Theory of correlated holes (and electrons): From satellites to Luttinger liquids

Nelson Oyindenyifa Nenuwe

Koji Sato, Yaroslav Tserkovnyak

A Cooper-pair or electron-hole splitter is a device capable of spatially separating entangled fermionic quasiparticles into mesoscopic solid-state systems such as quantum dots or quantum wires. We theoretically study such a splitter based on a pair of helical Luttinger liquids, which arise naturally at the edges of a quantum spin Hall insulator. Equipping each helical liquid with a beam splitter, current-current cross correlations can be used to construct a Bell inequality whose violation would indicate nonlocal orbital entanglement of the injected electrons and/or holes. Due to the Luttinger-liquid correlations, however, the entanglement is suppressed depending on ambient temperature and voltage bias.

G. Baskaran

We discuss certain physical contents of the two-dimensional Luttinger liquid state using the spin and charge current backflow in strongly correlated electron systems. Also we attempt a description of the Luttinger liquid state in the slave boson formalism. Conventional slave boson mean field theory does not possess an important property expected of a Luttinger liquid, namely a pseudo fermi surface for holons. This arises from the bose condensation of holes. We attempt to rectify this by discussing the physics of the fermionic backflow associated with the hole motion. We argue that the fermionic backflow suppresses the Bose condensation. To understand this we introduce the notion of ‘Statistics Transfer’-the medium transfer certain statistics to the slave particle (e's). A variational wave function in which boson condensation is manifestly absent is introduced. The form of the wave function is justified by the concept of statistics transfer. The spinon and holon excitations both exhibiting pseudo fermi surfaces are constructed.

Heinz J. Schulz

P K Isihara, Yoshinori Nakane, A. Isihara

Alexander A. Ovchinnikov

Using the XX- spin chain as an example we show that in general the asymptotic expansion of the correlator at large distances is not given by the sum over the low-lying particle-hole intermediate states. Only the first two terms in the expansion agree with the predictions of the Luttinger liquid theory. The other terms are in general given by the intermediate states with the particles and holes with the quantum numbers far away from the Fermi- points (at the distances of order of the length of the chain). We argue that the whole expansion cannot be described by the Luttinger liquid theory.