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arXiv:cond-mat/0306395 · Physical Review Letters

Theory of Doped Mott insulators: Duality between Pairing and Magnetism

Qiang-Hua Wang

Published Feb 4, 2004• 14 citations
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Abstract

By bosonizing the electronic t-J model exactly on any two-dimensional (2D) lattices, and integrating out the gauge fluctuations combined to slave particles beyond mean fields, we obtain a theory in terms of physical Cooper pair and spin condensates. In the sense of mutual Berry phase they turn out to be dual to each other. The mutual duality is the missing key in the resonant-valance-bond idea [Science 235, 1196 (1987)]] to work as a paradigm of doped 2D Mott insulators. We argue that the essential aspects of high-T(c) phenomenology can be explained in the present framework.

DOI
10.1103/physrevlett.92.057003

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By bosonizing the electronic t-J model exactly on any two-dimensional (2D) lattices, and integrating out the gauge fluctuations combined to slave particles beyond mean fields, we obtain a theory in terms of physical Cooper pair and spin condensates. In the sense of mutual Berry phase they turn out to be dual to each other. The mutual duality is the missing key in the resonant-valance-bond idea [Science 235, 1196 (1987)]] to work as a paradigm of doped 2D Mott insulators. We argue that the essential aspects of high-T(c) phenomenology can be explained in the present framework.
We study the phases of doped spin S=1∕2S=1∕2S=1∕2 quantum antiferromagnets on the square lattice as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at doping $\ensuremath{\delta}=0$ to superconductors at moderate $\ensuremath{\delta}$. The interplay between density-wave and VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0S=0S=0 sector. We extend the dimer model to include fermionic S=1∕2S=1∕2S=1∕2 excitations and show that its mean-field, static gauge-field saddle points have projective symmetries (PSG's) similar to those of ``slave''-particle U(1) and SU(2) gauge theories. We account for the nonperturbative effects of gauge fluctuations by a duality mapping of the S=0S=0S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper [L. Balents et al., preceding paper, Phys. Rev. B 71, 144508 (2005)] by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid, and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1S=1S=1 excitations and their coupling to superflow and density-wave fluctuations.
We improve a previous theory of doped Mott insulators with duality between pairing and magnetism by a further duality transform. As the result we obtained a quantum Ginzburg-Landau theory describing the Cooper pair condensate and the dual of spin condensate. We address the superconductivity by doping a Mott insulator, which we call the Mott superconductivity. Some fingerprints of such novelty in cuprates are the scaling between neutron resonance energy and superfluid density, and the induced quantized spin moment by vortices or Zn impurity (together with circulating charge super-current to be checked by experiments).
The guiding conception of vortex-condensation-driven Mott insulating behavior is central to the theory of the nodal liquid. We amplify our earlier description of this idea and show how vortex condensation in two-dimensional (2D) electronic systems is a natural extension of 1D Mott insulating and 2D bosonic Mott insulating behavior. For vortices in an underlying superconducting pair field, there is an important distinction between the condensation of flux hc/2ehc/2ehc/2e and flux hc/ehc/ehc/e vortices. The former case leads to spin-charge confinement, exemplified by the band insulator and the charge-density wave. In the latter case, spin and charge are liberated, leading directly to a 2D Mott insulator exhibiting spin-charge separation. Possible upshots include not only the nodal liquid, but also an undoped antiferromagnetic insulating phase with gapped excitations exhibiting spin-charge separation.
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We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `slave' particle U(1) and SU(2) gauge theories. We account for the non-perturbative effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper (L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1 excitations and their coupling to superflow and density wave fluctuations.
We present a theoretical approach to describing the Mott transition of electrons on a two-dimensional lattice that begins with the low-energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations that correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a priori assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low-energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon Fermi surface coupled to a U(1)U(1)U(1) gauge field, which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin antisymmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.