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Register a new userSingle-hole wave function in two dimensions: A case study of the doped Mott insulator
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We study a ground-state ansatz for the single-hole doped $t$-$J$ model in two dimensions via a variational Monte Carlo (VMC) method. Such a single-hole wave function possesses finite angular momenta generated by hidden spin currents, which give rise to a novel ground state degeneracy in agreement with recent exact diagonalization (ED) and density matrix renormalization group (DMGR) results. We further show that the wave function can be decomposed into a quasiparticle component and an incoherent momentum distribution in excellent agreement with the DMRG results up to an $8times 8 $ lattice. Such a two-component structure indicates the breakdown of Landaus one-to-one correspondence principle, and in particular, the quasiparticle spectral weight vanishes by a power law in the large sample-size limit. By contrast, turning off the phase string induced by the hole hopping in the so-called $sigmacdot ttext{-}J$ model, a conventional Bloch-wave wave function with a finite quasiparticle spectral weight can be recovered, also in agreement with the ED and DMRG results. The present study shows that a singular effect already takes place in the single-hole-doped Mott insulator, by which the bare hole is turned into a non-Landau quasiparticle with translational symmetry breaking. Generalizations to pairing and finite doping are briefly discussed.
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We propose a class of wave functions that provide a unified description of antiferromagnetism and d-wave superconductivity in (doped) Mott insulators. The wave function has a Jastrow form and prohibits double occupancies. In the absence of holes, the wave function describes antiferromagnetism accurately. Off diagonal long range order develops at finite doping and the superconducting order parameter has d-wave symmetry. We also show how nodal quasiparticles and neutral spin excitations can be constructed from this wave function.
The motion of a single hole in a Mott antiferromagnet is investigated based on the t-J model. An exact expression of the energy spectrum is obtained, in which the irreparable phase string effect [Phys. Rev. Lett. 77, 5102 (1996)] is explicitly present. By identifying the phase string effect with spin backflow, we point out that spin-charge separation must exist in such a system: the doped hole has to decay into a neutral spinon and a spinless holon, together with the phase string. We show that while the spinon remains coherent, the holon motion is deterred by the phase string, resulting in its localization in space. We calculate the electron spectral function which explains the line shape of the spectral function as well as the ``quasiparticle spectrum observed in angle-resolved photoemission experiments. Other analytic and numerical approaches are discussed based on the present framework.
How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-$T_c$ cuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La$_{2-x}$Sr$_x$CuO$_4$ ($0 le x le 0.15$). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-$T_c$ cuprates.
The evolution from an anomalous metallic phase to a Mott insulator within the two-dimensional Hubbard model is investigated by means of the Cellular Dynamical Mean-Field Theory. We show that the density-driven Mott metal-insulator transition is approached in a non-uniform way in different regions of the momentum space. This gives rise to a breakup of the Fermi surface and to the formation of hot and cold regions, whose position depends on the hole or electron like nature of the carriers in the system.
We show that lightly doped holes will be self-trapped in an antiferromagnetic spin background at low-temperatures, resulting in a spontaneous translational symmetry breaking. The underlying Mott physics is responsible for such novel self-localization of charge carriers. Interesting transport and dielectric properties are found as the consequences, including large doping-dependent thermopower and dielectric constant, low-temperature variable-range-hopping resistivity, as well as high-temperature strange-metal-like resistivity, which are consistent with experimental measurements in the high-T$_c$ cuprates. Disorder and impurities only play a minor and assistant role here.
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