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Ziqiang Wang

Publications and source records attributed to Ziqiang Wang.

233 records · Page 13Linked to original sources
arXiv2001

Thermodynamic and Tunneling Density of States of the Integer Quantum Hall Critical State

We examine the long wave length limit of the self-consistent Hartree-Fock approximation irreducible static density-density response function by evaluating the charge induced by an external charge. Our results are consistent with the compressibility sum rule and inconsistent with earlier work that did not account for consistency between the exchange-local-field and the disorder potential. We conclude that the thermodynamic density of states is finite, in spite of the vanishing tunneling density of states at the critical energy of the integer quantum Hall transition.

cond-mat.mes-hall↗
arXiv2001

Superconductivity near Itinerant Ferromagnetic Quantum Criticality

Superconductivity mediated by spin fluctuations in weak and nearly ferromagnetic metals is studied close to the zero-temperature magnetic transition. We solve analytically the Eliashberg equations for p-wave pairing and obtain the normal state quasiparticle self-energy and the superconducting transition temperature $T_c$ as a function of the distance to the quantum critical point. We show that the reduction of quasiparticle coherence and life-time due to scattering by quasistatic spin fluctuations is the dominant pair-breaking process, which leads to a rapid suppression of $T_c$ to a nonzero value near the quantum critical point. We point out the differences and the similarities of the problem to that of the theory of superconductivity in the presence of paramagnetic impurities.

cond-mat.supr-con↗
arXiv2000

Comment on ``Analytic Structure of One-Dimensional Localization Theory: Re-Examining Mott's Law''

The low-frequency conductivity of a disordered Fermi gas in one spatial dimension is governed by the Mott-Berezinskii law $σ(ω) \propto ω^2 \ln ω^2$. In a recent Letter [Phys. Rev. Lett. 84, 1760 (2000)] A. O. Gogolin claimed that this law is invalid, challenging our basic understanding of disordered systems and a massive amount of previous theoretical work. We point out two calculational errors in Gogolin's paper. Once we correct them, the Mott-Berezinskii formula is fully recovered. We also present numerical results supporting the Mott-Berezinskii formula but ruling out that of Gogolin.

cond-mat.mes-hall↗
arXiv2000

Quantum-disordered slave-boson theory of underdoped cuprates

We study the stability of the spin gap phase in the U(1) slave-boson theory of the t-J model in connection to the underdoped cuprates. We approach the spin gap phase from the superconducting state and consider the quantum phase transition of the slave-bosons at zero temperature by introducing vortices in the boson superfluid. At finite temperatures, the properties of the bosons are different from those of the strange metal phase and lead to modified gauge field fluctuations. As a result, the spin gap phase can be stabilized in the quantum critical and quantum disordered regime of the boson system. We also show that the regime of quantum disordered bosons with the paired fermions can be regarded as the strong coupling version of the recently proposed nodal liquid theory.

cond-mat.str-el↗
arXiv2000

Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the non-interacting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but non-zero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency, $ω$, and temperature, $T$, is determined by the scaling variable $ω/T^p$ (where $p$ is the exponent for the temperature dependence of the inelastic scattering rate) and not by $ω/T$, as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent, $p$, and the thermal exponent, $z_T$, in terms of the scaling dimension, $-α< 0$, of the interaction strength and the dynamical exponent $z$ (which has the value $z=2$), obtaining $p=1+2α/z$ and $z_T=2/p$.

cond-mat.mes-hall↗
arXiv1999

Instabilities Toward Charge Density Wave and Paired Quantum Hall State of Half-Filled Landau Levels

We study the stability of spin-resolved Landau levels at electron filling factor $ν=n+1/2$, where n is a positive integer. Representing the half-filled topmost Landau level by fermions and the n filled inner Landau levels by n bosons, coupled to the Chern-Simons gauge fields, we show that the ground states exhibit charge density wave order for $n(n+1/2)>15.54 π(a_B^*)^2 n_e$, where $n_e$ is the 2D carrier density and $a_B^*$ is the effective Bohr radius. We find that the pairing interaction mediated by the fluctuating gauge field is enhanced near the charge density wave instability such that p-wave pairing of the Chern-Simons fermions prevails for $3.49(π{\ab}^2)n_e<n^2(n+1/2)<20.22π(a_B^*)^2 n_e$. The competition between charge density wave order and paired quantum Hall state is discussed in connection to recent experiments.

cond-mat.mes-hall↗
arXiv1999

Compressibility of the Two-Dimensional infinite-U Hubbard Model

We study the interactions between the coherent quasiparticles and the incoherent Mott-Hubbard excitations and their effects on the low energy properties in the $U=\infty$ Hubbard model. Within the framework of a systematic large-N expansion, these effects first occur in the next to leading order in 1/N. We calculate the scattering phase shift and the free energy, and determine the quasiparticle weight Z, mass renormalization, and the compressibility. It is found that the compressibility is strongly renormalized and diverges at a critical doping $δ_c=0.07\pm0.01$. We discuss the nature of this zero-temperature phase transition and its connection to phase separation and superconductivity.

cond-mat.str-el↗
arXiv1999

Bulk Tunneling at Integer Quantum Hall Transitions

The tunneling into the {\em bulk} of a 2D electron system (2DES) in strong magnetic field is studied near the integer quantum Hall transitions. We present a nonperturbative calculation of the tunneling density of states (TDOS) for both Coulomb and short-ranged electron-electron interactions. In the case of Coulomb interaction, the TDOS exhibits a 2D quantum Coulomb gap behavior, $ν(\ve)=C_Q\ave/e^4$, with $C_Q$ a nonuniversal coefficient of quantum mechanical origin. For short-ranged interactions, we find that the TDOS at low bias follows $ν(\ve)/ν(0)=1+(\ave/\ve_0)^γ$, where $γ$ is a universal exponent determined by the scaling dimension of short-ranged interactions.

cond-mat.mes-hall↗
arXiv1998

Conductance Correlations Near Integer Quantum Hall Transitions

In a disordered mesoscopic system, the typical spacing between the peaks and the valleys of the conductance as a function of Fermi energy $E_F$ is called the conductance energy correlation range $E_c$. Under the ergodic hypothesis, the latter is determined by the half-width of the ensemble averaged conductance correlation function: $F= < δg(E_F) δg(E_F + ΔE) >$. In ordinary diffusive metals, $E_c\sim D/L^2$, where $D$ is the diffusion constant and $L$ is the linear dimension of the phase-coherent sample. However, near a quantum phase transition driven by the location of the Fermi energy $E_F$, the above picture breaks down. As an example of the latter, we study, for the first time, the conductance correlations near the integer quantum Hall transitions of which $E_F$ is a critical coupling constant. We point out that the behavior of $F$ is determined by the interplay between the static and the dynamic properties of the critical phenomena.

cond-mat.mes-hall↗
arXiv1998

Conductances, Conductance Fluctuations, and Level Statistics on the Surface of Multilayer Quantum Hall States

The transport properties on the two-dimensional surface of coupled multilayer heterostructures are studied in the integer quantum Hall states. We emphasize the criticality of the surface state and the phase coherent transport properties in the thermodynamic limit. A new, stable numerical algorithm for large scale conductance calculations in the transfer matrix approach is discussed in detail. It is then applied to a directed network model describing the quantum mechanical tunneling and impurity scattering of the multilayer edge states. We calculate the two-probe conductance in the direction parallel to the external magnetic field, its fluctuations and statistical distributions as a function of the interlayer tunneling strength. Using finite size scaling, the asymptotic scaling functions of the ensemble averaged conductance and the conductance fluctuations are calculated for a fixed aspect ratio and found to be in remarkable agreement with the analytical results obtained using the supersymmetric nonlinear $σ$-model approach. The conductance distribution is determined in the quasi-one-dimensional metallic, insulating, as well as the crossover regime where comparisons are made to that at the single-layer quantum Hall transition. We present, for the first time, a detailed study of the level statistics in the eigenvalue spectrum of the transfer matrix. Coexistence of metallic and insulating statistics is observed in the crossover regime, which is attributed to the emergence of a finite range level repulsion in the crossover regime, separating the metallic (Wigner-surmise) behavior at small level spacings from the insulating (uncorrelated or Poisson) behavior at large level spacings.

cond-mat.mes-hall↗
arXiv1997

Localization and Metal-Insulator Transition in Multi-Layer Quantum Hall Structures

We study the phase structure and Hall conductance quantization in weakly coupled multi-layer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation. It is shown that (i) finite interlayer tunnelings (however small) give rise to successive metallic and insulating phases and metal-insulator transitions in the unitary universality class. (ii) The Hall conductivity is not renormalized in the metallic phases in the 3D regime. (iii) The Hall conductances are quantized in the insulating phases. In the bulk quantum Hall phases, the effective field theory describes the transport on the surface.

cond-mat.mes-hall↗
arXiv1996

Weakly Coupled Antiferromagnetic Quantum Spin Chains

Quasi-one-dimensional quantum antiferromagnets formed by a d-dimensional hypercubic lattice of weakly coupled spin-1/2 antiferromagnetic Heisenberg chains are studied by combining exact results in one-dimension and renormalization group analyses of the interchain correlations. It is shown that d-dimensional magnetic long-range order develops at zero-temperature for infinitesimal antiferromagnetic or ferromagnetic interchain couplings. In the presence of weak bond alternations, the order-disorder transition occurs at a finite interchain coupling. Relevances to the lightly doped quantum antiferromagnets and multi-layer quantum Hall systems are discussed.

cond-mat.str-el↗
arXiv1996

Critical Conductance and Its Fluctuations at Integer Hall Plateau Transitions

Under periodic boundary condition in the transverse direction, we calculate the averaged zero-temperature two-terminal conductance ($ $) and its statistical fluctuations ($<(\dg)^{2n}>$ for $n\le 4$) at the critical point of integer quantum Hall plateau transitions. We find {\it universal} values for $ =(0.58\pm0.03){e^2\over h}$, and $<(\dg)^{2n}>=({e^2\over h})^{2n}A_{2n}$, where $A_{2,4,6,8}=0.081\pm0.005$; $0.013\pm0.003$; $0.0026\pm0.005$; and $(8\pm2)\times10^{-4}$ respectively. We also determine the leading finite size scaling corrections to these observables. Comparisons with experiments will be made.

cond-mat.mes-hall↗
arXiv1996

The Effects of Electron-Electron Interactions on the Integer Quantum Hall Transitions

We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the {\it integer} quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $-0.66\pm0.04$. Thus the non-interacting fixed point (characterized $z=2$ and $ν\approx 2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ($z=1$, $ν\approx 2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.

cond-mat↗
arXiv1996

Transitions Between Hall Plateaus and the Dimerization Transition of a Hubbard Chain

We show that the plateau transitions in the quantum Hall effect is the same as the dimerization transition of a half-filled, one dimensional, $U(2n)$ Hubbard model at $n=0$. We address the properties of the latter by a combination of perturbative renormalization group and Monte Carlo simulations. Results on both critical and off-critical properties are presented.

cond-mat↗
arXiv1995

Phase Transitions in the Symmetric Kondo Lattice Model in Two and Three Dimensions

We present an application of high-order series expansion in the coupling constants for the ground state properties of correlated lattice fermion systems. Expansions have been generated up to order $(t/J)^{14}$ for $d=1$ and $(t/J)^8$ for $d=2,\ 3$ for certain properties of the symmetric Kondo lattice model. Analyzing the susceptibility series, we find evidence for a continuous phase transition from the ``spin liquid'' phase characteristic of a ``Kondo Insulator'' to an antiferromagnetically ordered phase in dimensions $d\ge2$ as the antiferromagnetic Kondo coupling is decreased. The critical point is estimated to be at $(t/J)_c\approx0.7$ for square lattice and $(t/J)_c\approx0.5$ for simple-cubic lattice.

cond-mat↗