22 research outputs found
Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
We describe the spin dynamics of an arbitrary localized impurity in an
insulating two dimensional antiferromagnet, across the host transition from a
paramagnet with a spin gap to a Neel state. The impurity spin susceptibility
has a Curie-like divergence at the quantum-critical coupling, but with a
universal, effective spin which is neither an integer nor a half-odd-integer.
In the Neel state, the transverse impurity susceptibility is a universal number
divided by the host spin stiffness (which determines the energy cost to slow
twists in the orientation of the Neel order). These, and numerous other results
for the thermodynamics, Knight shift, and magnon damping have significant
applications to experiments on layered transition metal oxides.Comment: 12 pages, 3 figures; Additional details and results are in
cond-mat/991202
Power Aware Routing for Sensor Databases
Wireless sensor networks offer the potential to span and monitor large
geographical areas inexpensively. Sensor network databases like TinyDB are the
dominant architectures to extract and manage data in such networks. Since
sensors have significant power constraints (battery life), and high
communication costs, design of energy efficient communication algorithms is of
great importance. The data flow in a sensor database is very different from
data flow in an ordinary network and poses novel challenges in designing
efficient routing algorithms. In this work we explore the problem of energy
efficient routing for various different types of database queries and show that
in general, this problem is NP-complete. We give a constant factor
approximation algorithm for one class of query, and for other queries give
heuristic algorithms. We evaluate the efficiency of the proposed algorithms by
simulation and demonstrate their near optimal performance for various network
sizes
Medians and Beyond: New Aggregation Techniques for Sensor Networks
Wireless sensor networks offer the potential to span and monitor large
geographical areas inexpensively. Sensors, however, have significant power
constraint (battery life), making communication very expensive. Another
important issue in the context of sensor-based information systems is that
individual sensor readings are inherently unreliable. In order to address these
two aspects, sensor database systems like TinyDB and Cougar enable in-network
data aggregation to reduce the communication cost and improve reliability. The
existing data aggregation techniques, however, are limited to relatively simple
types of queries such as SUM, COUNT, AVG, and MIN/MAX. In this paper we propose
a data aggregation scheme that significantly extends the class of queries that
can be answered using sensor networks. These queries include (approximate)
quantiles, such as the median, the most frequent data values, such as the
consensus value, a histogram of the data distribution, as well as range
queries. In our scheme, each sensor aggregates the data it has received from
other sensors into a fixed (user specified) size message. We provide strict
theoretical guarantees on the approximation quality of the queries in terms of
the message size. We evaluate the performance of our aggregation scheme by
simulation and demonstrate its accuracy, scalability and low resource
utilization for highly variable input data sets
Impurity spin dynamics in 2D antiferromagnets and superconductors
We discuss the universal theory of localized impurities in the paramagnetic
state of 2D antiferromagnets where the spin gap is assumed to be significantly
smaller than a typical exchange energy. We study the impurity spin
susceptibility near the host quantum transition from a gapped paramagnet to a
Neel state, and we compute the impurity-induced damping of the spin-1 mode of
the gapped antiferromagnet. Under suitable conditions our results apply also to
d-wave superconductors.Comment: 2 pages, 1 fig. Proceedings of the M2S-HTSC-VI conference, Houston
2000, submitted to Physica C. More details can be found in cond-mat/991202
A1: A Distributed In-Memory Graph Database
A1 is an in-memory distributed database used by the Bing search engine to
support complex queries over structured data. The key enablers for A1 are
availability of cheap DRAM and high speed RDMA (Remote Direct Memory Access)
networking in commodity hardware. A1 uses FaRM as its underlying storage layer
and builds the graph abstraction and query engine on top. The combination of
in-memory storage and RDMA access requires rethinking how data is allocated,
organized and queried in a large distributed system. A single A1 cluster can
store tens of billions of vertices and edges and support a throughput of 350+
million of vertex reads per second with end to end query latency in single
digit milliseconds. In this paper we describe the A1 data model, RDMA optimized
data structures and query execution
Intermediate temperature dynamics of one-dimensional Heisenberg antiferromagnets
We present a general theory for the intermediate temperature (T) properties
of Heisenberg antiferromagnets of spin-S ions on p-leg ladders, valid for 2Sp
even or odd. Following an earlier proposal for 2Sp even (Damle and Sachdev,
cond-mat/9711014), we argue that an integrable, classical, continuum model of a
fixed-length, 3-vector applies over an intermediate temperature range; this
range becomes very wide for moderate and large values of 2Sp. The coupling
constants of the effective model are known exactly in terms of the energy gap
above the ground state (for 2Sp even) or a crossover scale (for 2Sp odd).
Analytic and numeric results for dynamic and transport properties are obtained,
including some exact results for the spin-wave damping. Numerous quantitative
predictions for neutron scattering and NMR experiments are made. A general
discussion on the nature of T>0 transport in integrable systems is also
presented: an exact solution of a toy model proves that diffusion can exist in
integrable systems, provided proper care is taken in approaching the
thermodynamic limit.Comment: 38 pages, including 12 figure
Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
We present the universal theory of arbitrary, localized impurities in a
confining paramagnetic state of two-dimensional antiferromagnets with global
SU(2) spin symmetry. The energy gap of the host antiferromagnet to spin-1
excitations, \Delta, is assumed to be significantly smaller than a typical
nearest neighbor exchange. In the absence of impurities, it was argued in
earlier work (Chubukov et al. cond-mat/9304046) that the low-temperature
quantum dynamics is universally and completely determined by the values of
\Delta and a spin-wave velocity c. Here we establish the remarkable fact that
no additional parameters are necessary for an antiferromagnet with a dilute
concentration of impurities, n_{imp} - each impurity is completely
characterized by a integer/half-odd-integer valued spin, S, which measures the
net uncompensated Berry phase due to spin precession in its vicinity. We
compute the impurity-induced damping of the spin-1 collective mode of the
antiferromagnet: the damping occurs on an energy scale \Gamma= n_{imp} (\hbar
c)^2/\Delta, and we predict a universal, asymmetric lineshape for the
collective mode peak. We argue that, under suitable conditions, our results
apply unchanged (or in some cases, with minor modifications) to d-wave
superconductors, and compare them to recent neutron scattering experiments on
YBCO by Fong et al. (cond-mat/9812047). We also describe the universal
evolution of numerous measurable correlations as the host antiferromagnet
undergoes a quantum phase transition to a Neel ordered state.Comment: 36 pages, 12 figures; added reference