Updated core libraries of the ALPS project

Gaenko, Alexander; Antipov, Andrey E.; Carcassi, Gabriele; Chen, T.; Chen, Xiuhong; Dong, Qian; Gamper, Lukas; Gukelberger, Jan; Igarashi, Ryo; Iskakov, Sergei; Könz, Mario S.; LeBlanc, James; Levy, Ryan; N., P.; Paki, Joseph; Shinaoka, Hiroshi; Todo, Synge; Troyer, Matthias; Gull, Emanuel

doi:10.1016/j.cpc.2016.12.009

Cited by 101 publications

(76 citation statements)

References 17 publications

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“…Both the single-particle Green's function and two-particle susceptibilities are defined on that grid. To examine the spectral properties, we use the ALPS implementation [50,51] of the maximum-entropy method [52] to perform the analytic continuation of Matsubara data to the real frequency space.…”

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confidence: 99%

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Gull

2020

Phys. Rev. Research

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We study magnetic and charge susceptibilities in the half-filled two-dimensional triangular Hubbard model within the dual fermion approximation in the metallic, Mott insulating, and crossover regions of parameter space. In the insulating state, we find strong spin fluctuations at the K point at low energy corresponding to the 120 • antiferromagnetic order. These spin fluctuations persist into the metallic phase and move to higher energy. We also present data for simulated neutron spectroscopy and spin-lattice relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba8CoNb6O24 and to the relaxation times on κ-(ET)2Cu2(CN)3. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds., suggests that these compounds are close to a two-dimensional triangular structure and exhibit interesting electron correlation behavior including, potentially, a quantum spin liquid phase [7] in the ground state [8]. These compounds, as well as the low energy physics of the fully isotropic triangular material Ba 8 CoNb 6 O 24 [9], may be described by a half-filled single orbital Hubbard model on a triangular two-dimensional lattice, with an on-site Coulomb interaction strength comparable to or larger than the bandwidth [10].Because of the subtle competition of metallic, ordered, and spin liquid phases in the ground state, this model has been studied extensively with a wide range of numerical tools, including exact diagonalization (ED) [11][12][13], density matrix renormalization group theory (DMRG) [8], variational Monte Carlo (VMC) [14][15][16][17], variational cluster approximation [18][19][20], strong coupling expansions [21], path integral renormalization group techniques [22], and cluster dynamical mean field theory (DMFT) in the cellular [23][24][25][26][27] and dynamical cluster [28,29] variants. The focus in most of these studies has been on the precise location of the phase boundaries, ordering (or the absence thereof), and on the nature of these phases.Experimentally, much of our knowledge about correlated triangular systems is obtained from single-and two-particle scattering experiments such as photoemission [30], Raman spectroscopy [31], nuclear magnetic resonance (NMR) [2,32], or inelastic neutron scattering [9,33]. To understand these experimental results, it is necessary to calculate the corresponding response functions as a function of energy and momentum. For neutron spectroscopy and angular-resolved photoemission spectroscopy, in particular, both fine momentum and energy resolutions are desired. Such results are difficult to obtain, as computational methods formulated on finite lattices (such as ED, DMRG, and cluster DMFT) pro-

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confidence: 99%

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Gull

2020

Phys. Rev. Research

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“…To confirm the thermodynamic consistency of our implementation, we present the evaluation of thermodynamic properties for solid LiH in continuation 55 may give different results, we compare our values for band gaps (obtained using analytical continuation) to the ones available in the literature, where QP equations were used with the bare perturbation theory. Our GF2 implementation for periodic systems uses a compact Chebyshev polynomial 76 representation of Green's functions that converges exponentially (for alternative techniques see 77,78 ) and relies on the open source ALPS library 79 . We use periodic density-fitted integrals in Gaussian orbitals, evaluated using the open source pySCF package 80,81 .…”

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confidence: 99%

Effect of propagator renormalization on the band gap of insulating solids

et al. 2019

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We present momentum-resolved spectral functions and band gaps from bare and self-consistent second order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasi-particle formalism used on top of bare second order perturbation theory, no unphysical behaviour of the band gap is observed. Our implementation of a fully self-consistent, Φderivable and thermodynamically consistent finite temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean field theory or selfenergy embedding theories can be implemented.

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“…We would like to thank Lei Wang for enlightening discussions. Our simulations make use of the ν-SVM formulation [58], the LIBSVM library [59,60], and the ALPSCore library [61]. The source codes and raw data supporting the findings of this study have been made openly available [63].…”

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confidence: 99%

Probing hidden spin order with interpretable machine learning

2019

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The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-learning protocol that can identify general nematic order and their order parameter from seemingly featureless spin configurations, thus providing comprehensive insight on the presence or absence of hidden orders. We demonstrate the capabilities of our method by extracting the analytical form of nematic order parameter tensors up to rank 6. This may prove useful in the search for novel spin states and for ruling out spurious spin liquid candidates.The statistical learning of phases is nowadays an active field of research [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Despite the enormous recent progress, learning or classifying intricate phases in manybody systems remains a daunting task. Many recent algorithmic advances are tried and tested in only the simplest of models, and their applicability to more complex situations remains an open question. The ability to interpret results to gain physical insight has been identified as one of the key challenges in the application of machine learning techniques to the domain of physics. Still, recent approaches struggle and this is only exacerbated when going beyond those simple models. However, those situations can also be arenas for machine learning methods to demonstrate their features and prove their worth, in comparison to-or complementary to-traditional methods.One such arena may be found in frustrated spin and spin-orbital-coupled systems [18]. These systems have rich phase diagrams, supporting various spin nematic (multipolar ordered) [19][20][21][22][23][24][25][26][27][28] and spin liquid phases [29][30][31][32][33][34][35]. However, to distinguish these two types of phases is often tricky, since both of them are invisible to conventional magnetic measurements. Indeed, there have been steady reports of "hidden" multipolar orders from a magnetically disordering state [36][37][38][39][40][41][42][43][44][45][46][47][48]. Moreover, identifying the right characterization of a spin-nematic order can also be a nontrivial task. For instance, in the low temperature phase of the classical Heisenberg-Kagomé antiferromagnet, a hidden quadrupolar order was found first [36], followed by the realization of an additional octupolar order [37] and its optimal order parameter [39,40].The aforementioned multipolar orders are only the simplest ones admitted by the subgroup structure of O(3). There are indeed myriads of more complicated multipolar orders where even the abstract classification of their order parameters has only been accomplished two years ago [49][50][51]. Along with the diverse interactions and lattice geometries in frustrated systems, identifying or ruling out certain orders becomes a difficult task for traditional methods, as there is n...

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Updated core libraries of the ALPS project

Cited by 101 publications

References 17 publications

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Effect of propagator renormalization on the band gap of insulating solids

Probing hidden spin order with interpretable machine learning

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