Recent studies reported that antiferromagnetic (AF) states become stable and d -wave superconducting ( d -SC) states are almost excluded in underdoped strongly correlated Hubbard models in two dimensions. In a viewpoint of many-body variational theory, this result stems from a band-renormalization effect (BRE) in AF states. Here, using a variational Monte Carlo method, BRE on AF and d -SC states are studied in the t-t'-J model, in which d -SC (AF) states have been considered to be more stable (fragile) than in the Hubbard model. Many features are qualitatively similar to the Hubbard model including effectiveness of BRE and the existence of a Lifshitz transition in AF states. However, a d -SC state becomes more stable than an AF state widely in the underdoped regime for J/t =0.3, in contrast to the Hubbard model.Recent studies reported that antiferromagnetic (AF) states become stable and d -wave superconducting ( d -SC) states are almost excluded in underdoped strongly correlated Hubbard models in two dimensions. In a viewpoint of many-body variational theory, this result stems from a band-renormalization effect (BRE) in AF states. Here, using a variational Monte Carlo method, BRE on AF and d -SC states are studied in the t-t'-J model, in which d -SC (AF) states have been considered to be more stable (fragile) than in the Hubbard model. Many features are qualitatively similar to the Hubbard model including effectiveness of BRE and the existence of a Lifshitz transition in AF states. However, a d -SC state becomes more stable than an AF state widely in the underdoped regime for J/t =0.3, in contrast to the Hubbard model.

Journal of Physics Conference SeriesJul 1, 20171 citation

Antiferromagnetism and correlation of electrons in a one-band Hubbard model

Andrzej M. Oleś, Józef Spałek

The European Physical Journal BSep 1, 198119 citations

Physics of cuprates with the two-band Hubbard model: The validity of the one-band Hubbard model

Alexandru Macridin, Mark Jarrell, Thomas Maier +1 more

We calculate the properties of the two-band Hubbard model using the dynamical cluster approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron- and hole-doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin, and $d$ -wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.We calculate the properties of the two-band Hubbard model using the dynamical cluster approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron- and hole-doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin, and $d$-wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.

arXiv:cond-mat/0411092Physical Review BApr 29, 200595 citations

Physics of the Hubbard model and high temperature superconductivity

Takashi Yanagisawa

The electronic state of high-temperature cuprates is investigated on the basis of the two-dimensional Hubbard model. We investigate the three-band Hubbard model (which is sometimes called the d-p model) as well as the single-band Hubbard model. In particular, the three-band Hubbard model with d and p orbitals in the CuO 2 plane probably captures the physics of high-temperature superconductivity. Numerical studies of the two-dimensional d-p and Hubbard models have shown that they exhibit antiferromagnetism, stripes, d-wave pairing, coexistent antiferromagnetism with superconductivity, and arc spectra. They are basic phenomena seen in the high-temperature cuprates.The electronic state of high-temperature cuprates is investigated on the basis of the two-dimensional Hubbard model. We investigate the three-band Hubbard model (which is sometimes called the d-p model) as well as the single-band Hubbard model. In particular, the three-band Hubbard model with d and p orbitals in the CuO 2 plane probably captures the physics of high-temperature superconductivity. Numerical studies of the two-dimensional d-p and Hubbard models have shown that they exhibit antiferromagnetism, stripes, d-wave pairing, coexistent antiferromagnetism with superconductivity, and arc spectra. They are basic phenomena seen in the high-temperature cuprates.

Journal of Physics Conference SeriesMar 1, 20085 citations

d

-wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.