Steady states and universal conductance in a quenched Luttinger model
2016 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, 1-32 p.Article in journal (Refereed) Epub ahead of print
We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian (Formula presented.) with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian (Formula presented.) which differs from (Formula presented.) by the strength of the interaction. Asymptotically in time, as (Formula presented.), after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference (Formula presented.) between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. Both I and (Formula presented.) depend on (Formula presented.) and (Formula presented.). Only for the case (Formula presented.) does (Formula presented.) equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, (Formula presented.), has a universal value equal to the conductance quantum (Formula presented.) for the spinless case.
Place, publisher, year, edition, pages
Springer-Verlag New York, 2016. 1-32 p.
IdentifiersURN: urn:nbn:se:kth:diva-193328DOI: 10.1007/s00220-016-2631-xOAI: oai:DiVA.org:kth-193328DiVA: diva2:1009221
QC 201610032016-09-302016-09-302016-10-03Bibliographically approved