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arXiv:cond-mat/9506070

Marshall sign and the doped $t-J$ model

Zheng-Yu Weng, D. N. Sheng, Y. C. Chen

Published Jun 15, 1995• 0 citations
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Abstract

Marshall sign as a sole source of sign problem hidden in an antiferromagnet is explored under doping. By tracking the Marshall sign, a zero spectral weight $Z$ is revealed in the doped antiferromagnetic system. $Z=0$ is caused by a phase string induced by the ``bare'' hole. By eliminating such a phase string through nonlocal transformations, a non-perturbative scheme is obtained. It is argued that this formalism provides a unique way to get access to the real ground state of the doped $t-J$ model for both one- and two-dimensions.

DOI
10.48550/arxiv.cond-mat/9506070

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Marshall sign and the doped t−Jt-Jt−J model
Marshall sign as a sole source of sign problem hidden in an antiferromagnet is explored under doping. By tracking the Marshall sign, a zero spectral weight ZZZ is revealed in the doped antiferromagnetic system. Z=0Z=0Z=0 is caused by a phase string induced by the ``bare'' hole. By eliminating such a phase string through nonlocal transformations, a non-perturbative scheme is obtained. It is argued that this formalism provides a unique way to get access to the real ground state of the doped t−Jt-Jt−J model for both one- and two-dimensions.
By explicitly tracking the Marshall sign, a phase string induced by hopping is revealed in the one-hole-doped t−Jt-Jt−J model. It is rigorously shown that such a phase string cannot be eliminated through low-lying spin excitations, and it either causes the spectral weight Z=0Z=0Z=0, or leads to the localization of the doped hole. Implications for finite doping are also discussed.
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 ZZZ 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{\mathrm{T}}_{\mathrm{c}}Tc​ cuprates.
The antiferromagnetic Heisenberg spin chain of odd spin SSS is in the Haldane phase with several defining physical properties, such as thermodynamical ground-state degeneracy, symmetry-protected edge states, and nonzero string order parameter. If nonzero hole concentration $\ensuremath{\delta}$ and hole hopping energy ttt are considered, the spin chain is replaced by a $\text{spin}\ensuremath{-}S$ $t\ensuremath{-}J$ chain. The motivation of this paper is to generalize the discussions of the Haldane phase to the doped spin chain. The first result of this paper is that, for the model considered here, the Z2{\mathbb{Z}}_{2}Z2​ sign structure in the usual Ising basis can be totally removed by two consecutive unitary transformations consisting of a spatially local one and a nonlocal one. Direct from the sign structure, the second result of this paper is that the Marshall theorem and the Lieb-Mattis theorem for pure spin systems are generalized to the $t\ensuremath{-}J$ chain for arbitrary SSS and $\ensuremath{\delta}$. A corollary of the theorem provides us with the ground-state degeneracy in the thermodynamic limit. The third result of this paper is about the phase diagram. We show that the defining properties of the Haldane phase survive in the small t/Jt/Jt/J limit. The large t/Jt/Jt/J phase supports a gapped spin sector with similar properties (ground-state degeneracy, edge state, and string order parameter) of the Haldane chain, although the charge sector is gapless.
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.
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.