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arXiv:0709.4550 · Physical Review B

Strong-coupling analysis of QED3 for excitation spectrum broadening in the undoped high-temperature superconductors

Takao Morinari

Published Feb 27, 2008• 1 citation
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Abstract

Theory of quantum electrodynamics in three spatial-time dimensions is applied to the two-dimensional $S=1∕2$ quantum Heisenberg antiferromagnet in order to investigate a doped hole in high-temperature superconductors. Strong coupling analysis of the U(1) gauge field interaction is carried out to describe spectral broadening observed in the undoped compounds. It is found that the fermionic quasiparticle spectrum is of Gaussian form with the width about $3J$, with $J$ being the superexchange interaction energy. The energy shift of the spectrum is on the order of the quasiparticle bandwidth, which suggests that the system is in the strong coupling regime with respect to the gauge field interaction describing the phase fluctuations about the $\ensuremath{\pi}$-flux state.

DOI
10.1103/physrevb.77.075128

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Theory of quantum electrodynamics in three spatial-time dimensions is applied to the two-dimensional S=1∕2S=1∕2S=1∕2 quantum Heisenberg antiferromagnet in order to investigate a doped hole in high-temperature superconductors. Strong coupling analysis of the U(1) gauge field interaction is carried out to describe spectral broadening observed in the undoped compounds. It is found that the fermionic quasiparticle spectrum is of Gaussian form with the width about 3J3J3J, with JJJ being the superexchange interaction energy. The energy shift of the spectrum is on the order of the quasiparticle bandwidth, which suggests that the system is in the strong coupling regime with respect to the gauge field interaction describing the phase fluctuations about the \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux state.
It is argued that in two-dimension duality connects the CP1 representation of the S = 1/2 antiferromagnetic Heisenberg model with the Schwinger model in which Dirac fermions are interact via a U(1) gauge field. Application of this duality to underdoped high-temperature superconductors suggests that the high-energy fermionic excitation at the Mott insulating parent compound turns out to be a low-lying excitation in the spin disordered regime. A picture for high-temperature superconductivity is proposed.
Quantum electrodynamics in 2+1 dimensions (QED3{\mathrm{QED}}_{3}QED3​) is a strongly coupled conformal field theory (CFT) of a U(1) gauge field coupled to 2N2N2N two-component massless fermions. The N=2N=2N=2 CFT has been proposed as a ground state of the spin-1/2 kagome Heisenberg antiferromagnet. We study QED3{\mathrm{QED}}_{3}QED3​ in the presence of weak quenched disorder in its two spatial directions. When the disorder explicitly breaks the fermion flavor symmetry from SU(2N)\mathrm{SU}(2N)SU(2N) $\ensuremath{\rightarrow}$ U(1) $\ifmmode\times\else\texttimes\fi{}$ SU(N)\mathrm{SU}(N)SU(N) but preserves time-reversal symmetry, we find that the theory flows to a nontrivial fixed line at nonzero disorder with a continuously varying dynamical critical exponent z>1z>1z>1. We determine the zero-temperature flavor (spin) conductivity along the critical line. Our calculations are performed in the large-NNN limit, and the disorder is handled using the replica method.
Quantum electrodynamics in 2+1 dimensions ( QED3 ) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated J1−J2 Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED3 , in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of QED3 , which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by QED3 . Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to N=48 sites. Published by the American Physical Society 2024
We study the effect of gapless quasiparticles in a d-wave superconductor on the T=0T=0T=0 end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to three-dimensional XY\mathrm{XY}XY phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions, the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted XY\mathrm{XY}XY universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields N, and we estimate the correlation length exponent $(\ensuremath{\nu}=0.65)$ and the vortex field anomalous dimension $({\ensuremath{\eta}}_{\ensuremath{\Phi}}=\ensuremath{-}0.48)$ at the quantum critical point for the physical case N=2.N=2.N=2. The stable critical point in the theory disappears for the number of Dirac fermions N>Nc,N>{N}_{c},N>Nc​, with ${N}_{c}\ensuremath{\approx}3.4$ in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.
The low-energy spin excitations in the flux phase of the (2+1)-dimensional large-nnn SU(n)\mathrm{SU}(n)SU(n)Heisenberg antiferromagnet are relativistic fermions coupled to a U(1) gauge field. These excitations are studied in the physical n=2n=2n=2 case with the use of a 1n\frac{1}{n}n1​ expansion. A Chern-Simons term is included to remove gauge configurations forbidden in the n=2n=2n=2 theory.
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.