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arXiv:1709.09655 · Physical review. B./Physical review. B

Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model

Lorenzo Fratino, M. Charlebois, P. Sémon, G. Sordi, A.–M. S. Tremblay

Published Dec 19, 2017• 25 citations
arXivHTMLPDF

Abstract

Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength $U$, hole doping $\ensuremath{\delta}$, and temperature $T$. The N\'eel phase boundary is nonmonotonic as a function of $U$ and $\ensuremath{\delta}$. Frustration induced by second-neighbor hopping reduces N\'eel order more effectively at small $U$. The doped AF is stabilized at large $U$ by kinetic energy and at small $U$ by potential energy. The transition between the AF insulator and the doped metallic AF is continuous. At large $U$, we find in-gap states similar to those observed in scanning tunneling microscopy. We predict that, contrary to the Hubbard bands, these states are only slightly spin polarized.

DOI
10.1103/physrevb.96.241109

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Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength UUU, hole doping \ensuremathδ\ensuremath{\delta}\ensuremathδ, and temperature TTT. The N'eel phase boundary is nonmonotonic as a function of UUU and \ensuremathδ\ensuremath{\delta}\ensuremathδ. Frustration induced by second-neighbor hopping reduces N'eel order more effectively at small UUU. The doped AF is stabilized at large UUU by kinetic energy and at small UUU by potential energy. The transition between the AF insulator and the doped metallic AF is continuous. At large UUU, we find in-gap states similar to those observed in scanning tunneling microscopy. We predict that, contrary to the Hubbard bands, these states are only slightly spin polarized.
Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and ddd-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The ddd-wave order parameter is found to scale like the superexchange coupling JJJ for on-site interaction UUU comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc∕Tcmax{T}_{c}∕{T}_{c}^{\mathit{max}}Tc​∕Tcmax​ phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of ddd-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, ddd-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
Experiments on layered materials call for a study of the influence of short-range spin correlations on the Mott transition. To this end, we solve the cellular dynamical mean-field equations for the Hubbard model on a plaquette with continuous-time quantum Monte Carlo calculations. The normal-state phase diagram as a function of temperature T, interaction strength U, and filling n reveals that upon increasing n towards the insulator, there is a surface of first-order transition between two metals at nonzero doping. For T above the critical end line there is a maximum in scattering rate.
We investigate the properties of the frustrated underdoped Hubbard model on the square lattice using two complementary approaches, i.e., the dynamical cluster extension of the dynamical mean-field theory and the variational Monte Carlo simulations of Gutzwiller-Jastrow wave functions with backflow corrections. We compare and discuss data for the energy and the double occupancies, as obtained from both approaches. At small dopings, we observe a rapid crossover from a weakly correlated metal at low interaction strength UUU to a non-Fermi-liquid correlated state with strong local spin correlations. Furthermore, we investigate the stability of the correlated state against phase separation. We observe phase separation only for large values of UUU or very large frustration. No phase separation is present for the parameter range relevant for the cuprates.
We study the relationship between the pseudogap and Fermi-surface topology in the two-dimensional Hubbard model by means of the cellular dynamical mean-field theory. We find two possible mean-field metallic solutions on a broad range of interactions, doping, and frustration: a conventional renormalized metal and an unconventional pseudogap metal. At half filling, the conventional metal is more stable and displays an interaction-driven Mott metal-insulator transition. However, for large interactions and small doping, a region that is relevant for cuprates, the pseudogap phase becomes the ground state. By increasing doping, we show that a first-order transition from the pseudogap to the conventional metal is tied to a change of the Fermi surface from hole- to electronlike, unveiling a correlation-driven mechanism for a Lifshitz transition. This explains the puzzling link between the pseudogap phase and Fermi surface topology that has been pointed out in recent experiments.
We have studied the single-band Hubbard model on a two-dimensional square lattice slightly below half filling. Using the canonical transformation and a form of variational wave function that allows an expansion in terms of hole concentration $\ensuremath{\delta}$ with respect to half filling, we find that a nonzero $\ensuremath{\delta}$ results in a frustration of the antiferromagnetic (AF) order favored by the superexchange interaction. Use of a variational Monte Carlo calculation enables us to construct a phase diagram in the $\frac{t}{U\ensuremath{-}\ensuremath{\delta}}$ plane in which the AF order disappears at $\ensuremath{\delta}\ensuremath{\approx}0.06$ for a typical value of tU=14\frac{t}{U}=\frac{1}{4}Ut​=41​.