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arXiv:cond-mat/0006234

Nodal Liquids and Duality

Nick E. Mavromatos, Sarben Sarkar

Published Jun 14, 2000• 0 citations
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Abstract

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'.

DOI
10.48550/arxiv.cond-mat/0006234

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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).
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.
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.
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.
Using a phenomenological model, we discuss the consequences of spinon-holon binding in the U(1)U(1)U(1) slave-boson approach to $t\text{\ensuremath{-}}J$ model in the weak-coupling limit. We find that spinon-holon binding produces a pseudogap normal state with a segmented Fermi surface and the superconducting state is formed by opening an ``additional'' ddd-wave gap on the segmented Fermi surface. The ddd-wave gap merges with the pseudogap smoothly as temperature $T\ensuremath{\rightarrow}0$. The quasiparticles in the superconducting state are coupled to external electromagnetic field with a coupling constant of order ${x}^{\ensuremath{\gamma}∕2}\phantom{\rule{0.3em}{0ex}}(x=\text{hole concentration})$, where $0\ensuremath{\leqslant}\ensuremath{\gamma}\ensuremath{\leqslant}1$.
The compact U(1) gauge field occurs in many fractionalized descriptions of low dimensional quantum magnetism and heavy fermion systems. In this respect a fundamental question about the gauge field is whether it is confined or not in the presence of Fermi surface. In this paper we show that the U(1) gauge field with a possible positive anomalous dimension in the presence of Fermi surface has to be in the confined state, although it is strongly coupled to abundant gapless fermionic excitations near the Fermi surface in two spatial dimensions. This means that some quantum spin liquids and/or fractionalized metallic states described in terms of this kind of gauge fields with positive anomalous dimensions are unstable to other possible symmetry-breaking states, as a result, they are not be appropriate candidates for ground states in related systems. The instability obtained shows some novel features of the quantum spin liquids and/or fractionalized metallic states in the presence of Fermi surface which have not been reported in the literature. The result could be useful for further study in the quantum spin liquids and many related slave-particle gauge theories in strongly correlated electron systems.