arXiv subjects

Eduardo Fradkin

Publications and source records attributed to Eduardo Fradkin.

178 records · Page 10Linked to original sources

arXiv1997

Interacting electrons on a half line coupled to impurities

We generalize the bosonization methods for systems in the half line that we discussed elsewhere, to study the effects of interactions on electronic systems coupled to impurities. We introduce a model for a quantum wire coupled with a quantum dot by a purely capacitive interaction. We show that the effect on the quantum wire is a dynamical boundary condition which reflects the charge fluctuations of the quantum dot. Special attention is given to the role of the fermion boundary conditions and their interplay with the electron interactions on the bosonized effective theory.

cond-mat.mes-hall↗

arXiv1996

Modular Invariance, Self-Duality and The Phase Transition Between Quantum Hall Plateaus

We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting charged particles. One of the models is manifestly invariant under both Duality and Periodic shifts of the statistical angle and, hence, it has a full Modular Invariance. We derive the transformation laws for the correlation functions under the modular group and use them to derive symmetry constraints for the conductances. These allow us to calculate exactly the conductivities at the modular fixed points. We show that, at least at the modular fixed points, the system is critical. Away from the fixed points, the behavior of the model is determined by extra symmetries such as Time Reversal. We speculate that if the natural connection between spin and statistics holds, the model may exhibit an effective analyticity at low energies. In this case, the conductance is completely determined by its behavior under modular transformations.

cond-mat↗

arXiv1996

Kondo effect in flux phases

We consider a band of fermions in two space dimensions with a flux phase (relativistic) dispersion relation coupled to a local magnetic impurity via an $ s-d$ interaction. This model describes spinons of a flux phase and it is also a qualitative model of the quasiparticles in a $d_{x^2-y^2}$ superconductor. We find a zero-temperature phase transition at a finite coupling constant between a weak coupling unscreened impurity state and a strong coupling regime with a Kondo effect. We use large-$N$ methods to study the phase transition in this Kondo system away from marginality. The Kondo energy scales linearly with the distance to the transition . The zero-field magnetic suceptibility at zero temperature diverges linearly. Similar behavior is found in the $T$-matrix which shows a resonance at the Kondo scale. However, in addition to this simple scaling, we always find the presence of logarithmic corrections-to-scaling. Such behavior is typical of systems at an upper critical dimension. We derive an effective fermion model in one space dimension for this problem. Unlike the usual Kondo problem, this system has an intrinsic multichannel nature which follows from the spinor structure of $2+1$-dimensional relativistic fermions.

cond-mat↗

arXiv1996

Bilayers of Chiral Spin States

We study the behavior of two planes of Quantum Heisenberg Antiferromagnet in the regime in which a Chiral Spin Liquid is stabilized in each plane. The planes are coupled by an exchange interaction of strength $J_3$. We show that in the regime of small $J_3$ (for both ferromagnetic {\it and} antiferromagnetic coupling), the system dynamically selects an \underline{antiferromagnetic} ordering of the ground state {\it chiralities} of the planes. For the case of an antiferromagnetic interaction between the planes, we find that, at some critical value $J_3^c$ of the inter-layer coupling, there is a phase transition to a valence-bond state on the interlayer links. We derive an effective Landau-Ginzburg theory for this phase transition. It contains two $U(1)$ gauge fields coupled to the order parameter field. We study the low energy spectrum of each phase. In the condensed phase an ``anti-Higgs-Anderson" mechanism occurs. It effectively restores time-reversal invariance by rendering massless one of the gauge fields while the other field locks the chiral degrees of freedom locally. There is no phase transition for ferromagnetic couplings.

cond-mat↗

arXiv1995

Gauge Invariance and Finite Temperature Effective Actions of Chern-Simons Gauge Theories with Fermions

We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be {\it at most} an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition should hold there too. We discuss consequences of our results to the thermodynamics of anyon superfluids and fractional quantum Hall systems.

hep-th↗

arXiv1995

Exact effective action for fermions in one dimension with backscattering at a boundary

We report exact results for the partition function for free Dirac fermions on a half line with physically sensible boundary conditions. An exact effective action for general backscattering amplitudes is derived. The action also includes the effects of both a (time-dependent) forward scattering amplitude and a dynamical chiral twist of the fermion boundary conditions. For a small backscattering amplitude, the effective action has the expected boundary Sine-Gordon form. We discuss applications of our results to one-dimensional Fermi systems with local backscattering.

cond-mat↗

arXiv1995

Bosonization rules in $1/2 +1$ dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green's function and determine the effects of the boundaries on its analytic structure.

cond-mat↗

arXiv1995

Bosonization of Three Dimensional Non-Abelian Fermion Field Theories

We discuss bosonization in three dimensions of an $SU(N)$ massive Thirring model in the low-energy regime. We find that the bosonized theory is related (but not equal) to $SU(N)$ Yang-Mills-Chern-Simons gauge theory. For free massive fermions bosonization leads, at low energies, to the pure $SU(N)$ (level $k=1$) Chern-Simons theory.

hep-th↗

arXiv1994

Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers

We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible optical properties. In general, for the so called $(m, m, n)$ states, we find that the spectrum of collective excitations has a gap, and the wave function has the Jastrow-Slater form, with the exponents determined by the coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode which may be related with the spontaneous appearance of the interlayer coherence. Our results also indicate that the gapless mode makes a contribution to the wave function of the $(m,m,m)$ states analogous to the phonon contribution to the wave function of superfluid $\rm{He}_4$. We calculate the Hall conductance, and the charge and statistics of the quasiparticles. We also present an $SU(2)$ generalization of this theory relevant to spin unpolarized or partially polarized single layers.

cond-mat↗

arXiv1994

Chern_simons Theory of the Anisotropic Quantum Heisenberg Antiferromagnet on a Square Lattice

We consider the anisotropic quantum Heisenberg antiferromagnet (with anisotropy $λ$) on a square lattice using a Chern-Simons (or Wigner-Jordan) approach. We show that the Average Field Approximation (AFA) yields a phase diagram with two phases: a Ne{è}l state for $λ>λ_c$ and a flux phase for $λ<λ_c$ separated by a second order transition at $λ_c<1$. We show that this phase diagram does not describe the $XY$ regime of the antiferromagnet. Fluctuations around the AFA induce relevant operators which yield the correct phase diagram. We find an equivalence between the antiferromagnet and a relativistic field theory of two self-interacting Dirac fermions coupled to a Chern-Simons gauge field. The field theory has a phase diagram with the correct number of Goldstone modes in each regime and a phase transition at a critical coupling $λ^* > λ_c$. We identify this transition with the isotropic Heisenberg point. It has a non-vanishing Ne{\` e}l order parameter, which drops to zero discontinuously for $λ<λ^*$.

hep-th↗

arXiv1993

Separation of Spin and Charge Quantum Numbers in Strongly Correlated Systems

In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurence of spin and charge separation. Specifically, we discuss this issue in the context of the Heisenberg model for spin-1/2 on a square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor antiferromagnetic couplings. Our formulation makes explicit the existence of a local SU(2) gauge symmetry once the spin-1/2 operators are replaced by bound states of spinons. The mean-field theory for the spinons is solved numerically as a function of the ratio $J_2/J_1$ for the so-called s-RVB Ansatz. A second order phase transition exists into a novel flux state for $J_2/J_1>(J_2/J_1)_{\rm cr}$. We identify the range $0<J_2/J_1<(J_2/J_1)_{\rm cr}$ as the s-RVB phase. It is characterized by the existence of a finite gap to the elementary excitations (spinons) and the breakdown of all the continuous gauge symmetries. An effective continuum theory for the spinons and the gauge degrees of freedom is constructed just below the onset of the flux phase. We argue that this effective theory is consistent with the deconfinement of the spinons carrying the fundamental charge of the gauge group. We contrast this result with the study of the one dimensional quantum antiferromagnet within the same approach. We show that in the one dimensional model, the spinons of the gauge picture are always confined and thus cannot be identified with the gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.

cond-mat↗

arXiv1993

Bosonization of Fermi liquids

We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.

cond-mat↗

arXiv1993

Bosonization of the Low Energy Excitations of Fermi Liquids

We bosonize the low energy excitations of Fermi Liquids in any number of dimensions in the limit of long wavelengths. The bosons are coherent superposition of electron-hole pairs and are related with the displacement of the Fermi Surface in some arbitrary direction. A coherent-state path integral for the bosonized theory is derived and it is shown to represent histories of the shape of the Fermi Surface. The Landau equation for the sound waves is shown to be exact in the semiclassical approximation for the bosons.

cond-mat↗

arXiv1993

The Thermodynamics of Quantum Systems and Generalizations of Zamolodchikov's C-theorem

In this paper we examine the behavior in temperature of the free energy on quantum systems in an arbitrary number of dimensions. We define from the free energy a function $C$ of the coupling constants and the temperature, which in the regimes where quantum fluctuations dominate, is a monotonically increasing function of the temperature. We show that at very low temperatures the system is controlled by the zero-temperature infrared stable fixed point while at intermediate temperatures the behavior is that of the unstable fixed point. The $C$ function displays this crossover explicitly. This behavior is reminiscent of Zamolodchikov's $C$-theorem of field theories in 1+1 dimensions. Our results are obtained through a thermodynamic renormalization group approach. We find restrictions on the behavior of the entropy of the system for a $C$-theorem-type behavior to hold. We illustrate our ideas in the context of a free massive scalar field theory, the one-dimensional quantum Ising Model and the quantum Non-linear Sigma Model in two space dimensions. In regimes in which the classical fluctuations are important the monotonic behavior is absent.

cond-mat↗

arXiv1992

Response functions and Spectrum of Collective Excitations of Fractional Quantum Hall Effect Systems

We calculate the electromagnetic response functions of a Fractional Quantum Hall system within the framework of the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before. Our results are valid in a semiclassical expansion around the average field approximation (AFA). We reexamine the AFA and the role of fluctuations. We argue that, order-\-by-\-order in the semiclassical expansion, the response functions obey the correct symmetry properties required by Galilean and Gauge Invariance and by the incompressibility of the fluid. In particular, we find that the low-momentum limit of the semiclassical approximation to the response functions is exact and that it saturates the $f$-sum rule.We obtain the spectrum of collective excitations of FQHE systems in the low-momentum limit. We find a rich spectrum of modes which includes a host of quasiparticle- quasihole bound states and, in general,two collective modes coalescing at the cyclotron frequency. The Hall conductance is obtained from the current-density correlation function, and it has the correct value already at the semiclassical level. We applied these results to the problem of the screening of external charges and fluxes by the electron fluid, and obtained asymptotic expressions of the charge and current density profiles, for different types of interactions. Finally, we reconsider the anyon superfluid within our scheme and derive the spectrum of collective modes for interacting hard-core bosons and semions. In addition to the gapless phase mode, we find a set of gapped collective modes.

cond-mat↗

arXiv1992

Ground state wave functionals for $1+1$-dimensional fermion field theories

We use path-\-integral methods to derive the ground state wave functions of a number of two-\-dimensional fermion field theories and related systems in one-\-dimensional many body physics. We derive the exact wave function for the Thirring/Luttinger and Coset fermion models and apply our results to derive the universal behavior of the wave functions of the Heisenberg antiferromagnets and of the Sutherland model. We find explicit forms for the wave functions in the density and in the Grassmann representations. We show that these wave functions always have the Jastrow factorized form and calculated the exponent. Our results agree with the exponents derived from the Bethe Ansatz for the Sutherland model and the Haldane-\-Shastri spin chain but apply to all the systems in the same universality class.

hep-th↗