24,095 research outputs found
The coupled SYK model at finite temperature
Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS₂ dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS₂ geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function
The quantum spin Hall effect and topological insulators
In topological insulators, spin-orbit coupling and time-reversal symmetry
combine to form a novel state of matter predicted to have exotic physical
properties.Comment: 7 pages, 5 figures, an introduction of the quantum spin Hall effect
and topological insulators. For a video introduction of topological
insulators, see http://www.youtube.com/watch?v=Qg8Yu-Ju3V
Spacelike hypersurfaces with negative total energy in de Sitter spacetime
De Sitter spacetime can be separated into two parts along two kinds of
hypersurfaces and the half-de Sitter spacetimes are covered by the planar and
hyperbolic coordinates respectively. Two positive energy theorems were proved
previously for certain -asymptotically de Sitter and \H-asymptotically de
Sitter initial data sets by the second author and collaborators. These initial
data sets are asymptotic to time slices of the two kinds of half-de Sitter
spacetimes respectively, and their mean curvatures are bounded from above by
certain constants. While the mean curvatures violate these conditions, the
spacelike hypersurfaces with negative total energy in the two kinds of half-de
Sitter spacetimes are constructed in this short paper.Comment: 11 pages, final version, to appear in J. Math. Phy
Momentum polarization: an entanglement measure of topological spin and chiral central charge
Topologically ordered states are quantum states of matter with topological
ground state degeneracy and quasi-particles carrying fractional quantum numbers
and fractional statistics. The topological spin is an
important property of a topological quasi-particle, which is the Berry phase
obtained in the adiabatic self-rotation of the quasi-particle by . For
chiral topological states with robust chiral edge states, another fundamental
topological property is the edge state chiral central charge . In this paper
we propose a new approach to compute the topological spin and chiral central
charge in lattice models by defining a new quantity named as the momentum
polarization. Momentum polarization is defined on the cylinder geometry as a
universal subleading term in the average value of a "partial translation
operator". We show that the momentum polarization is a quantum entanglement
property which can be computed from the reduced density matrix, and our
analytic derivation based on edge conformal field theory shows that the
momentum polarization measures the combination of
topological spin and central charge. Numerical results are obtained for two
example systems, the non-Abelian phase of the honeycomb lattice Kitaev model,
and the Laughlin state of a fractional Chern insulator described by a
variational Monte Carlo wavefunction. The numerical results verifies the
analytic formula with high accuracy, and further suggests that this result
remains robust even when the edge states cannot be described by a conformal
field theory. Our result provides a new efficient approach to characterize and
identify topological states of matter from finite size numerics.Comment: 13 pages, 8 figure
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