arXiv subjects
Publications and source records attributed to J. P. F. LeBlanc.
We present libami, a lightweight implementation of algorithmic Matsubara integration (AMI) written in C++. AMI is a tool for analytically resolving the sequence of nested Matsubara integrals that arise in virtually all Feynman perturbative expansions.
Motivated by the recent experimental realization of twisted trilayer graphene and the observed superconductivity that is associated with its flat bands at specific angles, we study trilayer graphene under the influence of different forms of light in the non-interacting limit. Specifically, we study four different types of stacking configurations with a single twisted layer. In all four cases, we study the impact of circularly polarized light and longitudinal light coming from a waveguide. We derive effective time-independent Floquet Hamiltonians and review light-induced changes to the band structure. For circularly polarized light, we find band flattening effects as well as band gap openings. We emphasize that there is a rich band topology, which we summarize in Chern number maps that are different for all four studied lattice configurations. The case of a so-called ABC stacking with top layer twist is especially rich and shows a different phase diagram depending on the handedness of the circularly polarized light. Consequently, we propose an experiment where this difference in typologies could be captured via optical conductivity measurements. In contrast for the case of longitudinal light that is coming from a waveguide, we find that the band structure is very closely related to the equilibrium one but the magic angles can be tuned in-situ by varying the intensity of the incident beam of light.
Room-temperature optical constants of crystalline Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ were determined using data extracted from Brillouin light scattering spectra. Optical extinction coefficient-to-refractive index ratios at a wavelength of 532 nm were obtained from bulk phonon peak linewidth and frequency shift measurements and range from $0.19 \leq 2κ/n \leq 0.29$ for directions close to the crystallographic $c$-axis. These ratios, and optical extinction coefficients, absorption coefficients, and imaginary parts of the dielectric function determined from these ratios and known refractive index, are in general agreement with values found in optical reflectance studies, but are 5-7 times larger than those extracted from optical interference measurements.
We systematically generate the perturbative expansion for the two-particle spin susceptibility in the Feynman diagrammatic formalism and apply this expansion to a model system - the single-band Hubbard model on a square lattice. We make use of algorithmic Matsubara integration (AMI) [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019)] to analytically evaluate Matsubara frequency summations, allowing us to symbolically impose analytic continuation to the real frequency axis. We minimize our computational expense by applying graph invariant transformations [Amir Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 101, 125109 (2020)]. We highlight extensions of the random-phase approximation and T-matrix methods that, due to AMI, become tractable. We present results for weak interaction strength where the direct perturbative expansion is convergent, and verify our results on the Matsubara axis by comparison to other numerical methods. By examining the spin susceptibility as a function of real-frequency via an order-by-order expansion we can identify precisely what role higher order corrections play on spin susceptibility and demonstrate the utility and limitations of our approach.
The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.
We present a general method to optimize the evaluation of Feynman diagrammatic expansions, which requires the automated symbolic assignment of momentum/energy conserving variables to each diagram. With this symbolic representation, we utilize the pole structure of each diagram to automatically sort the Feynman diagrams into groups that are likely to contain nearly equal or nearly cancelling diagrams, and we show that for some systems this cancellation is exact. This allows for a potentially massive cancellation during the numerical integration of internal momenta variables, leading to an optimal suppression of the `sign problem' and hence reducing the computational cost. Although we define these groups using a frequency space representation, the equality or cancellation of diagrams within the group remains valid in other representations such as imaginary time used in standard diagrammatic Monte Carlo. As an application of the approach we apply this method, combined with algorithmic Matsubara integration (AMI) [Phys. Rev. B 99, 035120 (2019)] and Monte Carlo methods, to the Hubbard model self-energy expansion on a 2D square lattice up to sixth order which we evaluate and compare with existing benchmarks.
We study the finite temperature Fermi-liquid to non-Fermi-liquid crossover in the 2D Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behaviour that is itself characterized by a long, but finite, correlation length scale. We perform fluctuation diagnostics to decompose the single-particle self energy into scattering $q$-vector and bosonic frequency contributions. Within this framework we find that the key contributions to the single-particle self energy that give non-Fermi-liquid character, even at weak coupling, are caused by relatively sharp $q=(π,π)$ spin fluctuations, while the decomposition in the bosonic frequency channel shows a complicated dependence on the relative strengths of zero, positive and negative frequency contributions. Finally, variation in density suggests that the tendency towards non-Fermi-liquid behavior is not substantially different for electron or hole doped systems.
We compute dynamic spin susceptibilities in the two-dimensional Hubbard model using the method of Dual Fermions and provide comparison to lattice Monte Carlo and cluster dynamical mean field theory. We examine the energy dispersion identified by peaks in ${\rm Im}χ(ω,q)$ which define spin modes and compare the exchange scale and magnon dispersion to neutron experiments on the parent La$_2$CuO$_4$ cuprate. We present the evolution of the spin excitations as a function of Hubbard interaction strengths and doping and explore the particle-hole asymmetry of the spin excitations. We also study the correlation lengths and the spin excitation dispersion peak structure and find a `Y'-shaped dispersion similar to neutron results on doped HgBa$_2$CuO$_{4+δ}$.
We present an algorithm to evaluate Matsubara sums for Feynman diagrams comprised of bare Green's functions with single-band dispersions with local U Hubbard interaction vertices. The algorithm provides an exact construction of the analytic result for the frequency integrals of a diagram that can then be evaluated for all parameters $U$, temperature $T$, chemical potential $μ$, external frequencies and internal/external momenta. This method allows for symbolic analytic continuation of results to the real frequency axis, avoiding any ill-posed numerical procedure. When combined with diagrammatic Monte-Carlo, this method can be used to simultaneously evaluate diagrams throughout the entire $T-U-μ$ phase space of Hubbard-like models at minimal computational expense.
The open source ALPS (Algorithms and Libraries for Physics Simulations) project provides a collection of physics libraries and applications, with a focus on simulations of lattice models and strongly correlated systems. The libraries provide a convenient set of well-documented and reusable components for developing condensed matter physics simulation code, and the applications strive to make commonly used and proven computational algorithms available to a non-expert community. In this paper we present an updated and refactored version of the core ALPS libraries geared at the computational physics software development community, rewritten with focus on documentation, ease of installation, and software maintainability.
We study the temperature and doping evolution of the NMR Knight shift, spin relaxation rate, and spin echo decay time in the pseudogap regime of the two-dimensional Hubbard model for parameters believed to be relevant to cuprate superconductors using cluster dynamical mean field theory. We recover the suppression of the Knight shift seen in experiment upon entering the pseudogap regime and find agreement between single and two-particle measures of the pseudogap onset temperature. The simulated spin-echo decay time shows a linear in T behavior at high T which flattens off as T is lowered, and increases as doping is increased. The relaxation rate shows a marked increase as T is lowered but no indication of a pseudogap on the Cu site, and a clear downturn on the O site, consistent with experimental results on single layer materials but different from double layer materials. The consistency of the simulated susceptibilities with experiment, along with similar agreement on the single-particle level and the absence of long-range order and symmetry breaking suggests that the pseudogap is well described by strong short-range correlation effects and that long-range order and multi-orbital effects are not required.
We present $\texttt{Maxent}$, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to the real axis. The code works for imaginary time and Matsubara frequency data and implements the 'Legendre' representation of finite temperature Green's functions. It implements a variety of kernels, default models, and grids for continuing bosonic, fermionic, anomalous, and other data. Our implementation is licensed under GPLv2 and extensively documented. This paper shows the use of the programs in detail.
The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and - more generally - of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA.
Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the $d_{x^2-y^2}$ superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half-filling. We find a change in sign of the vertex contributions to $d_{xy}$ superconductivity from repulsive near half filling to attractive at large doping. $p$-wave superconductivity is not found at the parameters we study, and $s$-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase $T_c$.
We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two-dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why $d-$wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength.
We propose a hybridization phenomenology to describe the pseudogap state of the underdoped cuprates. We show how a momentum independent pseudogap opens asymmetrically from the Fermi-surface but symmetric to the zeroes of the hybridized bonding dispersion, which results in false d-wave characteristics of the pseudogap at the Fermi level. By comparing against a d-wave form factor we illustrate the difficulty in identifying a momentum independent order in momentum averaged quantities such as the electronic Raman response. We identify a suppression in the single-particle density of states which produces a hump feature which should be observable experimentally in tunnelling $dI/dV$ spectra and distinguishes the s-wave and d-wave ordering scenarios.
Hexagonal warping provides an anisotropy to the dispersion curves of the helical Dirac fermions that exist at the surface of a topological insulator. A sub-dominant quadratic in momentum term leads to an asymmetry between conduction and valence band. A gap can also be opened through magnetic doping. We show how these various modifications to the Dirac spectrum change the polarization function of the surface states and employ our results to discuss their effect on the plasmons. In the long wavelength limit, the plasmon dispersion retains its square root dependence on its momentum, $\boldsymbol{q}$, but its slope is modified and it can acquire a weak dependence on the direction of $\boldsymbol{q}$. Further, we find the existence of several plasmon branches, one which is damped for all values of $\boldsymbol{q}$, and extract the plasmon scattering rate for a representative case.