214 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
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
Real-time dynamics in a quantum many-body system are inherently complicated
and hence difficult to predict. There are, however, a special set of systems
where these dynamics are theoretically tractable: integrable models. Such
models possess non-trivial conserved quantities beyond energy and momentum.
These quantities are believed to control dynamics and thermalization in low
dimensional atomic gases as well as in quantum spin chains. But what happens
when the special symmetries leading to the existence of the extra conserved
quantities are broken? Is there any memory of the quantities if the breaking is
weak? Here, in the presence of weak integrability breaking, we show that it is
possible to construct residual quasi-conserved quantities, so providing a
quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We
demonstrate this construction explicitly in the context of quantum quenches in
one-dimensional Bose gases and argue that these quasi-conserved quantities can
be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR
Motion of a distinguishable impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking
We consider the real time dynamics of an initially localized distinguishable
impurity injected into the ground state of the Lieb-Liniger model. Focusing on
the case where integrability is preserved, we numerically compute the time
evolution of the impurity density operator in regimes far from analytically
tractable limits. We find that the injected impurity undergoes a stuttering
motion as it moves and expands. For an initially stationary impurity, the
interaction-driven formation of a quasibound state with a hole in the
background gas leads to arrested expansion -- a period of quasistationary
behavior. When the impurity is injected with a finite center of mass momentum,
the impurity moves through the background gas in a snaking manner, arising from
a quantum Newton's cradle-like scenario where momentum is exchanged
back-and-forth between the impurity and the background gas.Comment: v1: 13 pages, 10 figures; v2: 14 pages, 13 figures and change of
titl
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
Transport Properties of Multiple Quantum Dots Arranged in Parallel: Results from the Bethe Ansatz
In this paper we analyze transport through a double dot system connected to
two external leads. Imagining each dot possessing a single active level, we
model the system through a generalization of the Anderson model. We argue that
this model is exactly solvable when certain constraints are placed upon the dot
Coulomb charging energy, the dot-lead hybridization, and the value of the
applied gate voltage. Using this exact solvability, we access the zero
temperature linear response conductance both in and out of the presence of a
Zeeman field. We are also able to study the finite temperature linear response
conductance. We focus on universal behaviour and identify three primary
features in the transport of the dots: i) a so-called RKKY Kondo effect; ii) a
standard Kondo effect; and iii) interference phenomena leading to sharp
variations in the conductance including conductance zeros. We are able to use
the exact solvability of the dot model to characterize these phenomena
quantitatively. While here we primarily consider a double dot system, the
approach adopted applies equally well to N-dot systems.Comment: 28 pages, 10 figures; references added in v
Signatures of rare states and thermalization in a theory with confinement
There is a dichotomy in the nonequilibrium dynamics of quantum many-body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding, this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus, establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here, we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new “meson” excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously
Fano Lineshapes Revisited: Symmetric Photoionization Peaks from Pure Continuum Excitation
In a photoionization spectrum in which there is no excitation of the discrete
states, but only the underlying continuum, we have observed resonances which
appear as symmetric peaks, not the commonly expected window resonances.
Furthermore, since the excitation to the unperturbed continuum vanishes, the
cross section expected from Fano's configuration interaction theory is
identically zero. This shortcoming is removed by the explicit introduction of
the phase shifted continuum, which demonstrates that the shape of a resonance,
by itself, provides no information about the relative excitation amplitudes to
the discrete state and the continuum.Comment: 4 pages, 3 figure
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