It has been argued in previous works by the authors that nodal excitations in (2 + 1)-dimensional doped antiferromagnets might exhibit, in the spin-charge separation framework and at specific regions of the parameter space, a supersymmetry between spinons and holons. This supersymmetry has been elevated to a N = 2 extended supersymmetry of composite operators of spinon and holons, corresponding to the effective "hadronic" degrees of freedom. In this work we elaborate further on this idea by describing in some detail the dynamics of a specific composite model corresponding to an Abelian Higgs model (SQED). The Abelian nature of the gauge group seems to be necessitated both by the composite structure used, and also by electric charge considerations for the various composites. We demonstrate the passage from a pseudogap to an unconventional superconducting phase, which notably is an exact non-perturbative analytic result, due to the underlying N = 2 supersymmetric Abelian gauge theory. We believe that these considerations may provide a first step towards a non-perturbative understanding of the phase diagrams of strongly-correlated electron systems.
It has been argued in previous works by the authors that nodal excitations in (2 + 1)-dimensional doped antiferromagnets might exhibit, in the spin-charge separation framework and at specific regions of the parameter space, a supersymmetry between spinons and holons. This supersymmetry has been elevated to a N = 2 extended supersymmetry of composite operators of spinon and holons, corresponding to the effective "hadronic" degrees of freedom. In this work we elaborate further on this idea by describing in some detail the dynamics of a specific composite model corresponding to an Abelian Higgs model (SQED). The Abelian nature of the gauge group seems to be necessitated both by the composite structure used, and also by electric charge considerations for the various composites. We demonstrate the passage from a pseudogap to an unconventional superconducting phase, which notably is an exact non-perturbative analytic result, due to the underlying N = 2 supersymmetric Abelian gauge theory. We believe that these considerations may provide a first step towards a non-perturbative understanding of the phase diagrams of strongly-correlated electron systems.
We investigate the possibility of hidden non-Abelian local phase symmetries in large-U doped planar Hubbard antiferromagnets, believed to simulate the physics of two-dimensional (magnetic) superconductors. We present a spin-charge separation ansatz, appropriate to incorporate holon spin flip, which allows for such a hidden local gauge symmetry to emerge in the effective action. The group is of the form ${\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}}_{S}(1)\ensuremath{\bigotimes}{\mathrm{U}}_{\mathrm{em}}(1),$ where SU(2) is a local non-Abelian group associated with the spin degrees of freedom, Uem(1) is that of ordinary electromagnetism, associated with the electric charge of the holes, and US(1) is a ``statistical'' Abelian gauge group pertaining to the fractional statistics of holes on the spatial plane. In certain regime of the parameters of the model, namely, strong US(1) and weak SU(2), there is the possibility of dynamical formation of a holon condensate. This leads to a dynamical breaking of $\mathrm{SU}(2)\ensuremath{\rightarrow}\mathrm{U}(1).$ The resulting Abelian effective theory is closely related to an earlier model proposed as the continuum limit of large-spin planar doped antiferromagnets, which lead to an unconventional scenario for two-dimensional parity-invariant superconductivity.
In the context of extended $t\ensuremath{-}J$ models, with intersite Coulomb interactions of the form $\ensuremath{-}V{\ensuremath{\sum}}_{〈i,j〉}{n}_{i}{n}_{j},$ with ni denoting the electron number operator at site i, nodal liquids are discussed. We use the spin-charge separation ansatz as applied to the nodes of a d-wave superconducting gap. Such a situation may be of relevance to the physics of high-temperature superconductivity. We point out the possibility of existence of certain points in the parameter space of the model characterized by dynamical supersymmetries between the spinon and holon degrees of freedom, which are quite different from the symmetries in conventional supersymmetric $t\ensuremath{-}J$ models. Such symmetries pertain to the continuum effective-field theory of the nodal liquid, and one's hope is that the ancestor lattice model may differ from the continuum theory only by renormalization-group irrelevant operators in the infrared. We give plausible arguments that nodal liquids at such supersymmetric points are characterized by superconductivity of Kosterlitz-Thouless type. The fact that quantum fluctuations around such points can be studied in a controlled way, probably makes such systems of special importance for an eventual nonperturbative understanding of the complex phase diagram of the associated high-temperature superconducting materials.
We investigate the possibility of hidden non-Abelian Local Phase symmetries in large-U doped planar Hubbard antiferromagnets, believed to simulate the physics of two-dimensional (magnetic) superconductors. We present a spin-charge separation ansatz, appropriate to incorporate holon spin flip, which allows for such a hidden local gauge symmetry to emerge in the effective action. The group is of the form SU(2) ⊗ US(1) ⊗ UE(1), where SU(2) is a local non-Abelian group associated with the spin degrees of freedom, UE(1) is that of ordinary electromagnetism, associated with the electric charge of the holes, and US(1) is a ‘statistical’ Abelian gauge group pertaining to the fractional statistics of holes on the spatial plane. In a certain regime of the parameters of the model, namely strong US(1) and weak SU(2), there is the possibility of dynamical formation of a holon condensate. This leads to a dynamical breaking of SU(2) → U(1). The resulting Abelian effective theory is closely related to an earlier model proposed as the continuum limit of large-spin planar doped antiferromagnets, which lead to an unconventional scenario for two-dimensional parity-invariant superconductivity.
Within the framework of a relativistic non-Abelian gauge theory approach to the physics of spin–charge separation in doped quantum antiferromagnetic planar systems, proposed recently by the authors, we are examining here the effects of constant external magnetic fields on excitations about the superconducting state in the model. The electrically-charged Dirac fermions (holons), describing excitations about specific points on the fermi surface, e.g. those corresponding to the nodes of a d-wave superconducting gap in high-T c cuprates, condense, resulting in the opening of a Kosterlitz–Thouless–like gap (KT) at such nodes. This leads, in general, to a second superconducting phase transition, which occurs at low temperatures[Formula: see text], in addition to the high-T c superconductivity [Formula: see text] due to the bulk of the fermi surface for holons in a (d-wave) spin–charge separated superconductor. In the presence of strong external magnetic fields at the surface regions of the planar superconductor, in the direction perpendicular to the superconducting planes, these KT gaps appear to be enhanced. Our preliminary analysis, based on analytic Schwinger–Dyson treatments, seems to indicate that for an even number of Dirac fermion species, required in our model as a result of gauging a particle–hole SU(2) symmetry, Parity or Time Reversal violation does not necessarily occurs. Based on these considerations, we argue that recent experimental findings, concerning thermal conductivity plateaux of quasiparticles in planar high-T c cuprates in strong external magnetic fields, may indicate the presence of such KT gaps, caused by charged Dirac-fermion excitations in these materials, as suggested in the above model.
In the context of extended t-J models, with intersite Coulomb interactions, nodal liquids are discussed. We use the spin-charge separation ansatz as applied to the nodes of a d-wave superconducting gap. Such a situation may be of relevance to the physics of high-temperature superconductivity. We point out the possibility that at certain points of the parameter space supersymmetric points may occur, characterized by dynamical supersymmetries between the spinon and holon degrees of freedom, which are quite different from the symmetries in conventional supersymmetric t-J models. Such symmetries pertain to the continuum effective field theory of the nodal liquid, and one's hope is that the ancestor lattice model may differ from the continuum theory only by renormalization-group irrelevant operators in the infrared. We give plausible arguments that nodal liquids at such supersymmetric points are characterized by superconductivity of Kosterlitz-Thouless type.
Using a SU(2) X U(1) gauge theory for a t-J model around a node of the Fermi surface, we discuss patterns of dynamical symmetry breaking, which may lead to a pseudogap phase and to the appearance of narrow one-dimensional spatial structures, induced by the presence of holes. A possible connection with stripe phases is briefly discussed by passing to an appropriate dual theory. We discuss confinement properties of spinons and holons and derive the spectrum of the (gapful) physical excitations which are composites of holons corresponding to '`mesons', and composites of spinons corresponding to `baryons'. (7 References).