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Register a new userNon-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
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Added by
Monika Aidelsburger
Publication date
2018
fields
Physics
and research's language is
English
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We experimentally and numerically investigate the sudden expansion of fermions in a homogeneous one-dimensional optical lattice. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly-interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained by the interaction energy produced in the quench.
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We use quantum kinetic theory to calculate the thermoelectric transport properties of the 2D single band Fermi-Hubbard model in the weak coupling limit. For generic filling, we find that the high-temperature limiting behaviors of the electrical ($sim T$) and thermal ($sim T^2$) resistivities persist down to temperatures of order the hopping matrix element $Tsim t$, almost an order of magnitude below the bandwidth. At half filling, perfect nesting leads to anomalous low temperature scattering and nearly $T$-linear electrical resistivity at all temperatures. We hypothesize that the $T$-linear resistivity observed in recent cold atom experiments is continuously connected to this weak coupling physics and suggest avenues for experimental verification. We find a number of other novel thermoelectric results, such as a low-temperature Wiedemann-Franz law with Lorenz coefficient $5pi^2/36$.
Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The paradigmatic model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterised by vanishing two-point spin correlations, gapped excitations, and a characteristic non-local order parameter. More recently it was understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry protected topological (SPT) phases of matter that is based on ideas connecting to quantum information and entanglement. Here, we realise such a topological Haldane phase with Fermi-Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system allows us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model employing a novel correlator.
Expansion dynamics of interacting fermions in a lattice are simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and non-paired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.
The Fermi-Hubbard model is one of the key models of condensed matter physics, which holds a potential for explaining the mystery of high-temperature superconductivity. Recent progress in ultracold atoms in optical lattices has paved the way to studying the models phase diagram using the tools of quantum simulation, which emerged as a promising alternative to the numerical calculations plagued by the infamous sign problem. However, the temperatures achieved using elaborate laser cooling protocols so far have been too high to show the appearance of antiferromagnetic and superconducting quantum phases directly. In this work, we demonstrate that using the machinery of dissipative quantum state engineering, one can efficiently prepare antiferromagnetic order in present-day experiments with ultracold fermions. The core of the approach is to add incoherent laser scattering in such a way that the antiferromagnetic state emerges as the dark state of the driven-dissipative dynamics. In order to elucidate the development of the antiferromagnetic order we employ two complementary techniques: Monte Carlo wave function simulations for small systems and a recently proposed variational method for open quantum systems, operating in the thermodynamic limit. The controlled dissipation channels described in this work are straightforward to add to already existing experimental setups.
The Extended Fermi-Hubbard model is a rather studied Hamiltonian due to both its many applications and a rich phase diagram. Here we prove that all the phase transitions encoded in its one dimensional version are detectable via non-local operators related to charge and spin fluctuations. The main advantage in using them is that, in contrast to usual local operators, their asymptotic average value is finite only in the appropriate gapped phases. This makes them powerful and accurate probes to detect quantum phase transitions. Our results indeed confirm that they are able to properly capture both the nature and the location of the transitions. Relevantly, this happens also for conducting phases with a spin gap, thus providing an order parameter for the identification of superconducting and paired superfluid phases
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