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International Journal of Modern Physics B

Lattice Effects in Flux Phases

Benoît Douçot

Published Mar 1, 1992• 0 citations
Publisher

Abstract

The uniform flux phases of the t-J model are studied using a slave boson representation. The gaussian fluctuations around the mean field saddle point are calculated. A key feature is the cancellation of Hall conductances of the spinons and the holons, in the limit of small doping. This cancellation leads to a pole in the global electromagnetic response function, in a mechanism which is very similar to anyon superconductivity. Our main focus has been to evaluate the Hall conductance of the global system as a function of frequency and wave vector. Using various examples, we show that because of the cancellation of the two Hall conductances in the static and long wave-length limit, the behaviour of the global system is very sensitive to lattice effects. For instance, P. Wiegmann has found that the global Hall conductance vanishes in the static and long wave length limit, if one uses the response functions for the two dimensional continuous system. However, a direct calculation of the response functions starting from the Hofstadter spectrum leads to a finite Hall conductance in the absence of an external field. We show how this formalism can be used to calculate the local magnetic field which muons are expected to measure. The electric field of the muons induces a finite Hall current which in turn creates a finite magnetic field at the muon sites. Screening of the magnetic field by the Meissner effect has been taken into account and dielectric screening as well. Preliminary results indicate that the predicted fields are approximately one order of magnitude larger than the upper bound from experimental results obtained by the Vancouver group.

DOI
10.1142/s0217979292000335

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The uniform flux phases of the t-J model are studied using a slave boson representation. The gaussian fluctuations around the mean field saddle point are calculated. A key feature is the cancellation of Hall conductances of the spinons and the holons, in the limit of small doping. This cancellation leads to a pole in the global electromagnetic response function, in a mechanism which is very similar to anyon superconductivity. Our main focus has been to evaluate the Hall conductance of the global system as a function of frequency and wave vector. Using various examples, we show that because of the cancellation of the two Hall conductances in the static and long wave-length limit, the behaviour of the global system is very sensitive to lattice effects. For instance, P. Wiegmann has found that the global Hall conductance vanishes in the static and long wave length limit, if one uses the response functions for the two dimensional continuous system. However, a direct calculation of the response functions starting from the Hofstadter spectrum leads to a finite Hall conductance in the absence of an external field. We show how this formalism can be used to calculate the local magnetic field which muons are expected to measure. The electric field of the muons induces a finite Hall current which in turn creates a finite magnetic field at the muon sites. Screening of the magnetic field by the Meissner effect has been taken into account and dielectric screening as well. Preliminary results indicate that the predicted fields are approximately one order of magnitude larger than the upper bound from experimental results obtained by the Vancouver group.
We investigate certain generalized flux phases arising in a mean-field approach to the t-J model. First we establish that the energy of noninteracting electrons moving in a uniform magnetic field has an absolute minimum as a function of the flux at exactly one flux quantum per particle. Using this result we show that if the hard-core nature of the hole bosons is taken into account, then the generalized flux states in the mean-field approximation constitute a solution where both the spinons and the holons experience an average flux of one flux quantum per particle. We elaborate the relation to the integer and fractional quantum Hall effect. Based on this analogy one expects that only states with certain fractional fillings (ν=1/odd integer) are stable against the fluctuations of the (gauge) field. We speculate that at arbitrary fillings the system minimizes its energy by phase separating into these stable states. Finally we work out the ground state energy for nonuniform (staggered) flux phases and establish that the often claimed equivalence of frustration and doping does not hold for these states.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
Using a large-N slave-boson formulation of the t-J model on the square lattice that has explicit spinon-holon decoupling of the correlated electron, we study the stability and electromagnetic response of the commensurate flux phase in the limit near half filling. A region of stability for the flux phase is found located between a dimer phase region near half filling and a fluxless metallic phase region far from half filling. The commensurate flux phase itself is found to be a superconductor of the anyon type. Furthermore, it is shown that the parity--time-reversal--violating characteristic of this phase results in a frequency-dependent Faraday effect. This effect manifests itself as a zero-field Hall effect in the low-frequency limit, where the off-diagonal conductance scales with the hole concentration. Associated with this result, it is also found that the commensurate flux phase supports a series of optical absorption peaks at energies on the order of J. Lastly, inclusion of instanton tunneling events in the effective gauge-field action results in the confinement of the spinon and holon degrees of freedom. This confinement effect, however, weakens exponentially as one approaches the Mott transition. The present results are discussed in the context of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting oxides.
We study wave functions for generalized flux phases by the variational Monte Carlo method. Flux tubes are attached to the holes, which produce additional phase factors besides those due to the motion of electrons. The phase factors cancel each other when the electrons and holes interchange position at some special electron densities and, as a result, there are no orbital currents in these states. We investigate especially the one-third filled case and find a slightly lower kinetic energy than the original commensurate flux phase. We also calculate the chirality to confirm that time-reversal symmetry is also broken in these states. The analogy to the quantum-Hall-effect wave functions leads us to study modified forms of off-diagonal long-range order in the pair-correlation function. The existence of this long-range order is shown explicitly by variational Monte Carlo calculations and renormalized mean-field approximations. The flux phases do not have the usual off-diagonal long-range order but do have a modified form similar to that in the quantum Hall effect. The relationships to the slave-boson mean-field theories and anyon systems are also discussed.
I consider a gas of ``free'' anyons with statistical parameter \ensuremath{\delta}, with hard cores, on a two-dimensional square lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a Chern-Simons gauge theory with coupling \ensuremath{\theta}=1/2\ensuremath{\delta}. At the semiclassical level, the system is found to be equivalent to a gas of fermions, with the same density, in an average effective magnetic field \ensuremath{\rho}/\ensuremath{\theta}. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If \ensuremath{\delta}=\ensuremath{\pi}/m and the density \ensuremath{\rho}=r/q, with m, r, and q integers, the system is a superfluid, provided that q is larger than twice the largest common factor of m and r. If q is even and the system is half filled, the state may be either a superfluid or a quantum Hall phase. For all other values of \ensuremath{\rho} and \ensuremath{\delta}, compatible with integer filling of the Landau bands, the system is in a quantum Hall phase. The dynamical stability of the superfluid state is ensured by the topological invariance of the quantized Hall conductance of the fermion problem. I find a close analogy between anyon superconductivity and the Schwinger mechanism. The effective Lagrangian for the low-energy modes coupled to the electromagnetic field is derived. The energies of fermion and flux states are logarithmically divergent, but finite for the anyon state. The system has flux quantization, a zero-temperature Hall effect with a quantized Hall conductance, Meissner effect, charged vortices, screening with induced magnetic fields for static charges, and different masses for the longitudinal and transverse components of the electromagnetic field.
A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and N levels per site is considered. This is a model which exhibits the integer quantum Hall effect (IQHE) in the presence of disorder. It presents an alternative to the continuous picture for the IQHE with Landau levels. The large- N limit can be solved: two Hall transitions appear and there is an interpolating behaviour between the two Hall plateaux. Although this approach to the IQHE is different from the traditional one with Landau levels because of different symmetries (continuous for Landau levels and discrete here), some characteristic features are reproduced. For instance, the slope of the Hall conductivity is infinite at the transition points and the electronic states are delocalized only at the transitions.