Magnetic susceptibility and simulated neutron signal in the two-dimensional Hubbard model

LeBlanc, James; Li, Shaozhi; Chen, Xi; Levy, Ryan; Antipov, Andrey E.; Millis, Andrew J.; Gull, Emanuel

doi:10.1103/physrevb.100.075123

Cited by 28 publications

(26 citation statements)

References 73 publications

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“…We next examine the charge properties. Figure 5 [49,57]. We also note that the maximum energy of the charge excitation does not change much as U increases before the Mott gap is opened, while it increases rapidly as the gap is opened.…”

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confidence: 71%

“…DF is accurate at high temperature [46] but uncontrolled in practice in the sense that adding systematic corrections, while possible in theory [47,48], is not feasible for the parameters studied here. A detailed assessment of the approximation errors of the susceptibility and the single-particle properties on the square lattice [49] showed that while dopingand interaction dependent scaling effects were present, the overall momentum dependence was accurate.…”

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confidence: 99%

“…For U = 8.2t and U = 12t, the spin excitation energy at the Γ point is nonzero, violating the total spin conservation. This is an artifact of the DF approximation [49,57]. Figure 2(a) shows the spin excitation energy ω m (q) at the K point as a function of U .…”

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confidence: 99%

“…Two sources contribute to this discrepancy. First, an energy scaling factor inherent to the DF approximation [49] may change the overall energy scale of the DF results, leading to a larger fit value. More importantly, the spin spectra of the Hubbard and Heisenberg models, when compared at zero temperature on a 3 × 3 lattice using ED, show agreement only for U > 20t and differ markedly at U = 12t [55].…”

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confidence: 99%

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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: 71%

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confidence: 99%

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confidence: 99%

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

Gull

2020

Phys. Rev. Research

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“…We note that recent theory work using dual fermion methods, cluster dynamical mean field theory, and quantum Monte Carlo have also see the gapped Y-shaped magnon spectrum (LeBlanc et al 2019). With the agreement between the analytical approaches of section 2.4 and cluster dynamical mean field theory for transport properties, it is worth examining the magnetic properties of the analytical models in future work.…”

Section: Antiferromagnetic Correlations In the Pseudogap Phasementioning

confidence: 79%

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering

et al. 2019

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Over the past two decades, advances in computational algorithms have revealed a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. On the one hand, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. On the other hand, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reflects a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues. * If one did not refermionise the spin sector, the non-linear interaction term within the bosonic theory reads −4g a =b cos Θ a cos Θ b , which is suggestive of a high symmetry. * This is easy to see in the purely bosonic language, as the interaction term −4g cos Θ sf cos Θ f at strong coupling pins the bosons to (Θ sf , Θ f ) = (2mπ, 2nπ or (Θ sf , Θ f ) = [2m + 1]π, [2n + 1]π with n, m ∈ Z. * Interestingly, recent gauge theory calculations that are proposed to apply to the pseudogap phase of the cuprates find such a deformation of the Fermi surface. See figure 7(a) of (Sachdev et al. 2018).

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The Sign Problem in Density Matrix Quantum Monte Carlo

Petras

Benschoten

Ramadugu

et al. 2021

J. Chem. Theory Comput.

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Density matrix quantum Monte Carlo (DMQMC) is a recently developed method for stochastically sampling the N-particle thermal density matrix to obtain exact-on-average energies for model and ab initio systems. We report a systematic numerical study of the sign problem in DMQMC based on simulations of atomic and molecular systems. In DMQMC, the density matrix is written in an outer product basis of Slater determinants. In principle, this means that DMQMC needs to sample a space that scales in the system size, N, as O[(exp(N))2]. In practice, removing the sign problem requires a total walker population that exceeds a system-dependent critical walker population (N c), imposing limitations on both storage and compute time. We establish that N c for DMQMC is the square of N c for FCIQMC. By contrast, the minimum N c in the interaction picture modification of DMQMC (IP-DMQMC) is only linearly related to the N c for FCIQMC. We find that this difference originates from the difference in propagation of IP-DMQMC versus canonical DMQMC: the former is asymmetric, whereas the latter is symmetric. When an asymmetric mode of propagation is used in DMQMC, there is a much greater stochastic error and is thus prohibitively expensive for DMQMC without the interaction picture adaptation. Finally, we find that the equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger systems with large basis sets. This suggests that IP-DMQMC offers a way to ameliorate the cost of moving between a Slater determinant space and an outer product basis.

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Magnetic susceptibility and simulated neutron signal in the two-dimensional Hubbard model

Cited by 28 publications

References 73 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

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering

The Sign Problem in Density Matrix Quantum Monte Carlo

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