Related papers: Thermal Hall Effect and Geometry with Torsion
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy--momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation…
We discuss some equivalence relations between the non-relativistic quantum mechanics for particles subjected to potentials and for particles moving freely on background geometries. In particular, we illustrate how selected geometries can be…
The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but…
Quantum geometry, a quantum mechanical quantity comprised of Berry curvature and quantum metric, describes the geometric structure of the electronic bands in solids. The correlation between nontrivial quantum geometry and quantum materials…
We compute magnon Hall conductivities in a minimal model of a two-dimensional altermagnet. To do so, we derive an analytic expression for the relevant quantum geometric tensor describing two-band bosonic Bogoliubov Hamiltonians, providing…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hall conductivity is quantized and that…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
We revisit the manifestly covariant large $c$ expansion of General Relativity, $c$ being the speed of light. Assuming the relativistic connection has no pole in $c^{-2}$, this expansion is known to reproduce Newton-Cartan gravity and a…
We search a gravitational system which allows a non-relativistic hybrid geometry interpolating the Schr\"odinger and Lifshitz spacetimes as a solution, as a continuation of the previous work employing a flow equation. As such a candidate an…
In this paper, we endeavour to obtain a modified form of the Foldy-Wouthuysen and Cini-Toushek transformations by resorting to the noncommutative nature of space-time geometry, starting from the Klein-Gordon equation. Also, we obtain a…
A microscopic formalism to calculate thermal transport coefficients is presented based on a thermal vector potential, whose time-derivative is related to a thermal force. The formalism is free from unphysical divergences reported to arise…
We clarify relations between the higher dimensional quantum Hall effect and A-class topological insulator. In particular, we elucidate physical implications of the higher dimensional non-commutative geometry in the context of A-class…
Geometric mechanics is a branch of mathematical physics that studies classical mechanics of particles and fields from the point of view of geometry. In a geometric language, symmetries can be expressed in a natural manner as vector fields…
In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity…
We consider a gravitational theory with an additional non-minimal coupling between baryonic matter fields and geometry. The coupling is second order in the energy momentum tensor and can be seen as a generalization of the energy-momentum…
It is proposed that Maxwell theory, with a topological term, in four non-commutative dimensions, where the co-ordinates obey the Heisenberg algebra, is an umbrella theory for the description of the two-dimensional Quantum Hall Effect…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…