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arXiv:cond-mat/9611072 · Physical review. B, Condensed matter

Hidden non-Abelian gauge symmetries in doped planar antiferromagnets

K. Farakos, Nick E. Mavromatos

Published Feb 1, 1998• 36 citations
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Abstract

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, ${\mathrm{U}}_{\mathrm{em}}(1)$ is that of ordinary electromagnetism, associated with the electric charge of the holes, and ${\mathrm{U}}_{S}(1)$ 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 ${\mathrm{U}}_{S}(1)$ 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.

DOI
10.1103/physrevb.57.3017

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Abstract The 2D Hubbard model with large repulsion is an important problem in condensed matter physics. At half filling, its ground state is an antiferromagnet (AMF). The dope AMF below half filling is believed to capture the physics of high Tc superconductors. And the fermion excitation of this dope AMF is theorized as splitting up into holons and spinons that carry charge and spin separately. It is believed that these exotic holons and spinons are the origins of the unusual properties of high Tc superconductors. Despite the interests in holons and spinons, the direct observations of these excitations remain difficult in solid state experiments. Here, we show that with the rapid advances in the experimental techniques in cold atoms, the direct observation of holons is possible in quantum quench dynamic processes in cold atom settings. We show that the well-known holon-strings generated by the motion of a holon as well as their interferences can be detected by the measurements spin–spin correlations and demonstrate the presence of the Marshall phase associated with a holon string reflecting an underlying AMF background. Moreover, we show that the interferences of the holon strings make a holon propagate anisotropically, with a diffusion pattern clearly distinct from that of spinless fermions. At the same time, we show that these interferences lead to a large suppression in magnetic order in the region swept through by the strings (even to about 95% for some bond). We further demonstrate the Marshall phase of the holon-strings by comparing the dynamics of holon in the tJ model with that of the so-called σ t J -model, which is the tJ model with the Marshall phase removed. The holons in these models propagate entirely differently.

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We investigate the possibility of hidden non-Abelian local phase symmetries in large-UUU 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)\ensuremath⨂US(1)\ensuremath⨂Uem(1),{\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}}_{S}(1)\ensuremath{\bigotimes}{\mathrm{U}}_{\mathrm{em}}(1),SU(2)\ensuremath⨂US​(1)\ensuremath⨂Uem​(1), where SU(2) is a local non-Abelian group associated with the spin degrees of freedom, Uem(1){\mathrm{U}}_{\mathrm{em}}(1)Uem​(1) is that of ordinary electromagnetism, associated with the electric charge of the holes, and US(1){\mathrm{U}}_{S}(1)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){\mathrm{U}}_{S}(1)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)\ensuremath→U(1).\mathrm{SU}(2)\ensuremath{\rightarrow}\mathrm{U}(1).SU(2)\ensuremath→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.
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.
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.
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.
A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z2_{2}2​ spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator
We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromagnetic state, analogous to the U(1) spin liquid phase in the slave-boson approach of the t-J model. We argue that the emergent U(1) gauge structure in this approach is based on a simplified picture for antiferromagnetic correlations. Considering that dynamics of doped holes frustrates a collinear antiferromagnetic spin configuration, we show that doped holes enhance ferromagnetic spin correlations and result in a complex magnetic structure. The presence of such a complex spin texture reduces the U(1) gauge structure down to Z2_{2}2​, thus a different effective field theory results for the spin-gapped non-Fermi liquid metal at low temperatures because there are no gapless U(1) gauge fluctuations.
We propose doping SU(3)SU(3)SU(3)-symmetric spin liquids as a route toward charge-6e6e6e superconductivity. This generalizes the idea of constructing charge-4e4e4e superconductivity from doped SU(4)SU(4)SU(4)-symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with SU(3)SU(3)SU(3) spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped Z3\mathbb{Z}_3Z3​ quantum spin liquid and SU(3)SU(3)SU(3)-related chiral spin liquids. Doping a Z3\mathbb{Z}_3Z3​ quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge-3e3e3e fermionic trions. Pairing these trions gives a time-reversal-symmetric charge-6e6e6e superconductor. Doping Abelian SU(3)1SU(3)_1SU(3)1​ and SU(6)1SU(6)_1SU(6)1​ chiral spin liquids yields chiral charge-6e6e6e superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian SU(3)2SU(3)_2SU(3)2​ chiral spin liquid leads to a non-Abelian chiral charge-6e6e6e superconductor intertwined with SO(3)−3SO(3)_{-3}SO(3)−3​ topological order and supporting non-Abelian h/(6e)h/(6e)h/(6e) superconducting vortices. We also identify several other phases, including Z3\mathbb{Z}_3Z3​ orthogonal metal, quantum anomalous Hall (crystal) phases enriched by Z3\mathbb{Z}_3Z3​ or Z2\mathbb{Z}_2Z2​ topological order, SU(3)SU(3)SU(3)-breaking charge-2e2e2e superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped SU(3)SU(3)SU(3) spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge-6e6e6e superconductivity.
Abstract The 2D Hubbard model with large repulsion is an important problem in condensed matter physics. At half filling, its ground state is an antiferromagnet (AMF). The dope AMF below half filling is believed to capture the physics of high Tc superconductors. And the fermion excitation of this dope AMF is theorized as splitting up into holons and spinons that carry charge and spin separately. It is believed that these exotic holons and spinons are the origins of the unusual properties of high Tc superconductors. Despite the interests in holons and spinons, the direct observations of these excitations remain difficult in solid state experiments. Here, we show that with the rapid advances in the experimental techniques in cold atoms, the direct observation of holons is possible in quantum quench dynamic processes in cold atom settings. We show that the well-known holon-strings generated by the motion of a holon as well as their interferences can be detected by the measurements spin–spin correlations and demonstrate the presence of the Marshall phase associated with a holon string reflecting an underlying AMF background. Moreover, we show that the interferences of the holon strings make a holon propagate anisotropically, with a diffusion pattern clearly distinct from that of spinless fermions. At the same time, we show that these interferences lead to a large suppression in magnetic order in the region swept through by the strings (even to about 95% for some bond). We further demonstrate the Marshall phase of the holon-strings by comparing the dynamics of holon in the tJ model with that of the so-called σ t J -model, which is the tJ model with the Marshall phase removed. The holons in these models propagate entirely differently.