Quantum phases of 1D Hubbard models with three- and four-body couplings

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Abstract

The experimental advances in cold atomic and molecular gases stimulate the investigation of lattice correlated systems beyond the conventional on-site Hubbard approximation, by possibly including multi-particle processes. We study fermionic extended Hubbard models in a one dimensional lattice with different types of particle couplings, including also three- and four-body interaction up to nearest neighboring sites. By using the Bosonization technique, we investigate the low-energy regime and determine the conditions for the appearance of ordered phases, for arbitrary particle filling. We find that three- and four-body couplings may significantly modify the phase diagram. In particular, diagonal three-body terms that directly couple the local particle densities have qualitatively different effects from off-diagonal three-body couplings originating from correlated hopping, and favor the appearance of a Luther-Emery phase even when two-body terms are repulsive. Furthermore, the four-body coupling gives rise to a rich phase diagram and may lead to the realization of the Haldane insulator phase at half-filling.

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Correlation functions of one-dimensional quantum systems

T Giamarchi, H. J. Schulz (1989)

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Quantum degenerate dipolar Fermi gas

Mingwu Lu, Nathaniel Burdick, Benjamin Lev (2012)

The interplay between crystallinity and superfluidity is of great fundamental and technological interest in condensed matter settings. In particular, electronic quantum liquid crystallinity arises in the non-Fermi liquid, pseudogap regime neighboring a cuprate's unconventional superconducting phase. While the techniques of ultracold atomic physics and quantum optics have enabled explorations of the strongly correlated, many-body physics inherent in, e.g., the Hubbard model, lacking has been the ability to create a quantum degenerate Fermi gas with interparticle interactions---such as the strong dipole-dipole interaction---capable of inducing analogs to electronic quantum liquid crystals. We report the first quantum degenerate dipolar Fermi gas, the realization of which opens a new frontier for exploring strongly correlated physics and, in particular, the quantum melting of smectics in the pristine environment provided by the ultracold atomic physics setting. A quantum degenerate Fermi gas of the most magnetic atom 161Dy is produced by laser cooling to 10 uK before sympathetically cooling with ultracold, bosonic 162Dy. The temperature of the spin-polarized 161Dy is a factor T/TF=0.2 below the Fermi temperature TF=300 nK. The co-trapped 162Dy concomitantly cools to approximately Tc for Bose-Einstein condensation, thus realizing a novel, nearly quantum degenerate dipolar Bose-Fermi gas mixture.

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Bosonization for Beginners --- Refermionization for Experts

Herbert Schoeller, Jan von Delft (1998)

This tutorial gives an elementary and self-contained review of abelian bosonization in 1 dimension in a system of finite size \(L\), following and simplifying Haldane's constructive approach. As a non-trivial application, we rigorously resolve (following Furusaki) a recent controversy regarding the tunneling density of states, \(\rho_{dos} (\omega)\), at the site of an impurity in a Tomonaga-Luttinger liquid: we use finite-size refermionization to show exactly that for g=1/2 its asymptotic low-energy behavior is \(\rho_{dos}(\omega) \sim \omega\). This agrees with the results of Fabrizio & Gogolin and of Furusaki, but not with those of Oreg and Finkel'stein (probably because we capture effects not included in their mean-field treatment of the Coulomb gas that they obtained by an exact mapping; their treatment of anti-commutation relations in this mapping is correct, however, contrary to recent suggestions in the literature). --- The tutorial is addressed to readers unfamiliar with bosonization, or for those interested in seeing ``all the details'' explicitly; it requires knowledge of second quantization only, not of field theory. At the same time, we hope that experts too might find useful our explicit treatment of certain subtleties -- these include the proper treatment of the so-called Klein factors that act as fermion-number ladder operators (and also ensure the anti-commutation of different species of fermion fields), the retention of terms of order 1/L, and a novel, rigorous formulation of finite-size refermionization of both \(e^{-i \Phi(x)}\) and the boson field \(\Phi (x)\) itself.