Related papers: Electron fractionalization and cuprate superconduc…
This paper is concerned with the idea that the electron is fractionalized in the cuprate high-$T_c$ materials. We show how the notion of topological order may be used to develop a precise theoretical characterization of a fractionalized…
The precise theoretical characterization of a fractionalized phase in spatial dimensions higher than one is through the concept of ``topological order''. We describe a physical effect that is a robust and direct consequence of this hidden…
We develop a new theoretical framework for describing and analyzing exotic phases of strongly correlated electrons which support excitations with fractional quantum numbers. Starting with a class of microscopic models believed to capture…
We discuss possible patterns of electron fractionalization in strongly interacting electron systems. A popular possibility is one in which the charge of the electron has been liberated from its Fermi statistics. Such a fractionalized phase…
Recently, we have elucidated the physics of electron fractionalization in strongly interacting electron systems using a $Z_2$ gauge theory formulation. Here we discuss the connection with the earlier U(1) gauge theory approaches based on…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
This article surveys the physics of systems proximate to Mott insulators, and presents a classification using conventional and topological order parameters. This classification offers a valuable perspective on a variety of conducting…
Electron quasiparticles play a crucial role in simplifying the description of many-body physics in solids with surprising success. Conventional Landau's Fermi-liquid and quasiparticle theories for high-temperature superconducting cuprates…
We study the electron spectral function of various zero-temperature spin-charge separated phases in two dimensions. In these phases, the electron is not a fundamental excitation of the system, but rather ``decays'' into a spin-1/2…
We propose several tests of the idea that the electron is fractionalized in the underdoped and undoped cuprates. These include the ac Josephson effect, and tunneling into small superconducting grains in the Coulomb blockade regime. In both…
Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure…
Theoretical ideas and experimental results concerning high temperature superconductors are reviewed. Special emphasis is given to calculations carried out with the help of computers applied to models of strongly correlated electrons…
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar-sometimes identical-ordering temperatures even…
One-dimensional metals, such as quantum wires or carbon nanotubes, can carry charge in arbitrary units, smaller or larger than a single electron charge. However, according to Luttinger theory, which describes the low-energy excitations of…
In the strongly correlated environment of high-temperature cuprate superconductors, the spin and charge degrees of freedom of an electron seem to separate from each other. A similar phenomenon may be present in the strong coupling phase of…
In the $t-J$ model, the electron fractionalization is unique due to the non-perturbative phase string effect. We formulated a lattice field theory taking this effect into full account. Basing on this field theory, we introduced a pair of…
Precisely what are the electrons in a high-temperature superconductor doing before they superconduct? Strong electronic correlations may give rise to composite rather than fractionalized excitations, as is typical in other strongly coupled…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
I discuss a proposed phase diagram of the cuprate superconductors as a function of temperature, carrier concentration, and a strong magnetic field perpendicular to the layers. I show how the phase diagram gives a unified interpretation of a…
Studies on the interplay between the charge order and the $d$-wave superconductivity in the copper-oxide high $T_{\rm c}$ superconductors are reviewed with a special emphasis on the exploration based on the unconventional concept of the…