Large Scale Numerics Uncovering New States of Matter
While in condensed matter systems the constituents are well known, namely electrons, neutrons and protons, their interplay may give rise to unexpected states of matter. In this contribution we concentrate on strongly correlated electrons in one dimension driven out of equilibrium. This requires in principle, the solution of Schrödinger’s equation dealing with a space of states, whose dimension increases exponentially with the number of electrons. Implementing an algorithm that requires only polynomially increasing computational resources, namely the time-dependent density matrix renormalization group (t-DMRG), we show that an electron injected into the system, fractionalizes in several portions, some of them carrying charge but no spin, and others carrying the spin and partial charge, in spite of the electron being an elementary particle in isolation. The characterization of such a fractionalization of charge and spin was made possible by the access to HPC plattforms with large memory processors.
A. M. and A. M. acknowledge support by the DFG through SFB/TRR 21. A. M. and J. M. P. C. thank the hospitality and support of the Beijing Computational Science Research Center, where part of the work was done. J. M. P. C. thanks the hospitality of the Institut für Theoretische Physik III, Universität Stuttgart, and the financial support by the Portuguese FCT both in the framework of the Strategic Project PEST-C/FIS/UI607/2011 and under SFRH/BSAB/1177/2011, the German transregional collaborative research center SFB/TRR21, and Max Planck Institute for Solid State Research. A. M. thanks the KITP, Santa Barbara, for hospitality. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. We are very grateful to HLRS (Stuttgart) and NIC (Jülich) for providing the necessary supercomputer resources.