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arXiv:1409.3241 · Physical Review B

Quasiparticle collapsing in an anisotropic t−J ladder

Zheng Zhu, Zheng-Yu Weng

Published Dec 31, 2015• 29 citations
arXivHTMLPDF

Abstract

Quasiparticle collapsing is a central issue in the study of strongly correlated electron systems. In the one-dimensional case, the quasiparticle collapsing in a form of spin-charge separation has been well established, but the problem remains elusive in dimensions higher than one. By using the density matrix renormalization group (DMRG) algorithm, we show that in an anisotropic two-leg $t\ensuremath{-}J$ ladder, an injected single hole behaves like a well-defined quasiparticle in the strong rung limit but undergoes a ``phase transition'' with the effective mass diverging at a quantum critical point (QCP) towards the isotropic limit. After the transition, the quasiparticle collapses into a loosely bound object of a charge (holon) and a spin-1/2 (spinon) accompanied by an unscreened phase string as well as a substantially enhanced binding energy between two doped holes. A phase diagram of multileg ladders is further obtained, which extrapolates the QCP towards the two-dimensional limit. The underlying mechanism generic for any dimensions is also discussed.

DOI
10.1103/physrevb.92.235156

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Quasiparticle collapsing is a central issue in the study of strongly correlated electron systems. In the one-dimensional case, the quasiparticle collapsing in a form of spin-charge separation has been well established, but the problem remains elusive in dimensions higher than one. By using the density matrix renormalization group (DMRG) algorithm, we show that in an anisotropic two-leg t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J ladder, an injected single hole behaves like a well-defined quasiparticle in the strong rung limit but undergoes a ``phase transition'' with the effective mass diverging at a quantum critical point (QCP) towards the isotropic limit. After the transition, the quasiparticle collapses into a loosely bound object of a charge (holon) and a spin-1/2 (spinon) accompanied by an unscreened phase string as well as a substantially enhanced binding energy between two doped holes. A phase diagram of multileg ladders is further obtained, which extrapolates the QCP towards the two-dimensional limit. The underlying mechanism generic for any dimensions is also discussed.
In this paper, we have systematically studied the single-hole problem in two-leg Hubbard and $t\ensuremath{-}J$ ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.
Spin-charge separation is a hallmark of one-dimensional fermionic systems, yet its realization in higher dimensions remains an open question. To address this issue, we investigate a two-leg t-J ladder using the density matrix renormalization group (DMRG) method and its time-dependent extension. By analyzing ground-state correlations and single-particle removal spectra, we systematically examine the effects of plaquette diagonal hopping, spin exchange, and hole doping. Within appropriate parameter regimes, these factors drive the system from the well-known Luther Emery phase, with gapped spin and gapless charge modes, into a Luttinger liquid phase characterized by gapless spin and charge excitations, where signatures of spin-charge separation emerge. In combination with previous studies using exact diagonalization, our results provide evidence that spin-charge separation may persist in wider ladder systems.
We examine a wavefunction ansatz in which a doped hole can experience a quantum transition from a charge +e+e+e Landau quasiparticle to a neutral spinon as a function of the underlying spin-spin correlation. As shown variationally, such a wavefunction accurately captures all the essential features revealed by exact diagonalization and density matrix renormalization group simulations in a two-leg $t\text{\ensuremath{-}}J$ ladder. Hence its analytic form can provide an explicit understanding of the mechanism for the unconventional ground state. The transition in the phase diagram is accompanied by a change of the hole composite from a tight charge-spin binding to a loosely-bound hole-spin pair. In the latter, the hole carries a finite spin current but with vanishing charge current in the degenerate ground states. We show that the charge of the hole composite here is dynamically diminished due to an internal relative hole-spin motion, which is fundamentally distinct from a simple charge-spin separation in a one-dimensional case. We further show that the same effect is also responsible for a strong pairing between two doped holes in such a non-Landau quasiparticle regime.
Variational wave function for an anisotropic single-hole-doped ttt-JJJ ladder
Based on three general guiding principles, i.e., no double occupancy constraint, accurate description of antiferromagnetism at half-filling, and the precise sign structure of the ttt-JJJ model, a new ground state wave function has been constructed recently [Weng, New J. Phys. 13, 103039 (2011)]. In this paper, we specifically study such kind of variational ground state for the one-hole-doped anisotropic two-leg ttt-JJJ ladder using variational Monte Carlo (VMC) method. The results are then systematically compared with those recently obtained by density matrix renormalization group (DMRG) simulation. An excellent agreement is found between the VMC and DMRG results, including a "quantum critical point" at the anisotropy parameter α=αc≈0.7α=α_c\approx0.7α=αc​≈0.7 (with the parameters t/J=3t/J=3t/J=3), and the emergence of charge modulation and momentum (Fermi point) reconstruction at α>αcα>α_cα>αc​ due to the quantum interference of the sign structure. In particular, the wave function indicates that a Landau's quasiparticle description remains valid at ααcαα_cααc​ due to the breakdown of the one-to-one correspondence of momentum and translational symmetry of the hole. The explicit form of the wave function provides a direct understanding on how the many-body strong correlation effect takes place non-perturbatively in a doped Mott insulator, which sheds interesting light on the two-dimensional case where the same type of wave function was proposed to describe the cuprate superconductor.
A long-standing issue in the physics of strongly correlated electronic systems is whether the motion of a single hole in quantum antiferromagnets can be understood in terms of the quasiparticle picture. Very recently, investigations of this issue have been within the experimental reach. Here we perform a large-scale density matrix renormalization group study, and provide the first unambiguous numerical evidence showing that in ladder systems, a single hole doped in the Mott antiferromagnet does not behave as a quasiparticle. Specifically, the injected hole is found to be always localized as long as the leg number is larger than one, with a vanishing quasiparticle weight and a localization length monotonically decreasing with the leg number. In addition, the single hole self-localization is insensitive to the parity (even-odd) of the leg number. Our findings may advance conceptual developments in different fields of condensed matter physics. First of all, the intriguing self-localization phenomenon is of pure strong correlation origin free of extrinsic disorders. Therefore, it is in sharp contrast to the well-known Anderson localization and recently found many-body localization, where extrinsic disordered potentials play crucial roles. Second, they confirm the analytical predictions of the so-called phase string theory, suggesting that the phase string effect lies in the core of the physics of doped Mott antiferromagnets.
We carry out density-matrix-renormalization group (DMRG) calculations for the problem of one doped hole in a two-leg t-J ladder. Recent studies have concluded that exotic "Mott" physics-arising from the projection onto the space of no double-occupied sites-is manifest in this model system, leading to charge localization and a new mechanism for charge modulation. In contrast, we show that there is no localization and that the charge-density modulation arises when the minimum in the quasiparticle dispersion moves away from π. Although singular changes in the quasiparticle dispersion do occur as a function of model parameters, all of the DMRG results can be qualitatively understood from a noninteracting "band-structure" perspective.