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Strongly Correlated Electrons in a Magnetic Field: Numerical Studies of the Hubbard-Hofstadter Model
Strongly Correlated Electrons in a Magnetic Field: Numerical Studies of the Hubbard-Hofstadter Model
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211153053
- ISBN
- 9798346388630
- DDC
- 536.7
- 저자명
- Ding, Jixun.
- 서명/저자
- Strongly Correlated Electrons in a Magnetic Field: Numerical Studies of the Hubbard-Hofstadter Model
- 발행사항
- [Sl] : Stanford University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 155 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-05, Section: B.
- 주기사항
- Advisor: Devereaux, Thomas;Kapitulnik, Aharon.
- 학위논문주기
- Thesis (Ph.D.)--Stanford University, 2024.
- 초록/해제
- 요약How to understand topological characteristics of strongly correlated systems is one of the biggest open questions in condensed matter physics today. The Hubbard-Hofstadter (HH) model is arguably the simplest model that incorporates the simultaneous influence of magnetic field and interaction between electrons in a lattice. This thesis employs unbiased numerical simulations of the Hubbard-Hofstadter model on square and triangular lattices in order to map out the phase diagram of the HH model and study the interplay between correlation effects and band topology. First, using determinant quantum Monte Carlo (DQMC) simulations, we study the thermodynamic properties of the HH model on a square lattice. We find that integer Hofstadter band gaps are preserved in the presence of weak Hubbard interactions. In the Mott insulating phase, a strong applied magnetic field weakens the Mott gap and delocalizes electrons, which contradicts intuition based on the non-interacting picture. Then, using a combination of DQMC and density matrix renormalization group (DMRG) techniques, we study the ground state and finite-temperature properties of the lowest Hofstadter band, focusing on understanding how quantum Hall ferromagnetism in a lattice differs from the Landau level limit. We observe the breakdown of SU(2) quantum Hall magnetism at large magnetic fields, Hofstadter subband ferromagnetism, particle-hole assymetric tendencies for skyrmion formation, as well as an intriguing high-field metal with spin texture. These results emphasize the importance of lattice effects, and point to the exciting possibility of realizing novel quantum liquids in lattice systems where interactions strongly mix multiple topological bands. Finally, we go beyond thermodynamic properties and use DQMC to study the transport properties of the HH model at half-filling in the Mott insulating regime. We find that when t'̸= 0 the HH model generically exhibits a nonzero thermal Hall effect. We argue that this nonzero thermal Hall effect is generically allowed by symmetry, and can be attributed to magnon-magnon scattering effects not captured by linear spin wave theory. Together, these projects demonstrate how unbiased numerical simulations of the Hubbard-Hofstadter model help us understand general principles underlying novel correlated electronic phenomena in magnetic fields.
- 일반주제명
- Heat
- 일반주제명
- Energy
- 일반주제명
- Electrons
- 일반주제명
- Superconductivity
- 일반주제명
- Electromagnetism
- 일반주제명
- Geometry
- 일반주제명
- Magnetic fields
- 일반주제명
- Conductivity
- 일반주제명
- Atomic physics
- 일반주제명
- Electromagnetics
- 일반주제명
- Low temperature physics
- 기타저자
- Stanford University.
- 기본자료저록
- Dissertations Abstracts International. 86-05B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211153053
■006m o d
■007cr#unu||||||||
■020 ▼a9798346388630
■035 ▼a(MiAaPQ)AAI31643353
■035 ▼a(MiAaPQ)Stanfordpr650zh2512
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a536.7
■1001 ▼aDing, Jixun.
■24510▼aStrongly Correlated Electrons in a Magnetic Field: Numerical Studies of the Hubbard-Hofstadter Model
■260 ▼a[Sl]▼bStanford University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a155 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-05, Section: B.
■500 ▼aAdvisor: Devereaux, Thomas;Kapitulnik, Aharon.
■5021 ▼aThesis (Ph.D.)--Stanford University, 2024.
■520 ▼aHow to understand topological characteristics of strongly correlated systems is one of the biggest open questions in condensed matter physics today. The Hubbard-Hofstadter (HH) model is arguably the simplest model that incorporates the simultaneous influence of magnetic field and interaction between electrons in a lattice. This thesis employs unbiased numerical simulations of the Hubbard-Hofstadter model on square and triangular lattices in order to map out the phase diagram of the HH model and study the interplay between correlation effects and band topology. First, using determinant quantum Monte Carlo (DQMC) simulations, we study the thermodynamic properties of the HH model on a square lattice. We find that integer Hofstadter band gaps are preserved in the presence of weak Hubbard interactions. In the Mott insulating phase, a strong applied magnetic field weakens the Mott gap and delocalizes electrons, which contradicts intuition based on the non-interacting picture. Then, using a combination of DQMC and density matrix renormalization group (DMRG) techniques, we study the ground state and finite-temperature properties of the lowest Hofstadter band, focusing on understanding how quantum Hall ferromagnetism in a lattice differs from the Landau level limit. We observe the breakdown of SU(2) quantum Hall magnetism at large magnetic fields, Hofstadter subband ferromagnetism, particle-hole assymetric tendencies for skyrmion formation, as well as an intriguing high-field metal with spin texture. These results emphasize the importance of lattice effects, and point to the exciting possibility of realizing novel quantum liquids in lattice systems where interactions strongly mix multiple topological bands. Finally, we go beyond thermodynamic properties and use DQMC to study the transport properties of the HH model at half-filling in the Mott insulating regime. We find that when t'̸= 0 the HH model generically exhibits a nonzero thermal Hall effect. We argue that this nonzero thermal Hall effect is generically allowed by symmetry, and can be attributed to magnon-magnon scattering effects not captured by linear spin wave theory. Together, these projects demonstrate how unbiased numerical simulations of the Hubbard-Hofstadter model help us understand general principles underlying novel correlated electronic phenomena in magnetic fields.
■590 ▼aSchool code: 0212.
■650 4▼aHeat
■650 4▼aEnergy
■650 4▼aElectrons
■650 4▼aSuperconductivity
■650 4▼aElectromagnetism
■650 4▼aGeometry
■650 4▼aMagnetic fields
■650 4▼aConductivity
■650 4▼aAtomic physics
■650 4▼aElectromagnetics
■650 4▼aLow temperature physics
■690 ▼a0791
■690 ▼a0748
■690 ▼a0607
■690 ▼a0598
■71020▼aStanford University.
■7730 ▼tDissertations Abstracts International▼g86-05B.
■790 ▼a0212
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17164833▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
