@inbook{604,
abstract = {In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem, based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose–Einstein condensates form angulons, and therefore can be described by straightforward solutions of a simple microscopic Hamiltonian. Casting the problem in the language of angulons allows us not only to greatly simplify it, but also to gain insights into the origins of the observed phenomena and to make predictions for future experimental studies.},
author = {Lemeshko, Mikhail and Schmidt, Richard},
booktitle = {Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero },
editor = {Dulieu, Oliver and Osterwalder, Andreas},
issn = {20413181},
pages = {444 -- 495},
publisher = {The Royal Society of Chemistry},
title = {{Molecular impurities interacting with a many-particle environment: From ultracold gases to helium nanodroplets}},
doi = {10.1039/9781782626800-00444},
volume = {11},
year = {2017},
}
@article{1015,
abstract = {Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures of macroscopic quantum phenomena. In two-dimensional superfluids quantized vortices play a key role in determining finite-temperature properties, as the superfluid phase and the normal state are separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless transition. Very recent experiments with two-dimensional superfluid fermions motivate the present work: we present theoretical results based on the renormalization group showing that the universal jump of the superfluid density and the critical temperature crucially depend on the interaction strength, providing a strong benchmark for forthcoming investigations.},
author = {Bighin, Giacomo and Salasnich, Luca},
issn = {20452322},
journal = {Scientific Reports},
publisher = {Nature Publishing Group},
title = {{Vortices and antivortices in two-dimensional ultracold Fermi gases}},
doi = {10.1038/srep45702},
volume = {7},
year = {2017},
}
@article{1076,
abstract = {Signatures of the Coulomb corrections in the photoelectron momentum distribution during laser-induced ionization of atoms or ions in tunneling and multiphoton regimes are investigated analytically in the case of a one-dimensional problem. A high-order Coulomb-corrected strong-field approximation is applied, where the exact continuum state in the S matrix is approximated by the eikonal Coulomb-Volkov state including the second-order corrections to the eikonal. Although without high-order corrections our theory coincides with the known analytical R-matrix (ARM) theory, we propose a simplified procedure for the matrix element derivation. Rather than matching the eikonal Coulomb-Volkov wave function with the bound state as in the ARM theory to remove the Coulomb singularity, we calculate the matrix element via the saddle-point integration method by time as well as by coordinate, and in this way avoiding the Coulomb singularity. The momentum shift in the photoelectron momentum distribution with respect to the ARM theory due to high-order corrections is analyzed for tunneling and multiphoton regimes. The relation of the quantum corrections to the tunneling delay time is discussed.},
author = {Klaiber, Michael and Daněk, Jiří and Yakaboylu, Enderalp and Hatsagortsyan, Karen and Keitel, Christoph},
issn = {24699926},
journal = { Physical Review A - Atomic, Molecular, and Optical Physics},
number = {2},
publisher = {American Physical Society},
title = {{Strong-field ionization via a high-order Coulomb-corrected strong-field approximation}},
doi = {10.1103/PhysRevA.95.023403},
volume = {95},
year = {2017},
}
@article{1109,
abstract = {Rotation of molecules embedded in He nanodroplets is explored by a combination of fs laser-induced alignment experiments and angulon quasiparticle theory. We demonstrate that at low fluence of the fs alignment pulse, the molecule and its solvation shell can be set into coherent collective rotation lasting long enough to form revivals. With increasing fluence, however, the revivals disappear -- instead, rotational dynamics as rapid as for an isolated molecule is observed during the first few picoseconds. Classical calculations trace this phenomenon to transient decoupling of the molecule from its He shell. Our results open novel opportunities for studying non-equilibrium solute-solvent dynamics and quantum thermalization. },
author = {Shepperson, Benjamin and Søndergaard, Anders and Christiansen, Lars and Kaczmarczyk, Jan and Zillich, Robert and Lemeshko, Mikhail and Stapelfeldt, Henrik},
journal = {Physical Review Letters},
number = {20},
publisher = {American Physical Society},
title = {{Laser-induced rotation of iodine molecules in helium nanodroplets: Revivals and breaking-free}},
doi = {10.1103/PhysRevLett.118.203203},
volume = {118},
year = {2017},
}
@article{1119,
abstract = {Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here we demonstrate that experimental data collected over the last 20 years provide evidence that molecules immersed in superfluid helium form recently-predicted angulon quasiparticles [Phys. Rev. Lett. 114, 203001 (2015)]. Most importantly, casting the many-body problem in terms of angulons amounts to a drastic simplification and yields effective molecular moments of inertia as straightforward analytic solutions of a simple microscopic Hamiltonian. The outcome of the angulon theory is in good agreement with experiment for a broad range of molecular impurities, from heavy to medium-mass to light species. These results pave the way to understanding molecular rotation in liquid and crystalline phases in terms of the angulon quasiparticle.},
author = {Lemeshko, Mikhail},
issn = {00319007},
journal = {Physical Review Letters},
number = {9},
publisher = {American Physical Society},
title = {{Quasiparticle approach to molecules interacting with quantum solvents}},
doi = {10.1103/PhysRevLett.118.095301},
volume = {118},
year = {2017},
}
@article{1120,
abstract = {The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 83 years ago. Here we reveal the self-localization transition for the rotational analogue of the polaron -- the angulon quasiparticle. We show that, unlike for the polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of the symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. The predicted effects can potentially be addressed in experiments on cold molecules trapped in superfluid helium droplets and ultracold quantum gases, as well as on electronic excitations in solids and Bose-Einstein condensates. },
author = {Li, Xiang and Seiringer, Robert and Lemeshko, Mikhail},
issn = {24699926},
journal = {Physical Review A},
number = {3},
publisher = {American Physical Society},
title = {{Angular self-localization of impurities rotating in a bosonic bath}},
doi = {10.1103/PhysRevA.95.033608},
volume = {95},
year = {2017},
}
@article{1133,
abstract = {It is a common knowledge that an effective interaction of a quantum impurity with an electromagnetic field can be screened by surrounding charge carriers, whether mobile or static. Here we demonstrate that very strong, "anomalous" screening can take place in the presence of a neutral, weakly polarizable environment, due to an exchange of orbital angular momentum between the impurity and the bath. Furthermore, we show that it is possible to generalize all phenomena related to isolated impurities in an external field to the case when a many-body environment is present, by casting the problem in terms of the angulon quasiparticle. As a result, the relevant observables such as the effective Rabi frequency, geometric phase, and impurity spatial alignment are straightforward to evaluate in terms of a single parameter: the angular-momentum-dependent screening factor.},
author = {Yakaboylu, Enderalp and Lemeshko, Mikhail},
issn = {00319007},
journal = {Physical Review Letters},
number = {8},
publisher = {American Physical Society},
title = {{Anomalous screening of quantum impurities by a neutral environment}},
doi = {10.1103/PhysRevLett.118.085302},
volume = {118},
year = {2017},
}
@article{1162,
abstract = {Selected universal experimental properties of high-temperature superconducting (HTS) cuprates have been singled out in the last decade. One of the pivotal challenges in this field is the designation of a consistent interpretation framework within which we can describe quantitatively the universal features of those systems. Here we analyze in a detailed manner the principal experimental data and compare them quantitatively with the approach based on a single-band model of strongly correlated electrons supplemented with strong antiferromagnetic (super)exchange interaction (the so-called t−J−U model). The model rationale is provided by estimating its microscopic parameters on the basis of the three-band approach for the Cu-O plane. We use our original full Gutzwiller wave-function solution by going beyond the renormalized mean-field theory (RMFT) in a systematic manner. Our approach reproduces very well the observed hole doping (δ) dependence of the kinetic-energy gain in the superconducting phase, one of the principal non-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermi velocity in the nodal direction is practically δ-independent and its universal value agrees very well with that determined experimentally. Also, a weak doping dependence of the Fermi wave vector leads to an almost constant value of the effective mass in a pure superconducting phase which is both observed in experiment and reproduced within our approach. An assessment of the currently used models (t−J, Hubbard) is carried out and the results of the canonical RMFT as a zeroth-order solution are provided for comparison to illustrate the necessity of the introduced higher-order contributions.},
author = {Spałek, Jozef and Zegrodnik, Michał and Kaczmarczyk, Jan},
issn = {24699950},
journal = {Physical Review B - Condensed Matter and Materials Physics},
number = {2},
publisher = {American Physical Society},
title = {{Universal properties of high temperature superconductors from real space pairing t-J-U model and its quantitative comparison with experiment}},
doi = {10.1103/PhysRevB.95.024506},
volume = {95},
year = {2017},
}
@article{1163,
abstract = {We investigate the effect of the electron-hole (e-h) symmetry breaking on d-wave superconductivity induced by non-local effects of correlations in the generalized Hubbard model. The symmetry breaking is introduced in a two-fold manner: by the next-to-nearest neighbor hopping of electrons and by the charge-bond interaction - the off-diagonal term of the Coulomb potential. Both terms lead to a pronounced asymmetry of the superconducting order parameter. The next-to-nearest neighbor hopping enhances superconductivity for h-doping, while diminishes it for e-doping. The charge-bond interaction alone leads to the opposite effect and, additionally, to the kinetic-energy gain upon condensation in the underdoped regime. With both terms included, with similar amplitudes, the height of the superconducting dome and the critical doping remain in favor of h-doping. The influence of the charge-bond interaction on deviations from symmetry of the shape of the gap at the Fermi surface in the momentum space is briefly discussed.},
author = {Wysokiński, Marcin and Kaczmarczyk, Jan},
issn = {09538984},
journal = {Journal of Physics: Condensed Matter},
number = {8},
publisher = {IOP Publishing Ltd.},
title = {{Unconventional superconductivity in generalized Hubbard model role of electron–hole symmetry breaking terms}},
doi = {10.1088/1361-648X/aa532f},
volume = {29},
year = {2017},
}
@article{939,
abstract = {We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e., the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn, the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications, the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.},
author = {Midya, Bikashkali and Konotop, Vladimir},
issn = {00319007},
journal = {Physical Review Letters},
number = {3},
publisher = {American Physical Society},
title = {{Waveguides with absorbing boundaries: Nonlinearity controlled by an exceptional point and solitons}},
doi = {10.1103/PhysRevLett.119.033905},
volume = {119},
year = {2017},
}
@article{994,
abstract = {The formation of vortices is usually considered to be the main mechanism of angular momentum disposal in superfluids. Recently, it was predicted that a superfluid can acquire angular momentum via an alternative, microscopic route -- namely, through interaction with rotating impurities, forming so-called `angulon quasiparticles' [Phys. Rev. Lett. 114, 203001 (2015)]. The angulon instabilities correspond to transfer of a small number of angular momentum quanta from the impurity to the superfluid, as opposed to vortex instabilities, where angular momentum is quantized in units of ℏ per atom. Furthermore, since conventional impurities (such as molecules) represent three-dimensional (3D) rotors, the angular momentum transferred is intrinsically 3D as well, as opposed to a merely planar rotation which is inherent to vortices. Herein we show that the angulon theory can explain the anomalous broadening of the spectroscopic lines observed for CH 3 and NH 3 molecules in superfluid helium nanodroplets, thereby providing a fingerprint of the emerging angulon instabilities in experiment.},
author = {Cherepanov, Igor and Lemeshko, Mikhail},
journal = {Physical Review Materials},
number = {3},
publisher = {American Physical Society},
title = {{Fingerprints of angulon instabilities in the spectra of matrix-isolated molecules}},
doi = {10.1103/PhysRevMaterials.1.035602},
volume = {1},
year = {2017},
}
@article{995,
abstract = {Recently it was shown that an impurity exchanging orbital angular momentum with a surrounding bath can be described in terms of the angulon quasiparticle [Phys. Rev. Lett. 118, 095301 (2017)]. The angulon consists of a quantum rotor dressed by a many-particle field of boson excitations, and can be formed out of, for example, a molecule or a nonspherical atom in superfluid helium, or out of an electron coupled to lattice phonons or a Bose condensate. Here we develop an approach to the angulon based on the path-integral formalism, which sets the ground for a systematic, perturbative treatment of the angulon problem. The resulting perturbation series can be interpreted in terms of Feynman diagrams, from which, in turn, one can derive a set of diagrammatic rules. These rules extend the machinery of the graphical theory of angular momentum - well known from theoretical atomic spectroscopy - to the case where an environment with an infinite number of degrees of freedom is present. In particular, we show that each diagram can be interpreted as a 'skeleton', which enforces angular momentum conservation, dressed by an additional many-body contribution. This connection between the angulon theory and the graphical theory of angular momentum is particularly important as it allows to systematically and substantially simplify the analytical representation of each diagram. In order to exemplify the technique, we calculate the 1- and 2-loop contributions to the angulon self-energy, the spectral function, and the quasiparticle weight. The diagrammatic theory we develop paves the way to investigate next-to-leading order quantities in a more compact way compared to the variational approaches.},
author = {Bighin, Giacomo and Lemeshko, Mikhail},
issn = {24699950},
journal = {Physical Review B - Condensed Matter and Materials Physics},
number = {8},
publisher = {American Physical Society},
title = {{Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment}},
doi = {10.1103/PhysRevB.96.085410},
volume = {96},
year = {2017},
}
@article{996,
abstract = {Iodine (I 2 ) molecules embedded in He nanodroplets are aligned by a 160 ps long laser pulse. The highest degree of alignment, occurring at the peak of the pulse and quantified by ⟨cos 2 θ 2D ⟩ , is measured as a function of the laser intensity. The results are well described by ⟨cos 2 θ 2D ⟩ calculated for a gas of isolated molecules each with an effective rotational constant of 0.6 times the gas-phase value, and at a temperature of 0.4 K. Theoretical analysis using the angulon quasiparticle to describe rotating molecules in superfluid helium rationalizes why the alignment mechanism is similar to that of isolated molecules with an effective rotational constant. A major advantage of molecules in He droplets is that their 0.4 K temperature leads to stronger alignment than what can generally be achieved for gas phase molecules -- here demonstrated by a direct comparison of the droplet results to measurements on a ∼ 1 K supersonic beam of isolated molecules. This point is further illustrated for more complex system by measurements on 1,4-diiodobenzene and 1,4-dibromobenzene. For all three molecular species studied the highest values of ⟨cos 2 θ 2D ⟩ achieved in He droplets exceed 0.96. },
author = {Shepperson, Benjamin and Chatterley, Adam and Søndergaard, Anders and Christiansen, Lars and Lemeshko, Mikhail and Stapelfeldt, Henrik},
issn = {00219606},
journal = {The Journal of Chemical Physics},
number = {1},
publisher = {AIP},
title = {{Strongly aligned molecules inside helium droplets in the near-adiabatic regime}},
doi = {10.1063/1.4983703},
volume = {147},
year = {2017},
}
@article{997,
abstract = {Recently it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles (Phys. Rev. Lett. 118, 095301 (2017)). Here we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a 2-sphere interacting with a gauge field of a non-abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.},
author = {Yakaboylu, Enderalp and Deuchert, Andreas and Lemeshko, Mikhail},
issn = {00319007},
journal = {APS Physics, Physical Review Letters},
number = {23},
publisher = {American Physiological Society},
title = {{Emergence of non-abelian magnetic monopoles in a quantum impurity problem}},
doi = {10.1103/PhysRevLett.119.235301},
volume = {119},
year = {2017},
}
@inproceedings{313,
abstract = {Tunneling of a particle through a potential barrier remains one of the most remarkable quantum phenomena. Owing to advances in laser technology, electric fields comparable to those electrons experience in atoms are readily generated and open opportunities to dynamically investigate the process of electron tunneling through the potential barrier formed by the superposition of both laser and atomic fields. Attosecond-time and angstrom-space resolution of the strong laser-field technique allow to address fundamental questions related to tunneling, which are still open and debated: Which time is spent under the barrier and what momentum is picked up by the particle in the meantime? In this combined experimental and theoretical study we demonstrate that for strong-field ionization the leading quantum mechanical Wigner treatment for the time resolved description of tunneling is valid. We achieve a high sensitivity on the tunneling barrier and unambiguously isolate its effects by performing a differential study of two systems with almost identical tunneling geometry. Moreover, working with a low frequency laser, we essentially limit the non-adiabaticity of the process as a major source of uncertainty. The agreement between experiment and theory implies two substantial corrections with respect to the widely employed quasiclassical treatment: In addition to a non-vanishing longitudinal momentum along the laser field-direction we provide clear evidence for a non-zero tunneling time delay. This addresses also the fundamental question how the transition occurs from the tunnel barrier to free space classical evolution of the ejected electron.},
author = {Camus, Nicolas and Yakaboylu, Enderalp and Fechner, Lutz and Klaiber, Michael and Laux, Martin and Mi, Yonghao and Hatsagortsyan, Karen and Pfeifer, Thomas and Keitel, Cristoph and Moshammer, Robert},
issn = {17426588},
location = {Kazan, Russian Federation},
number = {1},
publisher = {American Physical Society},
title = {{Experimental evidence for Wigner's tunneling time}},
doi = {10.1088/1742-6596/999/1/012004},
volume = {999},
year = {2017},
}
@article{1286,
abstract = {We use recently developed angulon theory [R. Schmidt and M. Lemeshko, Phys. Rev. Lett. 114, 203001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.203001] to study the rotational spectrum of a cyanide molecular anion immersed into Bose-Einstein condensates of rubidium and strontium. Based on ab initio potential energy surfaces, we provide a detailed study of the rotational Lamb shift and many-body-induced fine structure which arise due to dressing of molecular rotation by a field of phonon excitations. We demonstrate that the magnitude of these effects is large enough in order to be observed in modern experiments on cold molecular ions. Furthermore, we introduce a novel method to construct pseudopotentials starting from the ab initio potential energy surfaces, which provides a means to obtain effective coupling constants for low-energy polaron models.},
author = {Midya, Bikashkali and Tomza, Michał and Schmidt, Richard and Lemeshko, Mikhail},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = {4},
publisher = {American Physical Society},
title = {{Rotation of cold molecular ions inside a Bose-Einstein condensate}},
doi = {10.1103/PhysRevA.94.041601},
volume = {94},
year = {2016},
}
@article{1287,
abstract = {A planar waveguide with an impedance boundary, composed of nonperfect metallic plates, and with passive or active dielectric filling, is considered. We show the possibility of selective mode guiding and amplification when a homogeneous pump is added to the dielectric and analyze differences in TE and TM mode propagation. Such a non-conservative system is also shown to feature exceptional points for specific and experimentally tunable parameters, which are described for a particular case of transparent dielectric.},
author = {Midya, Bikashkali and Konotop, Vladimir},
journal = {Optics Letters},
number = {20},
pages = {4621 -- 4624},
publisher = {OSA},
title = {{Modes and exceptional points in waveguides with impedance boundary conditions}},
doi = {10.1364/OL.41.004621},
volume = {41},
year = {2016},
}
@article{1343,
abstract = {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 (AF) and superconducting quantum phases directly. In this work, we demonstrate
that using the machinery of dissipative quantum state engineering, one can observe the emergence of
the AF order in the Fermi-Hubbard model with fermions in optical lattices. The core of the approach
is to add incoherent laser scattering in such a way that the AF state emerges as the dark state of
the driven-dissipative dynamics. The proposed controlled dissipation channels described in this work
are straightforward to add to already existing experimental setups.},
author = {Kaczmarczyk, Jan and Weimer, Hendrik and Lemeshko, Mikhail},
journal = {New Journal of Physics},
number = {9},
publisher = {IOP Publishing Ltd.},
title = {{Dissipative preparation of antiferromagnetic order in the Fermi-Hubbard model}},
doi = {10.1088/1367-2630/18/9/093042},
volume = {18},
year = {2016},
}
@article{1347,
abstract = {During the past 70 years, the quantum theory of angular momentum has been successfully applied to describing the properties of nuclei, atoms, and molecules, and their interactions with each other as well as with external fields. Because of the properties of quantum rotations, the angular-momentum algebra can be of tremendous complexity even for a few interacting particles, such as valence electrons of an atom, not to mention larger many-particle systems. In this work, we study an example of the latter: A rotating quantum impurity coupled to a many-body bosonic bath. In the regime of strong impurity-bath couplings, the problem involves the addition of an infinite number of angular momenta, which renders it intractable using currently available techniques. Here, we introduce a novel canonical transformation that allows us to eliminate the complex angular-momentum algebra from such a class of many-body problems. In addition, the transformation exposes the problem's constants of motion, and renders it solvable exactly in the limit of a slowly rotating impurity. We exemplify the technique by showing that there exists a critical rotational speed at which the impurity suddenly acquires one quantum of angular momentum from the many-particle bath. Such an instability is accompanied by the deformation of the phonon density in the frame rotating along with the impurity.},
author = {Schmidt, Richard and Lemeshko, Mikhail},
journal = {Physical Review X},
number = {1},
publisher = {American Physical Society},
title = {{Deformation of a quantum many-particle system by a rotating impurity}},
doi = {10.1103/PhysRevX.6.011012},
volume = {6},
year = {2016},
}
@article{1352,
abstract = {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 C4 symmetry, the coexisting phase inherently contains admixture of the s-wave pairing components. As a result, the superconducting gap exhibits nonstandard features including changed nodal directions. Our results also show that in the optimally doped regime the pure superconducting phase is typically unstable towards developing nematicity (breaking of the C4 symmetry). This has implications for the cuprate high-Tc 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.},
author = {Kaczmarczyk, Jan and Schickling, Tobias and Bünemann, Jörg},
journal = {Physical Review B - Condensed Matter and Materials Physics},
number = {8},
publisher = {American Physical Society},
title = {{Coexistence of nematic order and superconductivity in the Hubbard model}},
doi = {10.1103/PhysRevB.94.085152},
volume = {94},
year = {2016},
}