8,961 research outputs found
On the multiplicity of Laplacian eigenvalues of graphs
summary:In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered
Unified tensor network theory for frustrated classical spin models in two dimensions
Frustration is a ubiquitous phenomenon in many-body physics that influences
the nature of the system in a profound way with exotic emergent behavior.
Despite its long research history, the analytical or numerical investigations
on frustrated spin models remain a formidable challenge due to their extensive
ground state degeneracy. In this work, we propose a unified tensor network
theory to numerically solve the frustrated classical spin models on various
two-dimensional (2D) lattice geometry with high efficiency. We show that the
appropriate encoding of emergent degrees of freedom in each local tensor is of
crucial importance in the construction of the infinite tensor network
representation of the partition function. The frustrations are thus relieved
through the effective interactions between emergent local degrees of freedom.
Then the partition function is written as a product of a one-dimensional (1D)
transfer operator, whose eigen-equation can be solved by the standard algorithm
of matrix product states rigorously, and various phase transitions can be
accurately determined from the singularities of the entanglement entropy of the
1D quantum correspondence. We demonstrated the power of our unified theory by
numerically solving 2D fully frustrated XY spin models on the kagome, square
and triangular lattices, giving rise to a variety of thermal phase transitions
from infinite-order Brezinskii-Kosterlitz-Thouless transitions, second-order
transitions, to first-order phase transitions. Our approach holds the potential
application to other types of frustrated classical systems like Heisenberg spin
antiferromagnets.Comment: 20 pages, 19 figure
Novel CMOS RFIC Layout Generation with Concurrent Device Placement and Fixed-Length Microstrip Routing
With advancing process technologies and booming IoT markets, millimeter-wave
CMOS RFICs have been widely developed in re- cent years. Since the performance
of CMOS RFICs is very sensi- tive to the precision of the layout, precise
placement of devices and precisely matched microstrip lengths to given values
have been a labor-intensive and time-consuming task, and thus become a major
bottleneck for time to market. This paper introduces a progressive
integer-linear-programming-based method to gener- ate high-quality RFIC layouts
satisfying very stringent routing requirements of microstrip lines, including
spacing/non-crossing rules, precise length, and bend number minimization,
within a given layout area. The resulting RFIC layouts excel in both per-
formance and area with much fewer bends compared with the simulation-tuning
based manual layout, while the layout gener- ation time is significantly
reduced from weeks to half an hour.Comment: ACM/IEEE Design Automation Conference (DAC), 201
- …