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  • 1. Budich, Jan Carl
    et al.
    Carlström, Johan
    Stockholm University, Faculty of Science, Department of Physics.
    Kunst, Flore K.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Symmetry-protected nodal phases in non-Hermitian systems2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 4, article id 041406Article in journal (Refereed)
    Abstract [en]

    Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless phases such as Weyl semimetals, here we investigate how NH symmetries affect the occurrence of exceptional points (EPs), that generalize the notion of nodal points in the spectrum beyond the Hermitian realm. Remarkably, we find that the dimension of the manifold of EPs is generically increased by one as compared to the case without symmetry. This leads to nodal surfaces formed by EPs that are stable as long as a protecting symmetry is preserved, and that are connected by open Fermi volumes. We illustrate our findings with analytically solvable two-band lattice models in one and two spatial dimensions, and show how they are readily generalized to generic NH crystalline systems.

  • 2.
    Carlström, Johan
    Stockholm University, Faculty of Science, Department of Physics.
    Diagrammatic Monte Carlo procedure for the spin-charge transformed Hubbard model2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 7, article id 075119Article in journal (Refereed)
    Abstract [en]

    Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionization of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems. This scheme allows eliminating large expansion parameters, as well as large corrections to the density matrix that generally prevent diagrammatic methods from being efficient in this regime. As an example, I compute the filling factor for the Hubbard model at infinite on-site repulsion and compare the results to controllable data obtained from numerical linked-cluster expansion. I find excellent agreement between the two methods, as well as rapid convergence of the diagrammatic series. I also report results for the momentum distribution and kinetic energy of the electrons.

  • 3.
    Carlström, Johan
    Stockholm University, Faculty of Science, Department of Physics. University of Massachusetts, United States of America.
    Spin-charge transformation of lattice fermion models: duality approach for diagrammatic simulation of strongly correlated systems2017In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 29, no 38, article id 385602Article in journal (Refereed)
    Abstract [en]

    I derive a dual description of lattice fermions, specifically focusing on the t-J and Hubbard models, that allow diagrammatic techniques to be employed efficiently in the strongly correlated regime, as well as for systems with a restricted Hilbert space. These constructions are based on spin-charge transformation, where the lattice fermions of the original model are mapped onto spins and spin-less fermions. This mapping can then be combined with Popov-Fedotov fermionisation, where the spins are mapped onto lattice fermions with imaginary chemical potential. The resulting models do not contain any large expansion parameters, even for strongly correlated systems. Also, they exhibit dramatically smaller corrections to the density matrix from nonlinear terms in the Hamiltonian. The combination of these two properties means that they can be addressed with diagrammatic methods, including simulation techniques based on stochastic sampling of diagrammatic expansions.

  • 4.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholt, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Strongly interacting Weyl semimetals: Stability of the semimetallic phase and emergence of almost free fermions2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 98, no 24, article id 241102Article in journal (Refereed)
    Abstract [en]

    Using a combination of analytical arguments and state-of-the-art diagrammatic Monte Carlo simulations, we show that the corrections to the dispersion in interacting Weyl semimetals are determined by the ultraviolet cutoff and the inverse screening length. If both of these are finite, then the diagrammatic series is convergent even in the low-temperature limit, which implies that the semimetallic phase remains stable. Meanwhile, the absence of a UV cutoff or screening results in logarithmic divergences at zero temperature. These results highlight the crucial impact of Coulomb interactions and screening, mediated, e.g., through the presence of parasitic bands, which are ubiquitous effects in real-world materials. Also, despite sizable corrections from Coulomb forces, the contribution from the frequency-dependent part of the self-energy remains extremely small, thus giving rise to a system of effectively almost free fermions with a strongly renormalized dispersion.

  • 5.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Exceptional links and twisted Fermi ribbons in non-Hermitian systems2018In: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 98, no 4, article id 042114Article in journal (Refereed)
    Abstract [en]

    The generic nature of band touching points in three-dimensional band structures is at the heart of the rich phenomenology, topological stability, and novel Fermi arc surface states associated with Weyl semimetals. Here we report on the corresponding scenario emerging in systems effectively described by non-Hermitian Hamiltonians. Remarkably, three-dimensional non-Hermitian systems have generic band touching along one-dimensional closed contours, forming exceptional rings and links in reciprocal space. The associated Seifert surfaces support open Fermi ribbons where the real part of the energy gap vanishes, providing a novel class of higher-dimensional bulk generalizations of Fermi arcs which are characterized by an integer twist number. These results have possible applications to a plethora of physical settings, ranging from mechanical systems and optical metamaterials with loss and gain to heavy fermion materials with finite-lifetime quasiparticles. In particular, photonic crystals provide fertile ground for simulating the exuberant phenomenology of exceptional links and their concomitant Fermi ribbons.

  • 6.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Symmetry-enforced stability of interacting Weyl and Dirac semimetals2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 16, article id 161102Article in journal (Refereed)
    Abstract [en]

    The nodal and effectively relativistic dispersion featuring in a range of novel materials including two-dimensional graphene and three-dimensional Dirac and Weyl semimetals has attracted enormous interest during the past decade. Here, by studying the structure and symmetry of the diagrammatic expansion, we show that these nodal touching points are in fact perturbatively stable to all orders with respect to generic two-body interactions. For effective low-energy theories relevant for single and multilayer graphene, type-I and type-II Weyl and Dirac semimetals, as well as Weyl points with higher topological charge, this stability is shown to be a direct consequence of a spatial symmetry that anticommutes with the effective Hamiltonian while leaving the interaction invariant. A more refined argument is applied to the honeycomb lattice model of graphene showing that its Dirac points are also perturbatively stable to all orders. We also give examples of nodal Hamiltonians that acquire a gap from interactions as a consequence of symmetries different from those of Weyl and Dirac materials.

  • 7.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Stålhammar, Marcus
    Stockholm University, Faculty of Science, Department of Physics.
    Budich, Jan Carl
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Knotted non-Hermitian metals2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 16, article id 161115Article in journal (Refereed)
    Abstract [en]

    We report on the occurrence of knotted metallic band structures as stable topological phases in non-Hermitian (NH) systems. These knotted NH metals are characterized by open Fermi surfaces, known in mathematics as Seifert surfaces, that are bounded by knotted lines of exceptional points. Quite remarkably, and in contrast to the situation in Hermitian systems, no fine tuning or symmetries are required in order to stabilize these exotic phases of matter. By explicit construction, we derive microscopic tight-binding models hosting knotted NH metals with strictly short-ranged hopping, and investigate the stability of their topological properties against perturbations. Building up on recently developed experimental techniques for the realization of NH band structures, we discuss how the proposed models may be experimentally implemented in photonic systems.

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