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arXiv:cond-mat/0210248 · International Journal of Modern Physics B

ASPECTS OF DUALITY IN NODAL LIQUIDS

Nick E. Mavromatos, Sarben Sarkar

Published Jan 30, 2003• 3 citations
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Abstract

Starting from a microscopic t–J like model and a SU(2) spin-charge separation ansatz, a relativistic continuum gauge Lagrangian is obtained in the vicinity of a nodal point of the Fermi surface. The excitations in the pseudogap phase are described by topological excitations in the dual model which has a Z2 global symmetry due to the effect of instantons. Confinement of spinon and holons emerge from this picture. The adjoint and fundamental strings are associated with stripes. As the spin gap decreases a local Z2 symmetry emerges.

DOI
10.1142/s0217979203015747

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Starting from a microscopic t–J like model and a SU(2) spin-charge separation ansatz, a relativistic continuum gauge Lagrangian is obtained in the vicinity of a nodal point of the Fermi surface. The excitations in the pseudogap phase are described by topological excitations in the dual model which has a Z2 global symmetry due to the effect of instantons. Confinement of spinon and holons emerge from this picture. The adjoint and fundamental strings are associated with stripes. As the spin gap decreases a local Z2 symmetry emerges.
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'.
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).
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.
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.
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{n}_{i}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.
Many popular models of fractionalized spin liquids contain neutral fermionic spinon excitations on a Fermi surface, carrying unit charges under a compact U(1) gauge force. We argue that except at possible critical points, instanton effects generically render such states unstable to confinement in two spatial dimensions, so that all elementary excitations are gauge neutral, and there is no spinon Fermi surface. Similar results are expected to apply to SU(2) spin liquids. However, fractionalized states can appear when the gauge symmetry is broken down to a discrete subgroup by the Higgs mechanism. Our argument generalizes earlier results on confinement in the pure gauge theory, and arguments for the instability of the U(1) ``staggered flux'' and ``algebraic'' spin liquids with a Dirac spectrum for fermionic spinons.