329 research outputs found
Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
We present a new variational method, based on the matrix product operator
(MPO) ansatz, for finding the steady state of dissipative quantum chains
governed by master equations of the Lindblad form. Instead of requiring an
accurate representation of the system evolution until the stationary state is
attained, the algorithm directly targets the final state, thus allowing for a
faster convergence when the steady state is a MPO with small bond dimension.
Our numerical simulations for several dissipative spin models over a wide range
of parameters illustrate the performance of the method and show that indeed the
stationary state is often well described by a MPO of very moderate dimensions.Comment: Accepted versio
Unifying Projected Entangled Pair States contractions
The approximate contraction of a Projected Entangled Pair States (PEPS)
tensor network is a fundamental ingredient of any PEPS algorithm, required for
the optimization of the tensors in ground state search or time evolution, as
well as for the evaluation of expectation values. An exact contraction is in
general impossible, and the choice of the approximating procedure determines
the efficiency and accuracy of the algorithm. We analyze different previous
proposals for this approximation, and show that they can be understood via the
form of their environment, i.e. the operator that results from contracting part
of the network. This provides physical insight into the limitation of various
approaches, and allows us to introduce a new strategy, based on the idea of
clusters, that unifies previous methods. The resulting contraction algorithm
interpolates naturally between the cheapest and most imprecise and the most
costly and most precise method. We benchmark the different algorithms with
finite PEPS, and show how the cluster strategy can be used for both the tensor
optimization and the calculation of expectation values. Additionally, we
discuss its applicability to the parallelization of PEPS and to infinite
systems (iPEPS).Comment: 28 pages, 15 figures, accepted versio
Algorithms for finite Projected Entangled Pair States
Projected Entangled Pair States (PEPS) are a promising ansatz for the study
of strongly correlated quantum many-body systems in two dimensions. But due to
their high computational cost, developing and improving PEPS algorithms is
necessary to make the ansatz widely usable in practice. Here we analyze several
algorithmic aspects of the method. On the one hand, we quantify the connection
between the correlation length of the PEPS and the accuracy of its approximate
contraction, and discuss how purifications can be used in the latter. On the
other, we present algorithmic improvements for the update of the tensor that
introduce drastic gains in the numerical conditioning and the efficiency of the
algorithms. Finally, the state-of-the-art general PEPS code is benchmarked with
the Heisenberg and quantum Ising models on lattices of up to
sites.Comment: 18 pages, 20 figures, accepted versio
Quantum simulation of the Schwinger model: A study of feasibility
We analyze some crucial questions regarding the practical feasibility of
quantum simulation for lattice gauge models. Our analysis focuses on two models
suitable for the quantum simulation of the Schwinger Hamiltonian, or QED in 1+1
dimensions, which we investigate numerically using tensor networks. In
particular, we explore the effect of representing the gauge degrees of freedom
with finite-dimensional systems and show that the results converge rapidly;
thus even with small dimensions it is possible to obtain a reasonable accuracy.
We also discuss the time scales required for the adiabatic preparation of the
interacting vacuum state and observe that for a suitable ramping of the
interaction the required time is almost insensitive to the system size and the
dimension of the physical systems. Finally, we address the possible presence of
noninvariant terms in the Hamiltonian that is realized in the experiment and
show that for low levels of noise it is still possible to achieve a good
precision for some ground-state observables, even if the gauge symmetry is not
exact in the implemented model.Comment: 10 pages, 10 figures, published versio
Correlated neutral B meson decays into CP eigenstates
In the two correlated meson decay experiment we propose to measure
intensities relating CP eigenstate () decays on sides,
which will be measurable in future upgrades of KEK and PEP. As a CP-forbidden
transition, we obtain . We calculate in a model independent way all the possible intensities
relating final CP and flavour eigenstate decays. Under CPT-invariance, the
asymmetries for processes related by CP vanish for
and measure linearly. We notice the impossibility to isolate
the sign of \cos (2\bet a) without an independent knowledge of the sign of
. This exhaustion of the possible Golden Plate and flavour
decays provides new observables which may throw light in our present
understanding of CKM physics.Comment: 9 pages, no figures. Minor changes to coincide with published PLB
versio
How much entanglement is needed to reduce the energy variance?
We explore the relation between the entanglement of a pure state and its
energy variance for a local one dimensional Hamiltonian, as the system size
increases. In particular, we introduce a construction which creates a matrix
product state of arbitrarily small energy variance for spins,
with bond dimension scaling as , where is a
constant. This implies that a polynomially increasing bond dimension is enough
to construct states with energy variance that vanishes with the inverse of the
logarithm of the system size. We run numerical simulations to probe the
construction on two different models, and compare the local reduced density
matrices of the resulting states to the corresponding thermal equilibrium. Our
results suggest that the spatially homogeneous states with logarithmically
decreasing variance, which can be constructed efficiently, do converge to the
thermal equilibrium in the thermodynamic limit, while the same is not true if
the variance remains constant.Comment: small changes to fix typos and bibliographic reference
Studying Indirect Violation of CP, T and CPT in a B-factory
In this work we analyze the observable asymmetries one can build from
entangled B-meson states, in order to extract information on the parameters
epsilon and delta which govern indirect violation of discrete symmetries. The
traditionally proposed observables, based on flavour tags, are not helpful for
the study of the Bd-system, where the tiny value of the width difference
between physical states clears up such asymmetry effects. Our study makes
instead use of CP tags in order to build new asymmetries where the different
parameters can be separated out. For this separation, it is decisive to achieve
a good time resolution in the measurement of entangled state decays.
Nevertheless, even with no temporal information, as would be the case in a
symmetric factory, it is still possible to extract some information on the
symmetries of the system. We discuss both genuine and non-genuine observables,
depending on whether absorptive parts can mimic or not asymmetry effects.Comment: 18 pages, to appear in Nucl. Phys B; some minor corrections inluded,
additional discussion added to some sections, references complete
Non-Abelian string breaking phenomena with Matrix Product States
Using matrix product states, we explore numerically the phenomenology of
string breaking in a non-Abelian lattice gauge theory, namely 1+1 dimensional
SU(2). The technique allows us to study the static potential between external
heavy charges, as traditionally explored by Monte Carlo simulations, but also
to simulate the real-time dynamics of both static and dynamical fermions, as
the latter are fully included in the formalism. We propose a number of
observables that are sensitive to the presence or breaking of the flux string,
and use them to detect and characterize the phenomenon in each of these setups.Comment: 20+5 pages, 14 figures, version 2 contains more numerical results,
version 3: published versio
Entanglement in fermionic systems
The anticommuting properties of fermionic operators, together with the
presence of parity conservation, affect the concept of entanglement in a
composite fermionic system. Hence different points of view can give rise to
different reasonable definitions of separable and entangled states. Here we
analyze these possibilities and the relationship between the different classes
of separable states. We illustrate the differences by providing a complete
characterization of all the sets defined for systems of two fermionic modes.
The results are applied to Gibbs states of infinite chains of fermions whose
interaction corresponds to a XY-Hamiltonian with transverse magnetic field.Comment: 13 pages, 3 figures, 4 table
Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical Superlattice
We analyze the possibility to prepare a Heisenberg antiferromagnet with cold
fermions in optical lattices, starting from a band insulator and adiabatically
changing the lattice potential. The numerical simulation of the dynamics in 1D
allows us to identify the conditions for success, and to study the influence
that the presence of holes in the initial state may have on the protocol. We
also extend our results to two-dimensional systems.Comment: 5 pages, 4 figures + Supplementary Material (5 pages, 6 figures),
published versio
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