Based on the $t\ensuremath{-}J$ model, it is shown that a hole moving on an antiferromagnetic spin background always induces a phase-string effect. Such a previously unnoticed phase string is revealed by explicitly tracking the Marshall sign and can be rigorously shown to be nonrepairable at low energy. Its quantum interference can drastically modify the long-wavelength behavior of the doped hole, leading to a vanishing spectral weight
Z at the ground-state energy. Implication for finite doping is also discussed.
We reexamine the problem of a hole moving in an antiferromagnetic spin background and find that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom. Previously unnoticed, such a stringlike phase originates from the hidden Marshall signs which are scrambled by the hopping of the hole. We can rigorously show that this phase string is nonrepairable at low energy and give a general proof that the spectral weight Z must vanish at the ground-state energy due to the phase-string effect. Thus, the quasiparticle description fails here and the quantum interference effect of the phase string dramatically affects the long-distance behavior of the injected hole. We introduce a so-called phase-string formulation of the t-J model for a general number of holes in which the phase-string effect can be explicitly tracked. As an example, by applying this new mathematical formulation in one dimension, we reproduce the well-known Luttinger-liquid behaviors of the asymptotic single-electron Green's function and the spin-spin correlation function. We can also use the present phase-string theory to justify previously developed spin-charge separation theory in two dimensions, which offers a systematic explanation for the transport and magnetic anomalies in the high-
Tc cuprates.
The motion of a single hole in a Mott antiferromagnet is investigated based on the $t\ensuremath{-}J$ 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.
We study a ground-state ansatz for the single-hole-doped $t\text{\ensuremath{-}}J$ model in two dimensions via a variational Monte Carlo 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 (DMRG) 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 $8\ifmmode\times\else\texttimes\fi{}8$ lattice. Such a two-component structure indicates the breakdown of Landau's 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 $\ensuremath{\sigma}\ifmmode\cdot\else\textperiodcentered\fi{}t\text{\ensuremath{-}}J$ 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.
For the
t-
J model, variational wave functions can generally be constructed based on an accurate description of antiferromagnetism (AFM) at half-filling and an exact phase-string sign structure under doping. The single-hole-doped and two-hole-doped states, as determined by variational Monte Carlo (VMC) simulations, display sharply contrasting behaviors. The single-hole state constitutes a ``cat state'' that resonates strongly between a quasiparticle component and a local loop-current component, with approximately equal weights. In the ground state, the quasiparticle spectral weight
Zk peaks at momenta
k0≡(±2π,±2π). The total-energy dispersion versus
k agrees remarkably well with the Green function Monte Carlo results. However, Landau's one-to-one correspondence hypothesis for quasiparticles breaks down here with the incoherent component exhibiting intrinsic magnetization originating from a minimal
2×2 loop current that forms a
4×4 pattern on the square lattice--a finding in excellent agreement with density matrix renormalization group (DMRG) calculations. In the two-hole ground state, a new pairing mechanism is revealed: the two holes are automatically fused into a tightly bound object consisting of an incoherent
dxy pairing along the diagonal direction by compensating the local loop currents. This hole pair is again a ``cat state'' that resonates strongly between the incoherent
dxy and a coherent
dx2−y2 Cooper channel to gain substantial hopping energy. Its size extends over an area of about
4×4 lattice spacings, much smaller than the divergent AFM correlation length, implying that it should survive as a minimal superconducting building block even in the dilute doping regime. Experimental implications and the generalization to the finite-doping case are briefly addressed.
Injecting a single hole into a one-dimensional Heisenberg spin chain is probably the simplest case of doping a Mott insulator. The motion of such a single hole will generally induce a many-body phase shift, which can be identified by an exact sign structure of the model known as the phase string. We show that the sign structure is nontrivial even in this simplest problem, which is responsible for the essential properties of Mott physics. We find that the characteristic momentum structure, the Luttinger liquid behavior, and the quantum phase interference of the hole under a periodic boundary condition can all be attributed to it. We use the density matrix renormalization group (DMRG) numerical simulation to make a comparative study of the t–J chain and a model in which the sign structure is switched off. We further show that the key DMRG results can be reproduced by a variational wave function with incorporating the correct sign structure. Physical implications of the sign structure for doped Mott insulators in general are also discussed.