The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature

Abstract

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a novel connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at unprecedentedly low temperatures T ≥ 0.067 for interactions up to U ≤ 8, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.

Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model

“…This indicates that the charge order at δ = 1/5 is extremely short-ranged. We conclude that the spin and charge correlations remain short-ranged at δ = 1/5, U = 6 at all temperatures, consistent with the phase diagram from ground-state AFQMC calculations [37], an inhomogeneous DMFT study [32] and the recent higher-T CDET diagrammatic Monte Carlo results [48].…”

“…At zero temperature, intertwined competing orders are only separated by tiny energy scales, of the order of 10 −2 t or less, which can now be resolved by advanced wave-function based methods [27]. At finite temperature, progress has been achieved using a variety of methods such as cluster extensions of DMFT [39,47,[68][69][70][71], diagrammatic Monte Carlo [48,72], DQMC [44,45], as well as METTS [46]. Nonetheless, limitations in the range of temperature that can be accessed and/or in the system sizes that can be studied have prevented a full 'handshake' between ground-state methods and finite-T methods, thus hampering a comprehensive physical picture of the crossovers or transitions in the spin and charge correlations down to T = 0.…”

“…Recently there has been a flurry of activities to study the finite-temperature properties of stripes as well as spin and charge correlations in the doped Hubbard model, including calculations using determinant Quantum Monte Carlo (DQMC) [44,45], minimally entangled typical thermal state (METTS) [46], the dynamical cluster approximation (DCA) [47], and connected determinant diagrammatic Monte Carlo (CDet) [48]. This has created an exciting synergy, from which a consistent picture is emerging on the temperature evolution of the antiferromagnetic spin correlations and charge inhomogeneities in the doped Hubbard model.…”

Magnetic properties and pseudogap formation in infinite-layer nickelates: insights from the single-band Hubbard model

“…The exact location of the change from a weak-coupling to a strong-coupling pseudogap regime is a matter of current debate. Three indicators for this change can be mentioned: (i) a sudden increase in electronic correlations leading to a change in Fermi surface topology [60], (ii) this strong correlation regime hosts relatively shortranged correlations with the occurrence of (partial) localization [40,63] and (iii) the electron-boson coupling vertex develops a significant imaginary part [75,76]. Our investigations of (i) and (ii) in this manuscript by means of the DΓA, hence, allow us to characterize the found pseudogap as driven by strong coupling (Mott) physics.…”

“…The maximum value of χ m (q, iΩ n = 0) is assumed at q = Q = (π, π) at T * . We note in passing that also incommensurate Néel order with Q = (π, π) may occur in different parameter regimes of the model [45,57,62,63]. For obtaining the correlation length ξ we perform an Ornstein-Zernike fit with [34,44,64,65]…”