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We report a large-scale density-matrix renormalization group study of the lightly doped Hubbard model on 4-leg cylinders at hole doping concentration $\delta=12.5\%$. By keeping a large number of states for long system sizes, we are able to…

We study the ground state properties of the hole-doped three-band Hubbard (Emery) model, describing the copper-oxygen planes of the cuprates, using large-scale 2D tensor network calculations. Our simulations reveal a period 4 stripe state…

We perform variational Monte Carlo simulations of the single-band Hubbard model on the square lattice with both nearest ($t$) and next-nearest ($t'$) neighbor hoppings. Our work investigates the consequences of increasing hole doping on the…

The enigma of unconventional superconductivity in doped cuprates presents a formidable challenge in the realm of condensed matter physics. Recent findings of strong near-neighbor attractions in one-dimensional cuprate chains suggest a new…

Understanding the electron pairing in hole-doped cuprate superconductors has been a challenge, in particular because the "normal" state from which it evolves is unprecedented. Now, after three and a half decades of research, involving a…

We explore the superconducting properties of the bilayer Hubbard model, which exhibits a high transition temperature ($T_{\rm c}$) for an $s_{\pm}$ pairing, using a cluster extension of the dynamical mean-field theory. Unlike the…

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…

The two-dimensional (2D) Hubbard model is widely believed to capture key ingredients of high-$T_c$ superconductivity in cuprate materials. However, compelling evidence remains elusive. In particular, various magnetic orders may emerge as…

The role of near-neighbor electron attraction $V$ in strongly correlated systems has been at the forefront of recent research of unconventional superconductivity. However, its implications in the doped Hubbard model on expansive systems…

The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and…

A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we…

Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems.…

The hypothesis that holes doped into high-Tc cuprate superconductors organize themselves in two-dimensional (2D) array of diagonal stripes is discussed, and, on the basis of this hypothesis, a new microscopic model of superconductivity is…

We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest neighbor hopping $t$, we also include a next-to-nearest neighbor hopping $t'$. For strong enough on-site repulsion, this model has a…

One of the major themes in correlated electron physics over the last quarter century has been the problem of high-temperature superconductivity in hole-doped copper-oxide compounds. Fundamental to this problem is the competition between…

A variational Monte Carlo calculation is used for studying the ground state of the two-dimensional Hubbard model, including hopping between both nearest and next-nearest neighbor sites. Superconductivity with d-wave symmetry is found to be…

We study the interplay of nematic and superconducting order in the two-dimensional Hubbard model and show that they can coexist, especially when superconductivity is not the energetically dominant phase. Due to a breaking of the $C_4$…

The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and…

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors…

Superconductivity in layered cuprates is induced by doping holes into a parent antiferromagnetic insulator. It is now recognized that another common emergent order involves charge stripes, and our understanding of the relationship between…