Browsing by Author "Vučičević, Jakša"

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    Analytical solution for time integrals in diagrammatic expansions: Application to real-frequency diagrammatic Monte Carlo
    Vučičević, Jakša; Stipsić, Pavle; Ferrero, Michel
    Recent years have seen a revived interest in the diagrammatic Monte Carlo (DiagMC) methods for interacting fermions on a lattice. A promising recent development allows one to now circumvent the analytical continuation of dynamic observables in DiagMC calculations within the Matsubara formalism. This is made possible by symbolic algebra algorithms, which can be used to analytically solve the internal Matsubara frequency summations of Feynman diagrams. In this paper, we take a different approach and show that it yields improved results. We present a closed-form analytical solution of imaginary-time integrals that appear in the time-domain formulation of Feynman diagrams. We implement and test a DiagMC algorithm based on this analytical solution and show that it has numerous significant advantages. Most importantly, the algorithm is general enough for any kind of single-time correlation function series, involving any single-particle vertex insertions. Therefore, it readily allows for the use of action-shifted schemes, aimed at improving the convergence properties of the series. By performing a frequency-resolved action-shift tuning, we are able to further improve the method and converge the self-energy in a nontrivial regime, with only 3-4 perturbation orders. Finally, we identify time integrals of the same general form in many commonly used Monte Carlo algorithms and therefore expect a broader usage of our analytical solution.
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    Charge transport in the Hubbard model at high temperatures: Triangular versus square lattice
    Vranić, Ana; Vučičević, Jakša; Kokalj, Jure; Skolimowski, Jan; Žitko, Rok; Mravlje, Jernej; Tanasković, Darko
    High-temperature bad-metal transport has been recently studied both theoretically and in experiments as one of the key signatures of strong electronic correlations. Here we use the dynamical mean field theory and its cluster extensions, as well as the finite-temperature Lanczos method to explore the influence of lattice frustration on the thermodynamic and transport properties of the Hubbard model at high temperatures. We consider the triangular and the square lattices at half-filling and at 15% hole doping. We find that for T greater than or similar to 1.5t the self-energy becomes practically local, while the finite-size effects become small at lattice size 4x4 for both lattice types and doping levels. The vertex corrections to optical conductivity, which are significant on the square lattice even at high temperatures, contribute less on the triangular lattice. We find approximately linear temperature dependence of dc resistivity in doped Mott insulator for both types of lattices.
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    Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections
    Vučičević, Jakša; Kokalj, Jure; Žitko, Rok; Wentzell, Nils; Tanasković, Darko; Mravlje, Jernej
    Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results, and the question of the exact solution for the conductivity in the Hubbard model remained open. In this Letter, we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity and identify the best available result to be compared to experiment. We find that, at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4×4, and the corresponding Lanczos diagonalization result is, therefore, close to the exact result in the thermodynamic limit.
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    Electrical conductivity in the Hubbard model: Orbital effects of magnetic field
    Vučičević, Jakša; Žitko, Rok
    Calculation of conductivity in the Hubbard model is a challenging task. Recent years have seen much progress in this respect and numerically exact solutions are now possible in certain regimes. In this paper we discuss the calculation of conductivity for the square-lattice Hubbard model in the presence of a perpendicular magnetic field, focusing on orbital effects. We present the relevant formalism in all detail and in full generality, and then discuss the simplifications that arise at the level of the dynamical mean field theory (DMFT). We prove that the Kubo bubble preserves gauge and translational invariance, and that in the DMFT the vertex corrections cancel regardless of the magnetic field. We present the DMFT results for the spectral function and both the longitudinal and Hall conductivities in several regimes of parameters. We analyze thoroughly the quantum oscillations of the longitudinal conductivity and identify a high-frequency oscillation component, arising as a combined effect of scattering and temperature, in line with recent experimental observations in moiré systems.
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    Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice
    Janković, Veljko; Vučičević, Jakša
    Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within the grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have an excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has a significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time-dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states.
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    Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters
    Ayral, Thomas; Vučičević, Jakša; Parcollet, Olivier
    We present an embedded-cluster method, based on the triply irreducible local expansion formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed from a self-consistently determined cluster impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW+extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.
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    Mott domain walls: A (strongly) non-Fermi liquid state of matter
    Tsung-Han, Lee; Vučičević, Jakša; Tanasković, Darko; Miranda, Eduardo; Dobrosavljević, Vladimir
    Most Mott systems display a low-temperature phase coexistence region around the metal-insulator transition. The domain walls separating the respective phases have very recently been observed displaying unusual properties both in simulations and in experiments. First, they often cover a significant volume fraction, thus cannot be neglected. Second, they resemble neither a typical metal nor a standard insulator, displaying unfamiliar temperature dependence of (local) transport properties. Here we take a closer look at such domain wall matter by examining an appropriate unstable solution of the Hubbard model. We show that transport in this regime is dominated by the emergence of “resilient quasiparticles” displaying strong non-Fermi liquid features, reflecting the quantum-critical fluctuations in the vicinity of the Mott point.
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    Mott domain walls: A (strongly) non-Fermi liquid state of matter
    Lee, Tsung-Han; Vučičević, Jakša; Tanasković, Darko; Miranda, E.; Dobrosavljević, Vladimir
    Most Mott systems display a low-temperature phase coexistence region around the metal-insulator transition. The domain walls separating the respective phases have very recently been observed displaying unusual properties both in simulations and in experiments. First, they often cover a significant volume fraction, thus cannot be neglected. Second, they resemble neither a typical metal nor a standard insulator, displaying unfamiliar temperature dependence of (local) transport properties. Here we take a closer look at such domain wall matter by examining an appropriate unstable solution of the Hubbard model. We show that transport in this regime is dominated by the emergence of "resilient quasiparticles"displaying strong non-Fermi liquid features, reflecting the quantum-critical fluctuations in the vicinity of the Mott point.
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    Paired states at 5/2: Particle-hole Pfaffian and particle-hole symmetry breaking
    Antonić, Luka; Vučičević, Jakša; Milovanović, Milica
    We study Cooper pairing in the Dirac composite fermion (CF) system. The presence of the mass term in the Dirac CF description (which may simulate Landau level mixing), i.e., breaking of particle-hole (PH) symmetry in this system, is a necessary condition for the existence of a PH Pfaffian-like topological state. In the scope of the random-phase approximation (RPA) and hydrodynamic approach, we find some signatures of pairing at finite frequencies. Motivated by this insight, we extend our analysis to the case of a different but still Dirac quasiparticle (CF) representation, appropriate in the presence of a mass term, and discuss the likelihood of PH Pfaffian and Pfaffian pairings in general. On the basis of gauge field effects, we find for a small Dirac mass, an anti-Pfaffian or Pfaffian instability depending on the sign of mass, while for large mass (Landau level mixing), irrespective of its sign, we find a PH Pfaffian-like instability.
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    Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods
    Vučičević, Jakša; Wentzell, Nils; Ferrero, Michel; Parcollet, Olivier
    The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible vertex function Γ have revealed an inherent limitation of this approach. Here we demonstrate how these undesirable properties of the LWF can lead to a failure of computational methods based on an approximation of the LWF. We apply the nested cluster scheme (NCS) to the Hubbard model and observe the existence of an additional stationary point of the self-consistent equations, associated with an unphysical branch of the LWF. In the strongly correlated regime, starting with the first divergence of Γ, this unphysical stationary point becomes attractive in the standard iterative technique used to solve DMFT. This leads to an incorrect solution, even in the large cluster size limit, for which we discuss diagnostics.
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    Real-frequency diagrammatic Monte Carlo at finite temperature
    Vučičević, Jakša; Ferrero, Michel
    Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara calculation ultimately requires the ill-defined analytical continuation from the imaginary-to the real-frequency domain. It was recently proposed [A. Taheridehkordi, Phys. Rev. B 99, 035120 (2019)2469-995010.1103/PhysRevB.99.035120] that the internal Matsubara summations of any interaction-expansion diagram can be performed analytically by using symbolic algebra algorithms. The result of the summations is then an analytical function of the complex frequency rather than Matsubara frequency. Here we apply this principle and develop a diagrammatic Monte Carlo technique which yields results directly on the real-frequency axis. We present results for the self-energy ς(ω) of the doped 32×32 cyclic square-lattice Hubbard model in a nontrivial parameter regime, where signatures of the pseudogap appear close to the antinode. We discuss the behavior of the perturbation series on the real-frequency axis and in particular show that one must be very careful when using the maximum entropy method on truncated perturbation series. Our approach holds great promise for future application in cases when analytical continuation is difficult and moderate-order perturbation theory may be sufficient to converge the result.
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    Universal Magnetic Oscillations of dc Conductivity in the Incoherent Regime of Correlated Systems
    Vučičević, Jakša; Žitko, Rok
    Using the dynamical mean field theory we investigate the magnetic field dependence of dc conductivity in the Hubbard model on the square lattice, fully taking into account the orbital effects of the field introduced via the Peierls substitution. In addition to the conventional Shubnikov-de Haas quantum oscillations, associated with the coherent cyclotron motion of quasiparticles and the presence of a welldefined Fermi surface, we find an additional oscillatory component with a higher frequency that corresponds to the total area of the Brillouin zone. These paradigm-breaking oscillations appear at elevated temperature. This finding is in excellent qualitative agreement with the recent experiments on graphene superlattices. We elucidate the key roles of the off-diagonal elements of the current vertex and the incoherence of electronic states, and explain the trends with respect to temperature and doping.