Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Hidden Non-Abelian Gauge Symmetries in Doped

Planar Antiferromagnets

Published Jan 1, 1996• 0 citations
OpenAlex

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 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.

Related papers

Hidden non-Abelian gauge symmetries in doped planar antiferromagnets

K. Farakos, Nick E. Mavromatos

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.

arXiv:cond-mat/9611072•Physical review. B, Condensed matter•Feb 1, 1998•36 citations

Gauge-Theory Approach to Planar Doped Antiferromagnets and External Magnetic Fields

K. Farakos, Nick E. Mavromatos

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.

arXiv:cond-mat/9710288•International Journal of Modern Physics B•Mar 30, 1998•42 citations

TOWARDS EXACT RESULTS IN NODAL ANTIFERROMAGNETIC PLANAR LIQUIDS

Jean Alexandre, Nick E. Mavromatos, Sarben Sarkar

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.

arXiv:cond-mat/0303611•International Journal of Modern Physics B•May 10, 2003•8 citations

A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z$_{2}$ spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator

Chenglong Jia, Ki‐Seok Kim

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 Z$_{2}$, 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.

arXiv:0811.2626•Nov 17, 2008•0 citations

Gauge theory of high temperature superconductivity

G. Baskaran

Superconductivity in the strongly correlated electronic systems described by the Hubbard model for slightly less than half-filled band is shown to arise from the condensation of charge + e holons which are bosons. The holon effective mass is found to be very close to that of the band electrons and they have a strong nearest neighbour repulsion induced by the spin fluctuations. They interact with an U(1) part of the collective SU(2) gauge field (named S-gauge field) of the spin system. This results in spontaneous symmetry breaking of the holon field and the appearance of the Anderson-Higgs phenomenon. The interesting possibility of the SU(2) gauge field-spinon coupled system retaining some gapless excitation spectrum inspite of the spontaneous symmetry breaking in the holon field is pointed out.

Physica Scripta•Jan 1, 1989•48 citations

Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order

Paulo Forni, Pietro M. Bonetti, Henrik Müller-Groeling +2 more

We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model in the framework of a SU(2) gauge theory of fluctuating magnetic order. The electrons are fractionalized in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons are treated in a renormalized mean-field theory and order in a Néel or spiral magnetic state in a broad range around half filling below a transition temperature T * . Fluctuations of the spin orientation are captured by the spinons. Their dynamics is governed by a nonlinear sigma model, with spin stiffnesses computed microscopically from the pseudospin susceptibility of the chargons. The SU(2) gauge group is higgsed in the chargon sector, and the spinon fluctuations prevent breaking of the physical spin symmetry at any finite temperature. The electron spin susceptibility obtained from the gauge theory shares many features with experimental observations in the pseudogap regime of cuprate superconductors: the dynamical spin susceptibility S ( q , ω ) has a spin gap, the static uniform spin susceptibility κ s decreases strongly with temperature below T * , and the NMR relaxation rate T 1 − 1 vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, S ( q , ω ) exhibits nematicity below a transition temperature T nem < T * , and at larger hole doping in the entire pseudogap regime below T * .

arXiv:2509.07826•Physical review. B./Physical review. B•Dec 8, 2025•2 citations
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.
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 ${\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}}_{S}(1)\ensuremath{\bigotimes}{\mathrm{U}}_{\mathrm{em}}(1),$ where SU(2) is a local non-Abelian group associated with the spin degrees of freedom, Uem(1){\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 $\mathrm{SU}(2)\ensuremath{\rightarrow}\mathrm{U}(1).$ 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.
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.
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.
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.
Superconductivity in the strongly correlated electronic systems described by the Hubbard model for slightly less than half-filled band is shown to arise from the condensation of charge + e holons which are bosons. The holon effective mass is found to be very close to that of the band electrons and they have a strong nearest neighbour repulsion induced by the spin fluctuations. They interact with an U(1) part of the collective SU(2) gauge field (named S-gauge field) of the spin system. This results in spontaneous symmetry breaking of the holon field and the appearance of the Anderson-Higgs phenomenon. The interesting possibility of the SU(2) gauge field-spinon coupled system retaining some gapless excitation spectrum inspite of the spontaneous symmetry breaking in the holon field is pointed out.
We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model in the framework of a SU(2) gauge theory of fluctuating magnetic order. The electrons are fractionalized in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons are treated in a renormalized mean-field theory and order in a Néel or spiral magnetic state in a broad range around half filling below a transition temperature T * . Fluctuations of the spin orientation are captured by the spinons. Their dynamics is governed by a nonlinear sigma model, with spin stiffnesses computed microscopically from the pseudospin susceptibility of the chargons. The SU(2) gauge group is higgsed in the chargon sector, and the spinon fluctuations prevent breaking of the physical spin symmetry at any finite temperature. The electron spin susceptibility obtained from the gauge theory shares many features with experimental observations in the pseudogap regime of cuprate superconductors: the dynamical spin susceptibility S ( q , ω ) has a spin gap, the static uniform spin susceptibility κ s decreases strongly with temperature below T * , and the NMR relaxation rate T 1 − 1 vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, S ( q , ω ) exhibits nematicity below a transition temperature T nem < T * , and at larger hole doping in the entire pseudogap regime below T * .