Abstract
In this paper, we study a strongly correlated quantum system that has become amenable to experiment by the advent of ultracold bosonic atoms in optical lattices, a chain of two different bosonic constituents. Excitations in this system are first considered within the framework of bosonization and the Luttinger liquid theory which are applicable if the Luttinger liquid parameters are determined numerically. The occurrence of a bosonic counterpart of fermionic spin–charge separation is signalled by a characteristic two-peak structure in the spectral functions found by dynamical density-matrix renormalization group (DMRG) in good agreement with analytical predictions. Experimentally, single-particle excitations as probed by spectral functions are currently not accessible in cold atoms. Therefore we consider the modifications needed for current experiments, namely the investigation of the real-time evolution of density perturbations instead of single-particle excitations, a slight inequivalence between the two intraspecies interactions in actual experiments, and the presence of a confining trap potential. Using time-dependent DMRG, we show that only quantitative modifications occur. With an eye to the simulation of strongly correlated quantum systems far from equilibrium, we detect a strong dependence of the time-evolution of entanglement entropy on the initial perturbation.
Highlights
One of the key proposals in the field of quantum computing, made by Feynman, is the idea to use one quantum system to simulate another one in order to circumvent the problem of the qualitatively different complexity of quantum systems and classical computers as the standard simulation tools of science
The use of Feshbach resonances or optical lattices has given us unprecedented control over interaction and dimensionality in strongly interacting quantum many-body systems of unique purity
This has been put to use in the creation of strongly correlated quantum systems that have been in the focus of interest in condensed-matter physics for a long time[1]
Summary
One of the key proposals in the field of quantum computing, made by Feynman, is the idea to use one quantum system to simulate another one in order to circumvent the problem of the qualitatively different complexity of quantum systems and classical computers as the standard simulation tools of science. Interacting two-component bosonic systems have no counterpart in condensed-matter physics, which is why they have found limited attention in the solidstate literature They are quite implemented in the field of ultracold atom gases[5, 6], and have generated quite some interest (for a review, see [7]). One will be confronted by certain limitations of ultracold atomic systems: currently, spectral functions are unavailable and one is restricted to monitor the time-evolution of excitations These show a separation of symmetric and antisymmetric density combinations (“charge” and “spin”) of the individual species from which results in good agreement with those from the spectral functions can be derived. Differing interaction parameters have not been realized experimentally so far; our typical interaction parameters are chosen
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