Thermal Hall Effect and Geometry with Torsion

Abstract

We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes the classic Luttinger's formulation of thermal transport. In particular, we clarify the geometric meaning of the fields conjugated to energy and energy current. These fields describe the geometric background with non-vanishing temporal torsion. We use the developed formalism to construct the equilibrium partition function of a non-relativistic system coupled to the NC geometry in 2+1 dimensions and to derive various thermodynamic relations

6 pages

References in corpus (3)

• Spacetime Symmetries of the Quantum Hall Effect
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Density-curvature response and gravitational anomaly

Cited by in corpus (21)

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• Aspects of hot Galilean field theory
• FQHE on curved backgrounds, free fields and large N
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• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Dissipative and Hall viscosity of a disordered 2D electron gas
• Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Galilean invariance at quantum Hall edge
• Exact Electromagnetic Response of Landau Level Electrons
• Ward Identities for Hall Transport
• Covariant Poisson's equation in torsional Newton-Cartan gravity
• Non-Relativistic Supersymmetry on Curved Three-Manifolds
• Geometry and large N limits in Laughlin states
• Electrons and composite Dirac fermions in the lowest Landau level
• Geometric and computational aspects of chiral topological quantum matter
• A pedagogical review of gravity as a gauge theory
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories