252 research outputs found
Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains
We describe an algorithm for studying the entanglement entropy and spectrum
of 2D systems, as a coupled array of one dimensional chains in their
continuum limit. Using the algorithm to study the quantum Ising model in 2D,
(both in its disordered phase and near criticality) we confirm the existence of
an area law for the entanglement entropy and show that near criticality there
is an additive piece scaling as with .
\textcolor{black}{Studying the entanglement spectrum, we show that entanglement
gap scaling can be used to detect the critical point of the 2D model. When
short range (area law) entanglement dominates we find (numerically and
perturbatively) that this spectrum reflects the energy spectrum of a single
quantum Ising chain.Comment: 8 pages (4 + supplementary material). 10 figure
On Ising Correlation Functions with Boundary Magnetic Field
Exact expressions of the boundary state and the form factors of the Ising
model are used to derive differential equations for the one-point functions of
the energy and magnetization operators of the model in the presence of a
boundary magnetic field. We also obtain explicit formulas for the massless
limit of the one-point and two-point functions of the energy operator.Comment: 19 pages, 5 uu-figures, macros: harvmac.tex and epsf.tex three
references adde
Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2)k Theory Using the Truncated Conformal Spectrum Approach
We study the Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by
the trace of the primary field in the adjoint representation, a theory
governing the low-energy behaviour of a class of strongly correlated electronic
systems. While the model is non-integrable, its dynamics can be investigated
using the numerical technique of the truncated conformal spectrum approach
combined with numerical and analytical renormalization groups (TCSA+RG). The
numerical results so obtained provide support for a semiclassical analysis
valid at . Namely, we find that the low energy behavior is sensitive to
the sign of the coupling constant, . Moreover for this
behavior depends on whether is even or odd. With even, we find
definitive evidence that the model at low energies is equivalent to the massive
sigma model. For odd, the numerical evidence is more equivocal, but
we find indications that the low energy effective theory is critical.Comment: 30 pages, 19 eps figures, LaTeX2e file. Version 2: manuscript
accepted for publication; small changes in text and in one of the figure
Magnetic Response in the Underdoped Cuprates
We examine the dynamical magnetic response of the underdoped cuprates by
employing a phenomenological theory of a doped resonant valence bond state
where the Fermi surface is truncated into four pockets. This theory predicts a
resonant spin response which with increasing energy (0 to 100meV) appears as an
hourglass. The very low energy spin response is found at (pi,pi +- delta) and
(pi +- delta,pi) and is determined by scattering from the pockets' frontside to
the tips of opposite pockets where a van Hove singularity resides. At energies
beyond 100 meV, strong scattering is seen from (pi,0) to (pi,pi). This theory
thus provides a semi-quantitative description of the spin response seen in both
INS and RIXS experiments at all relevant energy scales
Interference effects in interacting quantum dots
In this paper we study the interplay between interference effects in quantum
dots (manifested through the appearance of Fano resonances in the conductance),
and interactions taken into account in the self-consistent Hartree-Fock
approximation. In the non-interacting case we find that interference may lead
to the observation of more than one conductance peak per dot level as a
function of an applied gate voltage. This may explain recent experimental
findings, which were thought to be caused by interaction effects. For the
interacting case we find a wide variety of different interesting phenomena.
These include both monotonous and non-monotonous filling of the dot levels as a
function of an applied gate voltage, which may occur continuously or even
discontinuously. In many cases a combination of the different effects can occur
in the same sample. The behavior of the population influences, in turn, the
conductance lineshape, causing broadening and asymmetry of narrow peaks, and
determining whether there will be a zero transmission point. We elucidate the
essential role of the interference between the dot levels in determining these
outcomes. The effects of finite temperatures on the results are also examined.Comment: 11 pages, 9 fugures, REVTeX
Quantum quenches in two spatial dimensions using chain array matrix product states
We describe a method for simulating the real time evolution of extended quantum systems in two dimensions (2D). The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular, it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum [(2+1)-dimensional] Ising model. In quenches that cross a phase boundary we find that the return probability shows nonanalyticities in time
Superconductivity generated by coupling to a Cooperon in a 2-dimensional array of 4-leg Hubbard ladders
Starting from an array of four-leg Hubbard ladders weakly doped away from
half-filling and weakly coupled by inter-ladder tunneling, we derive an
effective low energy model which contains a partially truncated Fermi surface
and a well defined Cooperon excitation formed by a bound pair of holes. An
attractive interaction in the Cooper channel is generated on the Fermi surface
through virtual scattering into the Cooperon state. Although the model is
derived in the weak coupling limit of a four-leg ladder array, an examination
of exact results on finite clusters for the strong coupling t-J model suggests
the essential features are also present for a strong coupling Hubbard model on
a square lattice near half-filling.Comment: 20 pages, 4 figure
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