We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your...

/pdf/ultracold-atomic-gases-in-optical-lattices-mimicking-tfesylj4h7.pdf

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi-long-range order, and one dominated by the long-range interaction, with long-range N\'eel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central charges. In the phase with quasi-long-range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.

Entanglement entropy for the long-range Ising chain in a transverse field.

While manufacturing limitations are imposing constraints on Moore's law, researchers are searching for novel computing architectures based on quantum-mechanical effects. However, it remains to be shown that quantum annealing techniques consistently outperform classical simulated annealing to minimize optimization problems.

https://link.aps.org/pdf/10.1103/PhysRevX.5.031026

Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power σ of the distance. We show that there is a value of σ of the long-range model for which the critical behavior is very similar to that of the short range model in four dimensions. We also study a value of σ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.

Correspondence between long-range and short-range spin glasses

We consider the infinite-range spin glass in which the spins have $mg1$ components (a vector spin glass). Applying a magnetic field which is random in direction, there is a de Almeida-Thouless (AT) line below which the ``replica symmetric'' solution is unstable, just as for the Ising $(m=1)$ case. We calculate the location of this AT line for Gaussian random fields for arbitrary $m$ and verify our results by numerical simulations for $m=3$.

de Almeida-Thouless line in vector spin glasses.

/pdf/probing-the-almeida-thouless-line-away-from-the-mean-field-27wyzpon1w.pdf

Probing the Almeida-Thouless line away from the mean-field model

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Probing the Almeida-Thouless line away from the mean-field model