The discovery of high-Tc superconductivity in the cuprates, and the observation that strong correlations are important in connection with these compounds has led to a tremendous interest in understanding the physics of strongly correlated electronic models. In particular the two simplest models for strongly correlated electrons, namely the Hubbard and t–J models, have been the subject of intensive studies. In a milestone paper of 1987, P.W. Anderson proposed that a resonating valence bond (RVB) wave-function, which consists of a superposition of valence-bond states, contains the ingredients to account for a consistent theory of the Hubbard and t–J models. Motivated by the success of variational Monte- Carlo to describe some of the peculiar properties of the cuprates, we propose in this dissertation, on one hand, to extend the method to further strongly correlated models to describe other compounds such as graphene, carbon nanotube or the cobaltite compounds, and on the other hand we propose to focus on the pseudo-gap phase of the cuprates, which is still prompting for a consistent theory. In particular, the issue of checkerboard spatial modulations in the density of states in the low temperature regime of the cuprates is addressed. Finally, we have studied the possibility for spontaneous orbital currents in the cuprates, that might play a key role in the theory of high Tc superconductors.The discovery of high-Tc superconductivity in the cuprates, and the observation that strong correlations are important in connection with these compounds has led to a tremendous interest in understanding the physics of strongly correlated electronic models. In particular the two simplest models for strongly correlated electrons, namely the Hubbard and t–J models, have been the subject of intensive studies. In a milestone paper of 1987, P.W. Anderson proposed that a resonating valence bond (RVB) wave-function, which consists of a superposition of valence-bond states, contains the ingredients to account for a consistent theory of the Hubbard and t–J models. Motivated by the success of variational Monte- Carlo to describe some of the peculiar properties of the cuprates, we propose in this dissertation, on one hand, to extend the method to further strongly correlated models to describe other compounds such as graphene, carbon nanotube or the cobaltite compounds, and on the other hand we propose to focus on the pseudo-gap phase of the cuprates, which is still prompting for a consistent theory. In particular, the issue of checkerboard spatial modulations in the density of states in the low temperature regime of the cuprates is addressed. Finally, we have studied the possibility for spontaneous orbital currents in the cuprates, that might play a key role in the theory of high Tc superconductors.

Jan 1, 20072 citations

Approaches to the Hubbard Model

Cary Mcilwaine Maguire

Jan 1, 19910 citations

Beyond-Hubbard Pairing in a Cuprate Ladder

Hari Padma, Jinu Thomas, Sophia F. R. TenHuisen +13 more

The Hubbard model is believed to capture the essential physics of cuprate superconductors. However, recent theoretical studies suggest that it fails to reproduce a robust and homogeneous superconducting ground state. Here, using resonant inelastic x-ray scattering and density matrix renormalization group calculations, we show that magnetic excitations in the prototypical cuprate ladder Sr 14 Cu 24 O 41 are inconsistent with those of a simple Hubbard model. The magnetic response of hole carriers, contributing to an emergent branch of spin-flip excitations, is strongly suppressed. This effect is the consequence of strong d -wavelike pairing, enhanced by nearly an order of magnitude through a large nearest-neighbor attractive interaction and persisting up to at least 260 K. The close connection between the physics of cuprate ladders and that of the two-dimensional compounds suggests that such an enhanced hole pairing may be a universal feature of superconducting cuprates.The Hubbard model is believed to capture the essential physics of cuprate superconductors. However, recent theoretical studies suggest that it fails to reproduce a robust and homogeneous superconducting ground state. Here, using resonant inelastic x-ray scattering and density matrix renormalization group calculations, we show that magnetic excitations in the prototypical cuprate ladder Sr 14 Cu 24 O 41 are inconsistent with those of a simple Hubbard model. The magnetic response of hole carriers, contributing to an emergent branch of spin-flip excitations, is strongly suppressed. This effect is the consequence of strong d -wavelike pairing, enhanced by nearly an order of magnitude through a large nearest-neighbor attractive interaction and persisting up to at least 260 K. The close connection between the physics of cuprate ladders and that of the two-dimensional compounds suggests that such an enhanced hole pairing may be a universal feature of superconducting cuprates.

arXiv:2501.10287Physical Review XMay 12, 202510 citations

Position representation of effective electron-electron interactions in solids

Tor Jonas Sjöstrand, Fredrik Nilsson, Christoph Friedrich +1 more

An essential ingredient in many model Hamiltonians, such as the Hubbard model, is the effective electron-electron interaction $U$ , which enters as matrix elements in some localized basis. These matrix elements provide the necessary information in the model, but the localized basis is incomplete for describing $U$ . We present a systematic scheme for computing the manifestly basis-independent dynamical interaction in position representation, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\omega})$, and its Fourier transform to time domain, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\tau})$. These functions can serve as an unbiased tool for the construction of model Hamiltonians. For illustration we apply the scheme within the constrained random-phase approximation to the cuprate parent compounds ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}$ within the commonly used one- and three-band models, and to nonsuperconducting ${\mathrm{SrVO}}_{3}$ within the ${t}_{2g}$ model. Our method is used to investigate the shape and strength of screening channels in the compounds. We show that the $\mathrm{O}\phantom{\rule{0.16em}{0ex}}2{p}_{x,y}\ensuremath{-}\mathrm{Cu}\phantom{\rule{0.16em}{0ex}}3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ screening gives rise to regions with strong attractive static interaction in the minimal (one-band) model in both cuprates. On the other hand, in the minimal ( ${t}_{2g}$ ) model of ${\mathrm{SrVO}}_{3}$ only regions with a minute attractive interaction are found. The temporal interaction exhibits generic damped oscillations in all compounds, and its time integral is shown to be the potential caused by inserting a frozen point charge at $\ensuremath{\tau}=0$. When studying the latter within the three-band model for the cuprates, short time intervals are found to produce a negative potential.An essential ingredient in many model Hamiltonians, such as the Hubbard model, is the effective electron-electron interaction $U$, which enters as matrix elements in some localized basis. These matrix elements provide the necessary information in the model, but the localized basis is incomplete for describing $U$. We present a systematic scheme for computing the manifestly basis-independent dynamical interaction in position representation, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\omega})$, and its Fourier transform to time domain, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\tau})$. These functions can serve as an unbiased tool for the construction of model Hamiltonians. For illustration we apply the scheme within the constrained random-phase approximation to the cuprate parent compounds ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}$ within the commonly used one- and three-band models, and to nonsuperconducting ${\mathrm{SrVO}}_{3}$ within the ${t}_{2g}$ model. Our method is used to investigate the shape and strength of screening channels in the compounds. We show that the $\mathrm{O}\phantom{\rule{0.16em}{0ex}}2{p}_{x,y}\ensuremath{-}\mathrm{Cu}\phantom{\rule{0.16em}{0ex}}3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ screening gives rise to regions with strong attractive static interaction in the minimal (one-band) model in both cuprates. On the other hand, in the minimal (${t}_{2g}$) model of ${\mathrm{SrVO}}_{3}$ only regions with a minute attractive interaction are found. The temporal interaction exhibits generic damped oscillations in all compounds, and its time integral is shown to be the potential caused by inserting a frozen point charge at $\ensuremath{\tau}=0$. When studying the latter within the three-band model for the cuprates, short time intervals are found to produce a negative potential.

arXiv:1902.01176Physical review. B./Physical review. BMay 21, 20194 citations

An essential ingredient in many model Hamiltonians, such as the Hubbard model, is the effective electron-electron interaction

U

, which enters as matrix elements in some localized basis. These matrix elements provide the necessary information in the model, but the localized basis is incomplete for describing

U

. We present a systematic scheme for computing the manifestly basis-independent dynamical interaction in position representation, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\omega})$, and its Fourier transform to time domain, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\tau})$. These functions can serve as an unbiased tool for the construction of model Hamiltonians. For illustration we apply the scheme within the constrained random-phase approximation to the cuprate parent compounds

{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}

and

{\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}

within the commonly used one- and three-band models, and to nonsuperconducting

{\mathrm{SrVO}}_{3}

within the

{t}_{2g}

model. Our method is used to investigate the shape and strength of screening channels in the compounds. We show that the $\mathrm{O}\phantom{\rule{0.16em}{0ex}}2{p}_{x,y}\ensuremath{-}\mathrm{Cu}\phantom{\rule{0.16em}{0ex}}3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ screening gives rise to regions with strong attractive static interaction in the minimal (one-band) model in both cuprates. On the other hand, in the minimal (

{t}_{2g}

) model of

{\mathrm{SrVO}}_{3}

only regions with a minute attractive interaction are found. The temporal interaction exhibits generic damped oscillations in all compounds, and its time integral is shown to be the potential caused by inserting a frozen point charge at $\ensuremath{\tau}=0$. When studying the latter within the three-band model for the cuprates, short time intervals are found to produce a negative potential.