methods and the application of the infinite product expansion

山田昌彦（東大理）

10Jan28Sun（月）14:00-

Abstract

The Monte Carlo methods used in the Kondo lattice model and the Kitaev model are both classical Monte Carlo methods that include full exact diagonalization of the Hamiltonian in the calculation process. For this reason, the sparsity of the Hamiltonian matrix is not exploited well, and the order of the computational amount becomes extremely large. To solve this problem, I developed a new infinite product expansion method and applied it to the Monte Carlo of the Kondo lattice model and the Kitaev model. This expansion has enabled us to reduce the computational complexity of the Monte Carlo method from O(N^3)/O(N^4) to O(N)/O(N^2) for a system size N, making it possible to speed up and scale up simulations of the Kitaev model and the Kondo lattice model. By increasing N, we will study novel topological phase transitions in three-dimensional Kitaev models and novel topological excitations in frustrated Kondo lattice models.

Seminar

2

Emergence of vortex state in the S = 1 Kitaev-Heisenberg model with single-ion anisotropy

Ayushi Singhania (Okinawa Institue of Science and Technology)

6Jan6Sun(Thu) 13:50-

Abstract

The search for Kitaev spin liquid states has recently broadened to include a number of honeycomb materials with integer spin moments. The qualitative difference with their spin-1/2 counterparts is the presence of single- ion anisotropy (SIA). This motivates our investigation of the effects of SIA on the ground state of the spin-1 Kitaev-Heisenberg (KH) model using the density-matrix renormalization group which allows construction of detailed phase diagrams around the Kitaev points. We demonstrate that positive out-of-plane SIA induces an in-plane vortex state without the need for off-diagonal interactions. Conversely, negative SIA facilitates the emergence of a ferromagnetic state in presence of antiferromagnetic Heisenberg interactions, while a N ?eel state can emerge for ferromagnetic Heisenberg coupling. These findings, pertinent even for weak SIA, not only enhance our theoretical understanding of the spin-1 KH model but also propose experimental prospects for observing these novel magnetic states in material realizations.

Seminar

3

Fundamental gap bound in insulators

大西　由吾(Condensed Matter Theory group, MIT Physics)

5Jan28Sun(Tue) 10:30-

Abstract

Insulating states with a finite energy gap are ubiquitous. The finite energy gap between the ground state and the first excited state results in vanishing DC conductivity at zero temperature, i.e., insulating states. Much research effort has been put into exploring interesting insulating ground state properties, including topological responses such as the integer/fractional quantum Hall effect. On the other hand, the size of the energy gap seems not to have been paid much attention so far, even though realizing a large energy gap is crucial to experimentally observe these interesting ground state properties. In this talk, I will present two recent results on fundamental gap bounds in insulators [1,2]. The first one is a gap bound in terms of the dielectric constant, while the second bound is a gap bound in terms of the Chern number for integer/fractional Chern insulators. Both bounds are applicable to any gapped insulators, including strongly correlated systems. Our results reveal a relation between the ground state properties and the energy gap, suggesting a new research direction.

Seminar

4

Higher vortexability: zero field realization of higher Landau levels

藤本　大仁(東京大学工学研究科物理工学専攻　森本研究室)

4Jan4Sun(Thu) 10:30-

Abstract

The rise of moir? materials has led to experimental realizations of integer and fractional Chern insulators in small[1] or vanishing magnetic fields[2]. At the same time, a set of minimal conditions sufficient to guarantee an Abelian fractional state in a flat band was identified, namely "ideal" or "vortexable" quantum geometry[3,4]. Such vortexable bands share essential features with the lowest Landau level, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at ν = 1/2, 2/5 are known to be competitive[5]. The possibility of realizing these states at zero magnetic field, and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work[6], we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. We apply the definition to identify two models with 1LL structure ? a toy model of double bilayer twisted graphene and a more realistic model of strained Bernal graphene.

Seminar

5

Foliated BF theory and multipole symmetry

戎弘実(京都大学基礎物理学研究所)

1Jan15Sun(Mon) 14:00-

Abstract

分数量子ホール効果、スピン液体などのTopological ordered phase は主に 2 次元系に現れる新奇な相で、これらの相の重要な特徴は分数電荷の励起、すなわち anyon が存在することです。従来のanyonは励起されるとバルクのどこでも動くことができますが、最近になりfracton topological phaseと呼ばれる、この性質を満たさないtopological相が理論的に提案されました。この相では分数電荷の励起の動く範囲に制限がかかり、系の縮退度も局所的な情報によってしまいます。この性質から従来のtopologicalな場の量子論は構築できず、相を記述する新しい理論が必要となっています。この背景のもと、新しい対称性であるmulti-pole symmetry(多極子の保存に対応する対称性)に着目し、そのゲージ理論から新しいtopologicalな場の理論を構築することを議論します。

Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University

Fujimoto-Mizushima Laboratory

2024年 Seminar記録

Archives by Year

Seminar記録

Introduction and development of Monte Carlo methods and the application of the infinite product expansion

Abstract

Emergence of vortex state in the S = 1 Kitaev-Heisenberg model with single-ion anisotropy

Abstract

Fundamental gap bound in insulators

Abstract

Higher vortexability: zero field realization of higher Landau levels

Abstract

Foliated BF theory and multipole symmetry

Abstract