A duality web in 2+1 dimensions and condensed matter physics

COnDEnsED MattEr PhysICs

COnDEnsED MattEr PhysICs

Physics , Condensed Matter Homework

The key insight of Bogoliubov is that although the mean-field Hamiltonian (1) is clearly not diagonal in the space of states created by the operators ck,↑/↓, it may be diagonal in a basis of states created by operators related to these via a simple SU2 transformation. Indeed, it may be the case that ‘electrons’ and ‘holes’ are the wrong degrees of freedom to consider; we should at least look to...

Bosonization and Duality in Condensed Matter Systems

We show that abelian bosonization of 1+1 dimensional fermion systems can be interpreted as duality transformation and, as a conseguence, it can be generalized to arbitrary dimensions in terms of gauge forms of rank d − 1, where d is the dimension of the space. This permit to treat condensed matter systems in d > 1 as gauge theories. Furthermore we show that in the “scaling” limit the bosonized ...

Majorana and Condensed Matter Physics

1. Spin Response and Universal Connection In [1], Majorana considered the coupling of spins to magnetic fields. The paper is brief, but it contains two ingenious ideas whose importance extends well beyond the immediate problem he treated, and should be part of every physicists’ toolkit. The first of those ideas, is that having solved the problem for spin 12 , one can deduce the solution for gen...