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arXiv:1312.6893 · Scientific Reports

Nature of strong hole pairing in doped Mott antiferromagnets

Zheng Zhu, Hong‐Chen Jiang, D. N. Sheng, Zheng-Yu Weng

Published Jun 24, 2014• 42 citations
arXivHTMLPDF

Abstract

Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we report a DMRG investigation of hole binding in the same model, where a novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we show that, in addition to spin pairing due to superexchange interaction, the strong frustration of the phase string signs on the kinetic energy gets effectively removed by pairing the charges, which results in strong binding of two holes. By contrast, if the phase string signs are "switched off" artificially, the pairing strength diminishes significantly even if the superexchange coupling remains the same. In the latter, unpaired holes behave like coherent quasiparticles with pairing drastically weakened, whose sole origin may be attributed to the resonating-valence-bond (RVB) pairing of spins. Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed important light on the high-T(c) cuprate superconductors.

DOI
10.1038/srep05419

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Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we report a DMRG investigation of hole binding in the same model, where a novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we show that, in addition to spin pairing due to superexchange interaction, the strong frustration of the phase string signs on the kinetic energy gets effectively removed by pairing the charges, which results in strong binding of two holes. By contrast, if the phase string signs are "switched off" artificially, the pairing strength diminishes significantly even if the superexchange coupling remains the same. In the latter, unpaired holes behave like coherent quasiparticles with pairing drastically weakened, whose sole origin may be attributed to the resonating-valence-bond (RVB) pairing of spins. Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed important light on the high-T(c) cuprate superconductors.
The fate of a hole injected in an antiferromagnet is an outstanding issue of strongly correlated physics. It provides important insights into doped Mott insulators closely related to high-temperature superconductivity. Here, we report a systematic numerical study of t-J ladder systems based on the density matrix renormalization group. It reveals a surprising result for the single hole's motion in an otherwise well-understood undoped system. Specifically, we find that the common belief of quasiparticle picture is invalidated by the self-localization of the doped hole. In contrast to Anderson localization caused by disorders, the charge localization discovered here is an entirely new phenomenon purely of strong correlation origin. It results from destructive quantum interference of novel signs picked up by the hole, and since the same effect is of a generic feature of doped Mott physics, our findings unveil a new paradigm which may go beyond the single hole doped system.
Department of Physics and Astronomy, California State University, Northridge, CA, 91330, USA(Dated: December 30, 2013)The binding of two holes injected in antiferromagnets is studied based on the density matrix renormalizationgroup simulation for the t-J square ladders. It is shown that the binding strength is substantially enhanced ina spin background of short-range spin correlations as opposed to that of quasi-long-range spin correlations.However, it is further shown that such strong hole binding gets significantly diminished once phase strings areswitched off. In the latter case, a coherent quasiparticle picture is restored for an unpaired single hole. Bycontrast, the quantum frustration of the single hole’s motion due to phase strings can be effectively removed bypairing, and thus a strong binding force hidden in the kinetic energy term is revealed for the t-J model.
Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is ififif any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo approach. By comparing with density-matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t\text{\ensuremath{-}}J$ model, which is kinetic-energy driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.
The pairing mechanism in doped antiferromagnets is essential for understanding high-temperature superconductivity. In this work, we investigate the pairing mechanism in bosonic doped antiferromagnets via large-scale density matrix renormalization group calculations of the bosonic $t\ensuremath{-}J$ model. We discover a pair density wave (PDW) coexists with the antiferromagnetic (AFM) order forming a ``supersolid'' at small doping. The pairing is attributed to a hidden many-body Berry phase that introduces the sole ``sign problem'' into this bosonic model and imposes quantum phase frustration to the spin-charge interference pattern. Only via tightly pairing of doped holes can such frustration be most effectively erased in an AFM background. By contrast, the pairing vanishes as the Berry phase is trivialized in the ferromagnetic condensate at larger doping or switched off into the Bose-Hubbard model at large UUU. The present pairing mechanism---distinct from the conventional mechanisms based on Fermi surface instabilities---may provide a different perspective and new insights for understanding the complex nature of doped Mott insulators and is promising to be probed on qudit-based quantum simulators such as ultracold Rydberg atom arrays.
The mechanism of superconductivity in a purely interacting electron system has been one of the most challenging issues in condensed matter physics. In the BCS theory, the Landau's Fermi liquid is the ground state of weakly interacting fermions dictated by the fermion sign structure, and the superconducting instability only occurs when an additional pairing force is added. By contrast, as shown by density matrix renormalization group calculation, a quasi-one-dimensional superconducting state (specifically a Luther-Emery state) is an intrinsic ground state of the $t\ensuremath{-}J$ two-leg ladder and four-leg cylinder at finite doping. Such a Luther-Emery state with pairing can be directly turned into a Fermi-gas-like normal state without pairing by merely switching off the phase-string signs hidden in the model via two schemes, which reduce the sign structure to the trivial fermion signs associated with doped holes. It thus demonstrates a new pairing paradigm in a model-doped Mott insulator as due to the generic phase-string sign structure. Finally, as an example, the latter is explicitly shown to lead to a ``stringlike'' pairing force after adiabatically connecting to a strong anisotropic limit of the model.
Understanding the doped Mott insulator is a central challenge in condensed matter physics. In this work, we first explicitly identify a new sign structure in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model on the square lattice that replaces the conventional Fermi statistics for weakly interacting electrons. Then we show that the singular, i.e., the phase-string part of the sign structure in the partition function can be precisely turned off in a modified model. The density matrix renormalization group method is then employed to study these two models comparatively on finite-size systems, which is designed to unveil the consequences of the phase-string component. We find that the hole pairing is present not only in the quasi-long-range superconducting phase but also in the stripe phase of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model. However, once the phase-string is switched off, both the superconducting and stripe orders together with the underlying hole pairing disappear. The corresponding ground state reduces to a trivial Fermi-liquid-like state with small hole Fermi pockets that is decoupled from the antiferromagnetic spin background. It is in sharp contrast to the original $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model where large Fermi surfaces can be restored in the stripe phase found at ${t}^{\ensuremath{'}}/t<0$ or the superconducting phase at ${t}^{\ensuremath{'}}/t>0$ in the six-leg ladder calculation. Our study clearly demonstrates that the strong correlation effect in doped Mott insulator should be mainly attributed to the long-range quantum entanglement between the spin and charge, which is, nonperturbatively, beyond a simple spin-charge separation under the no double occupancy constraint.