Momentum space anisotropy in doped Mott insulators

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior ...

A central issue of Mott physics, with symmetries being fully retained in the spin background, concerns the charge excitation. In a two-leg spin ladder with spin gap, an injected hole can exhibit either a Bloch wave or a density wave by tuning the ladder anisotropy through a `quantum critical point' (QCP). The nature of such a QCP has been a subject of recent studies by density matrix renormalization group (DMRG). In this paper, we reexamine the ground state of the one doped h...

Recently, we have solved the long-standing problem of connecting the physics of the Mott insulator to the underdoped regime of the t-J model [PRB 82, 014504, 2010]. We have derived a renormalized Hamiltonian valid for small doping (x) which is characterized by a spin gap, and sublattice preserving hopping by a hole, and by a pair of holes, both accompanied by a spin-singlet backflow. The phase diagram obtained by continuing the spin states from half filling reproduces the pha...

We argue that aspects of the anomalous, low temperature, spin and charge dynamics of the high temperature superconductors can be understood by studying the corresponding physics of undoped Mott insulators. Such insulators display a quantum transition from a magnetically ordered Neel state to a confining paramagnet with a spin gap; the latter state has bond-centered charge order, a low energy S=1 spin exciton, confinement of S=1/2 spinons, and a free S=1/2 moment near non-magn...

High-temperature superconductivity in the copper-oxide ceramics remains an unsolved problem because we do not know what the propagating degrees of freedom are in the normal state. As a result, we do not know what are the weakly interacting degrees of freedom which pair up to form the superconducting condensate. That the electrons are not the propagating degrees of freedom in the cuprates is seen most directly from experiments that show spectral weight redistributions over all...

Recent scanning tunneling microscope (STM) measurements discovered remarkable electronic inhomogeneity, i.e. nano-scale spatial variations of the local density of states (LDOS) and the superconducting energy gap, in the high-Tc superconductor BSCCO. Based on the experimental findings we conjectured that the inhomogeneity arises from variations in local oxygen doping level and may be generic of doped Mott insulators which behave rather unconventionally in screening the dopant ...

A d-wave superconducting ground state for a doped Mott insulator is obtained. It is distinguished from a Gutzwiller-projected BCS superconductor by an explicit separation of Cooper pairing and resonating valence bond (RVB) pairing. Such a state satisfies the precise sign structure of the t-J model, just like that a BCS state satisfies the Fermi-Dirac statistics. This new class of wavefunctions can be intrinsically characterized and effectively manipulated by electron fraction...

Using a recently developed variational quantum Monte Carlo method, magnetic properties of high-$T_{\rm C}$ superconductors are studied at zero temperature ($T$), by numerical simulations on the 2D t-J model. Our focus here is to explore the difference in the properties of $p$-type and $n$-type cuprates as a function of the carrier concentrations close to half filling. As observed experimentally, it is found that the antiferromagnetically ordered phase persists even for a smal...

We introduce a valence-bond dynamical mean-field theory of doped Mott insulators. It is based on a minimal cluster of two orbitals, each associated with a different region of momentum space and hybridized to a self-consistent bath. The low-doping regime is characterized by singlet formation and the suppression of quasiparticles in the antinodal regions, leading to the formation of Fermi arcs. This is described in terms of an orbital-selective transition in reciprocal space. T...

Considering a system of ultracold atoms in an optical lattice, we propose a simple and robust implementation of a quantum simulator for the homogeneous t-J model with a well-controlled fraction of holes x. The proposed experiment can provide valuable insight into the physics of cuprate superconductors. A similar scheme applied to bosons, moreover, allows one to investigate experimentally the subtle role of inhomogeneity when a system passes from one quantum phase to another.