Reducing the numerical effort of finite-temperature density matrix renormalization group calculations

Finite-temperature transport properties of one-dimensional systems can be studied using the time dependent density matrix renormalization group via the introduction of auxiliary degrees of freedom which purify the thermal statistical operator. We demonstrate how the numerical effort of such calculations is reduced when the physical time evolution is augmented by an additional time evolution within the auxiliary Hilbert space. Specifically, we explore a variety of integrable and non-integrable, gapless and gapped models at temperatures ranging from T =∞ down to T/bandwidth= 0.05 and study both (i) linear response where (heat and charge) transport coefficients are determined by the current–current correlation function and (ii) non-equilibrium driven by arbitrary large temperature gradients. The modified density matrix renormalization algorithm removes an ‘artificial’ build-up of entanglement between the auxiliary and physical degrees of freedom. Thus, longer time scales can be reached. 3 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 15 (2013) 083031 1367-2630/13/083031+21$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft