Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

被引:72
作者
Can, Tankut [1 ]
Laskin, Michael [2 ]
Wiegmann, Paul B. [2 ]
机构
[1] SUNY Stony Brook, Simons Ctr Geometry & Phys, Stony Brook, NY 11794 USA
[2] Univ Chicago, Dept Phys, Chicago, IL 60637 USA
基金
美国国家科学基金会;
关键词
Quantum Hall effect; Kahler geometry; Laughlin wave function; ONE-COMPONENT PLASMA; 2; DIMENSIONS; FINITE-SIZE; PROJECTIVE EMBEDDINGS; RIEMANN SURFACES; SCALAR CURVATURE; CRITICAL SYSTEMS; GROUND-STATE; FREE-ENERGY; EXCITATIONS;
D O I
10.1016/j.aop.2015.02.013
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism. (C) 2015 Published by Elsevier Inc.
引用
收藏
页码:752 / 794
页数:43
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