Dissipative Preparation of Antiferromagnetic Order in the Fermi-Hubbard Model

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 model's 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.Comment: 9 pages, 5 figure

Coexistence of Nematic Order and Superconductivity in the Hubbard Model

We study the interplay of nematic and superconducting order in the two-dimensional Hubbard model and show that they can coexist, especially when superconductivity is not the energetically dominant phase. Due to a breaking of the $C_4$ symmetry, the coexisting phase inherently contains admixture of the $s$-wave pairing components. As a result, the superconducting gap exhibits very non-standard features including changed nodal directions. Our results also show that in the optimally doped regime the superconducting phase is typically unstable towards developing nematicity (breaking of the $C_4$ symmetry). This has implications for the cuprate high-$T_c$ superconductors, for which in this regime the so-called intertwined orders have recently been observed. Namely, the coexisting phase may be viewed as a precursor to such more involved patterns of symmetry breaking.Comment: 5 pages, 3 figure

Gutzwiller Wave-Function Solution for Anderson Lattice Model: Emerging Universal Regimes of Heavy Quasiparticle States

The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model (ALM). This approach allows for a systematic evaluation of the expectation values with GWF in the finite dimensional systems. It introduces results extending in an essential manner those obtained by means of standard Gutzwiller Approximation (GA) scheme which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss principal paramagnetic properties of ALM and their relevance to heavy fermion systems. We demonstrate the formation of an effective, narrow $f$-band originating from atomic $f$-electron states and subsequently interpret this behavior as a mutual intersite $f$-electron coherence; a combined effect of both the hybridization and the Coulomb repulsion. Such feature is absent on the level of GA which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow effective $f$-band rationalizes common assumption of such dispersion of $f$ levels in the phenomenological modeling of the band structure of CeCoIn$_5$. Moreover, we show that the emerging $f$-electron coherence leads in a natural manner to three physically distinct regimes within a single model, that are frequently discussed for 4$f$- or 5$f$- electron compounds as separate model situations. We identify these regimes as: (i) mixed-valence regime, (ii) Kondo-insulator border regime, and (iii) Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$ electrons half-filling, $\langle\hat n_{f}\rangle\rightarrow1$. The non-Landau features of emerging correlated quantum liquid state are stressed.Comment: Submitted to Phys. Rev.

Evaluation techniques for Gutzwiller wave functions in finite dimensions

We give a comprehensive introduction into a diagrammatic method that allows for the evaluation of Gutzwiller wave functions in finite spatial dimensions. We discuss in detail some numerical schemes that turned out to be useful in the real-space evaluation of the diagrams. The method is applied to the problem of d-wave superconductivity in a two-dimensional single-band Hubbard model. Here, we discuss in particular the role of long-range contributions in our diagrammatic expansion. We further reconsider our previous analysis on the kinetic energy gain in the superconducting state.Comment: 12 pages, 10 figure