Instantons in the Langevin dynamics: an application to spin glasses

We develop a general technique to calculate the probability of transitions over the barriers in spin-glasses in the framework of the dynamical theory. We use Lagrangian formulation of the instanton dynamics in which the transitions are represented by instantons. We derive the full set of the equations that determine the instantons but instead of solving them directly we prove that an instanton process can be mapped into a usual process going back in time which simplifies the problem significantly. We apply this general considerations to a simple example of the spherical Sherrington-Kirkpatrick model and we find the probability of the transition between the metastable states which is in agreement with physical expectations.Comment: 18 pages, 2 figure

Anomalous Charge Dynamics in the Superconducting State of Underdoped Cuprates

We present fermi liquid expressions for the low temperature behavior of the superfluid stiffness, explain why they differ from those suggested recently by Lee and Wen, and discuss their applicability to data on high-$T_c$ superconductors. We find that a consistent description requires a strong, doping dependent anisotropy, which affects states near the zone corners much more strongly than those near the zone diagonals

The first dozen years of the history of ITEP Theoretical Physics Laboratory

The theoretical investigations at ITEP in the years 1945-1958 are reviewed. There are exposed the most important theoretical results, obtained in the following branches of physics: 1) the theory of nuclear reactors on thermal neutrons; 2) the hydrogen bomb project ("Tube" in USSR and "Classical Super" in USA); 3) radiation theory; ~4) low temperature physics; 5) quantum electrodynamics and quantum field theories; 6) parity violation in weak interactions, the theory of $\beta$-decay and other weak processes; 7) strong interaction and nuclear physics. To the review are added the English translations of few papers, originally published in Russian, but unknown (or almost unknown) to Western readers.Comment: 55 pages, 5 fig

On the Spin Gap Phase of Strongly-Correlated Electrons

We discuss the possible existence of a spin-gap phase in the low-doping regime of strongly-correlated two-dimensional electrons within the gauge field description of the t-J model. The spin-gap phase was recently shown by Ubbens and Lee to be destroyed by gauge field quantum fluctuations for a single-layer 2D system in the absence of disorder and for a full gap. We show that the same conclusion applies both in the dirty limit and for the case of a gapless spinon condensate.Comment: 7 pages, uuencoded Postscript, including 1 figur

Confinement of Spin and Charge in High-Temperature Superconductors

By exploiting the internal gauge-invariance intrinsic to a spin-charge separated electron, we show that such degrees of freedom must be confined in two-dimensional superconductors experiencing strong inter-electron repulsion. We also demonstrate that incipient confinement in the normal state can prevent chiral spin-fluctuations from destroying the cross-over between strange and psuedo-gap regimes in under-doped high-temperature superconductors. Last, we suggest that the negative Hall anomaly observed in these materials is connected with this confinement effect.Comment: 12 pages, 1 postscript figure, to appear in PRB (RC), May 199

Singularities in the Fermi liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states

We consider a two dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. Using a fermionic Chern--Simons approach we study the description of the system's low energy excitations within an extension of Landau's Fermi liquid theory. We calculate perturbatively the effective mass and the quasi--particle interaction function characterizing this description. We find that at an even denominator filling fraction the fermion's effective mass diverges logarithmically at the Fermi level, and argue that this divergence allows for an {\it exact} calculation of the energy gaps of the fractional quantized Hall states asymptotically approaching these filling fractions. We find that the quasi--particle interaction function approaches a delta function. This singular behavior leads to a cancelation of the diverging effective mass from the long wavelength low frequency linear response functions at even denominator filling fractions.Comment: 46 pages, RevTeX, 5 figures included in a uuencoded postscript file. Minor revisions relative to the original version. The paper will be published in the Physical Review B, and can be retrieved from the World Wide Web, in http://cmtw.harvard.edu/~ster

Topologically protected quantum states and quantum computing in Josephson junctions arrays

We review recent results on a new class of Josephson arrays which have non-trivial topology and exhibit a novel quantum states at low temperatures. One of these states is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter. The second state is insulating and can be considered as a result of evolution of the former state due to Bose-condensation of usual superconductive vortices with a flux quantum 0. Quantum phase transition between these two states is controlled by variation of external magnetic field. Both the superconductive and insulating states are characterized by the presence of 2K-degenerate ground states, with K being the number of topologically different cycles existing in the plane of the array. This degeneracy is «protected» from the external perturbations (and noise) by the topological order parameter and spectral gap. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built in error correction. A number of relatively simple «echo-like» experiments possible on small-size arrays are discussed

D-wave superconductivity in doped Mott insulators

The effect of proximity to a Mott insulating phase on the charge transport properties of a superconductor is determined. An action describing the low energy physics is formulated and different scenarios for the approach to the Mott phase are distinguished by different variation with doping of the parameters in the action. A crucial issue is found to be the doping dependence of the quasiparticle charge which is defined here and which controls the temperature and field dependence of the electromagnetic response functions. Presently available data on high-T$_{c}$ superconductors are analysed. The data, while neither complete nor entirely consistent, suggest that neither the quasiparticle velocity nor the quasiparticle charge vanish as the Mott phase is approached, in contradiction to the predictions of several widely studied theories of lightly doped Mott insulators. Implications of the results for the structure of vortices in high-T$_{c}$ superconductors are determined. The numerical coefficients in the field-dependent specific heat are given for square and triangular vortex lattices.Comment: 12 pages. No figures. Submitted to JPCS (Proceedings of Chicago SNS conference

Quantum vortex fluctuations in cuprate superconductors

We study the effects of quantum vortex fluctuations in two-dimensional superconductors using a dual theory of vortices, and investigate the relevance to underdoped cuprates where the superconductor-insulator transition (SIT) is possibly driven by quantum vortex proliferation. We find that a broad enough phase fluctuation regime may exist for experimental observation of the quantum vortex fluctuations near SIT in underdoped cuprates. We propose that this scenario can be tested via pair-tunneling experiments which measure the characteristic resonances in the zero-temperature pair-field susceptibility in the vortex-proliferated insulating phase.Comment: RevTex 5 pages, 2 eps figures; expanded; to appear in Phys. Rev.

Finite-Temperature Transition into a Power-Law Spin Phase with an Extensive Zero-Point Entropy

We introduce an $xy$ generalization of the frustrated Ising model on a triangular lattice. The presence of continuous degrees of freedom stabilizes a {\em finite-temperature} spin state with {\em power-law} discrete spin correlations and an extensive zero-point entropy. In this phase, the unquenched degrees of freedom can be described by a fluctuating surface with logarithmic height correlations. Finite-size Monte Carlo simulations have been used to characterize the exponents of the transition and the dynamics of the low-temperature phase