arXiv subjects

Chetan Nayak

Publications and source records attributed to Chetan Nayak.

At least 145 records · Page 8Linked to original sources

arXiv2000

Tunneling between coupled Luttinger liquids

We consider the problem of tunneling between spinless 1D Luttinger liquid chains. We show how to map the problem onto the 4-state chiral clock model together with a free boson for the total charge mode. We use a variety of results, some of them exact, from the integrable chiral Potts model and the study of commensurate/incommensurate transitions to deduce the physics of coupled Luttinger liquids. For those intrachain interaction strengths for which interchain tunneling is relevant, we find that it can lead to the formation of symmetric and antisymmetric bands with split Fermi surfaces, depending on the relative strengths of interchain tunneling and interchain interactions. With split Fermi surfaces, the tunneling is coherent. It is not possible to have two gapless Fermi surfaces with the same Fermi momentum when interchain tunneling is relevant. However, interchain interactions can drive the formation of a gap, in which case interchain transport will be incoherent. We comment on the possible relevance of our results to c-axis transport in high-T_c superconductors.

cond-mat.str-el↗

arXiv2000

Bilayer Coherent and Quantum Hall Phases: Duality and Quantum Disorder

We consider a fully spin-polarized quantum Hall system with no interlayer tunneling at total filling factor $ν=1/k$ (where $k$ is an odd integer) using the Chern-Simons-Ginzburg-Landau theory. Exploiting particle-vortex duality and the concept of quantum disordering, we find a large number of possible compressible and incompressible ground states, some of which may have relevance to recent experiments of Spielman {\it et.al.}. We find interlayer coherent compressible states without Hall quantization and interlayer-incoherent incompressible with Hall quantization in addition to the usual $(k,k,k)$ Halperin states, which are both interlayer-coherent and incompressible.

cond-mat.mes-hall↗

arXiv2000

O(4)-Invariant Formulation of the Nodal Liquid

We consider the O(4) symmetric point in the phase diagram of an electron system in which there is a transition between d_{x^2 - y^2} density-wave order and d_{x^2 - y^2} superconductivity. If the pseudospin $SU(2)\subset O(4)$ symmetry is disordered by quantum fluctuations, the Nodal Liquid can result. In this context, we (1) construct a pseudospin $σ$-model; (2) discuss its topological excitations; (3) point out the possibility of a {\it pseudospin-Peierls} state and (4) propose a phase diagram for the underdoped cuprate superconductors.

cond-mat.str-el↗

arXiv2000

Density Wave States of Non-Zero Angular Momentum

We study the properties of states in which particle-hole pairs of non-zero angular momentum condense. These states generalize charge- and spin-density-wave states, in which s-wave particle-hole pairs condense. We show that the p-wave spin-singlet state of this type has Peierls ordering, while the d-wave spin-singlet state is the staggered flux state. We discuss model Hamiltonians which favor p-wave and d-wave density wave order. There are analogous orderings for pure spin models, which generalize spin-Peierls order. The spin-triplet density wave states are accompanied by spin-1 Goldstone bosons, but these excitations do not contribute to the spin-spin correlation function. Hence, they must be detected with NQR or Raman scattering experiments. Depending on the geometry and topology of the Fermi surface, these states may admit gapless fermionic excitations. As the Fermi surface geometry is changed, these excitations disappear at a transition which is third-order in mean-field theory. The singlet d-wave and triplet p-wave density wave states are separated from the corresponding superconducting states by zero-temperature O(4)-symmetric critical points

cond-mat.str-el↗

arXiv1999

Confinement of Slave-Particles in U(1) Gauge Theories of Strongly-Interacting Electrons

We show that slave particles are always confined in U(1) gauge theories of interacting electron systems. Consequently, the low-lying degrees of freedom are different from the slave particles. This is done by constructing a dual formulation of the slave-particle representation in which the no-double occupany constraint becomes linear and, hence, soluble. Spin-charge separation, if it occurs, is due to the existence of solitons with fractional quantum numbers.

cond-mat.str-el↗

arXiv1999

A Kondo impurity in a disordered metal: Anderson's theorem revisited

We consider a local moment which is coupled by a non-random Kondo $J$ to a band of conduction electrons in a random potential. We prove an analog of Anderson's theorem in a large-N limit of this model. The theorem states that when the disorder is weak, the disorder-averaged low-temperature thermodynamics is independent of the strength of the disorder; remarkably, it further states that fluctuation effects in the long-time limit are {\it independent even of the realization of the disorder}. We discuss the relationship of this theorem to theoretical and experimental studies of similar problems.

cond-mat.str-el↗

arXiv1999

Dual Vortex Theory of Strongly Interacting Electrons: Non-Fermi Liquid to the (Hard) Core

As discovered in the quantum Hall effect, a very effective way for strongly-repulsive electrons to minimize their potential energy is to aquire non-zero relative angular momentum. We pursue this mechanism for interacting two-dimensional electrons in zero magnetic field, by employing a representation of the electrons as composite bosons interacting with a Chern-Simons gauge field. This enables us to construct a dual description in which the fundamental constituents are vortices in the auxiliary boson fields. The resulting formalism embraces a cornucopia of possible phases. Remarkably, superconductivity is a generic feature, while the Fermi liquid is not -- prompting us to conjecture that such a state may not be possible when the interactions are sufficiently strong. Many aspects of our earlier discussions of the nodal liquid and spin-charge separation find surprising incarnations in this new framework.

cond-mat.str-el↗

arXiv1999

Schwinger-Keldysh Approach to Disordered and Interacting Electron Systems: Derivation of Finkelstein's Renormalization Group Equations

We develop a dynamical approach based on the Schwinger-Keldysh formalism to derive a field-theoretic description of disordered and interacting electron systems. We calculate within this formalism the perturbative RG equations for interacting electrons expanded around a diffusive Fermi liquid fixed point, as obtained originally by Finkelstein using replicas. The major simplifying feature of this approach, as compared to Finkelstein's is that instead of $N \to 0$ replicas, we only need to consider N=2 species. We compare the dynamical Schwinger-Keldysh approach and the replica methods, and we present a simple and pedagogical RG procedure to obtain Finkelstein's RG equations.

cond-mat.dis-nn↗

arXiv1998

Dual Order Parameter for the Nodal Liquid

The guiding conception of vortex-condensation-driven Mott insulating behavior is central to the theory of the nodal liquid. We amplify our earlier description of this idea and show how vortex condensation in 2D electronic systems is a natural extension of 1D Mott insulating and 2D bosonic Mott insulating behavior. For vortices in an underlying superconducting pair field, there is an important distinction between the condensation of flux hc/2e and flux hc/e vortices. The former case leads to spin-charge confinement, exemplified by the band insulator and the charge-density-wave. In the latter case, spin and charge are liberated leading directly to a 2D Mott insulator exhibiting *spin-charge separation*. Possible upshots include not only the nodal liquid, but also a novel undoped antiferromagnetic insulating phase with gapped excitations exhibiting spin-charge separation.

cond-mat.str-el↗

arXiv1998

Landau-Ginzburg Theories for Non-Abelian Quantum Hall States

We construct Landau-Ginzburg effective field theories for fractional quantum Hall states -- such as the Pfaffian state -- which exhibit non-Abelian statistics. These theories rely on a Meissner construction which increases the level of a non-Abelian Chern-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping Abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor $ν=1$, where the non-Abelian symmetry is a dynamically-generated SU(2) continuous extension of the discrete particle-hole symmetry of the lowest Landau level. We show how the physics of quasiparticles and their non-Abelian statistics arises in this Landau-Ginzburg theory. We describe its relation to edge theories -- where a coset construction plays the role of the Meissner projection -- and discuss extensions to other states.

cond-mat.mes-hall↗

arXiv1998

Quasiparticle transport and localization in high-T_c superconductors

We present a theory of the effects of impurity scattering in d_{x^2-y^2} superconductors and their quantum disordered counterparts, based on a non-linear sigma model formulation. We show the existence, in a quasi-two-dimensional system, of a novel spin-metal phase with a non-zero spin diffusion constant at zero temperature. With decreasing inter-layer coupling, the system undergoes a quantum phase transition (in a new universality class) to a localized spin-insulator. Experimental implications for spin and thermal transport in the high-temperature superconductors are discussed.

cond-mat.supr-con↗

arXiv1998

Wigner Glass, Spin-liquids, and the Metal-Insulator Transition

Recent experiments on the two dimensional electron gas in various semiconductor devices have revealed an unexpected metal-insulator transition and have challenged the previously held assumption that there is no such transition in two dimensions. While the experiments are still at the stage of rapid development, it is becoming evident that they cannot be understood from the conventional perspective of weak interactions. In the present paper, we propose the following. (1) The low-density insulating state is the Wigner Glass, a phase with quasi-long-range translational order and competing ferromagnetic and antiferromagnetic spin-exchange interactions. (2) The transition is the melting of this Wigner Glass, disorder being the agent allowing the transition to be second order. (3) Within the Wigner Glass phase, there are at least two, distinct magnetic ground-states, a ferromagnetic state at very low electron density and a spin-liquid state with a spin pseudo-gap at higher densities. (4) The metallic side of the transition is a non-Fermi liquid. These conclusions are encapsulated in Figure 1 which presents the proposed phase diagram as a function of disorder strength and density; we also suggest experimental signatures of the various phases and transitions.

cond-mat.str-el↗

arXiv1998

Nodal Liquid Theory of the Pseudo-Gap Phase of High-Tc Superconductors

We introduce and study the nodal liquid, a novel zero-temperature quantum phase obtained by quantum-disordering a d-wave superconductor. It has numerous remarkable properties which lead us to suggest it as an explanation of the pseudo-gap state in underdoped high-temperature superconductors. In the absence of impurities, these include power-law magnetic order, a T-linear spin susceptibility, non-trivial thermal conductivity, and two- and one-particle charge gaps, the latter evidenced, e.g. in transport and electron photoemission (which exhibits pronounced fourfold anisotropy inherited from the d-wave quasiparticles). We use a 2+1-dimensional duality transformation to derive an effective field theory for this phase. The theory is comprised of gapless neutral Dirac particles living at the former d-wave nodes, weakly coupled to the fluctuating gauge field of a dual Ginzburg-Landau theory. The nodal liquid interpolates naturally between the d-wave superconductor and the insulating antiferromagnet, and our effective field theory is powerful enough to permit a detailed analysis of a panoply of interesting phenomena, including charge ordering, antiferromagnetism, and d-wave superconductivity. We also discuss the zero-temperature quantum phase transitions which separate the nodal liquid from various ordered phases.

cond-mat.supr-con↗

arXiv1997

A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at $ν=1$ is an $SU(2)_2$ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chern-Simons theory with coupling constant $k=2$. The effective field theories for other Pfaffian states, such as the fermionic one at $ν=1/2$ are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.

cond-mat.mes-hall↗

arXiv1997

A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States

We present an approach to the computation of the non-Abelian statistics of quasiholes in quantum Hall states, such as the Pfaffian state, whose wavefunctions are related to the conformal blocks of minimal model conformal field theories. We use the Coulomb gas construction of these conformal field theories to formulate a plasma analogy for the quantum Hall states. A number of properties of the Pfaffian state follow immediately, including the Berry phases which demonstrate the quasiholes' fractional charge, the abelian statistics of the two-quasihole state, and equal-time ground state correlation functions. The non-Abelian statistics of multi-quasihole states follows from an additional assumption.

cond-mat.mes-hall↗

arXiv1996

Populated Domain Walls

Several experiments suggest that the charge carriers in the normal state of certain cuprate superconductors reside on domain walls. In an earlier paper, we suggested that several aspects of the anomalous dynamical behavior of these materials could be explained, at least qualitatively, on this basis. Here, using results on the ground state energy of the 1-dimensional Hubbard model (soluble by Bethe ansatz techniques) as a function of charge density, we argue that a non-zero charge density localized to domain walls is a very plausible consequence of strong short-range electron-electron repulsion. We also suggest a method to suppress meandering of the walls, and thereby enhance their signature in neutron diffraction.

cond-mat↗

arXiv1996

$2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States

By explicitly identifying a basis valid for any number of electrons, we demonstrate that simple multi-quasihole wavefunctions for the $ν=1/2$ Pfaffian paired Hall state exhibit an exponential degeneracy at fixed positions. Indeed, we conjecture that for $2n$ quasiholes the states realize a spinor representation of an expanded (continuous) nonabelian statistics group $SO(2n)$. In the four quasihole case, this is supported by an explicit calculation of the corresponding conformal blocks in the $c={1\over2}+1$ conformal field theory. We present an argument for the universality of this result, which is significant for the foundations of fractional statistics generally. We note, for annular geometry, an amusing analogue to black hole entropy. We predict, as a generic consequence, glassy behavior. Many of our considerations also apply to a form of the (3,3,1) state.

cond-mat↗

arXiv1996

Possible Electronic Structure of Domain Walls in Mott Insulators

We discuss the quantum numbers of domain walls of minimal length induced by doping Mott insulators, carefully distinguishing between holon and hole walls. We define a minimal wall hypothesis that uniquely correlates the observed spatial structure with the doping level for the low-temperature commensurate insulating state of La$_{2-x}$Ba$_x$CuO$_4$ and related materials at $x={1\over 8}$. We remark that interesting walls can be supported not only by conventional antiferromagnetic but also by orbital antiferromagnetic (staggered flux phase, $d$-density) bulk order. We speculate on the validity of the minimal wall hypothesis more generally, and argue that it plausibly explains several of the most striking anomalous features of the cuprate high-temperature superconductors.

cond-mat↗