Holographic Study on Quantum Criticality

Abstract

Holographic theory (or Gauge/gravity duality) has been a powerful tool to study the strongly correlated electron system, especially near the quantum critical point. There has been an impressive development for holographic calculation of fermion spectrum and transport phenomena recently. In this dissertation, we describe several works where I was involved and they consist of three parts as follows:

1. Analysis of Holographic fermion spectrum (Chapter 2-4) 2. Holographic DC conductivities including thermoelectric and thermal conductivities (Chapter 5, 6) 3. Optical conductivities in holographic method. (Chapter 7)

Indeed, these three parts cover almost all macroscopic quantities of condensed matter. Hence, the holographic computational techniques will be very useful for understanding the strongly correlated system, which has been difficult to solve in traditional condensed matter theory, since there is not an applicable computational method.|홀로그래픽 이론 (혹은 게이지/중력 이중성)은 강상관계 전자 이론, 특히 양자임계점 근처를 연구하는데 강력한 도구이다. 최근에 페르미온 스펙트럼이나 수송현상에 대한 홀로그래픽 계산에 있어서 상당한 발전이 있었다. 본 학위 논문에서는 저자가 참여한 연구내용을 기술할 것이고 이는 다음의 세 가지로 구성되어 있다.

1. 홀로그래픽 페르미온 스펙트럼에 대한 분석 (2장-4장) 2. 열전 전도성 및 열전도성을 포함한 홀로그래픽 직류 전도성 (5장, 6장) 3. 홀로그래픽 방법론을 통한 광학 전도 (7장)

실제로 이러한 세 가지 영역은 응집물질에서의 거시작인 물리량을 구성하는 거의 모든 것을 다루는 셈이다. 그러므로 홀로그래픽 계산 기술은 기존 응집 물질 이론에서는 적용 가능한 계산 방법이 없어서 해결하기 어려웠던 강상관계 물질을 이해하는데 매우 유용할 것이다.; Holographic theory (or Gauge/gravity duality) has been a powerful tool to study the strongly correlated electron system, especially near the quantum critical point. There has been an impressive development for holographic calculation of fermion spectrum and transport phenomena recently. In this dissertation, we describe several works where I was involved and they consist of three parts as follows:

1. Analysis of Holographic fermion spectrum (Chapter 2-4) 2. Holographic DC conductivities including thermoelectric and thermal conductivities (Chapter 5, 6) 3. Optical conductivities in holographic method. (Chapter 7)

Indeed, these three parts cover almost all macroscopic quantities of condensed matter. Hence, the holographic computational techniques will be very useful for understanding the strongly correlated system, which has been difficult to solve in traditional condensed matter theory, since there is not an applicable computational method.