28 research outputs found
A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
We prove that quantum many-body systems on a one-dimensional lattice locally
relax to Gaussian states under non-equilibrium dynamics generated by a bosonic
quadratic Hamiltonian. This is true for a large class of initial states - pure
or mixed - which have to satisfy merely weak conditions concerning the decay of
correlations. The considered setting is a proven instance of a situation where
dynamically evolving closed quantum systems locally appear as if they had truly
relaxed, to maximum entropy states for fixed second moments. This furthers the
understanding of relaxation in suddenly quenched quantum many-body systems. The
proof features a non-commutative central limit theorem for non-i.i.d. random
variables, showing convergence to Gaussian characteristic functions, giving
rise to trace-norm closeness. We briefly relate our findings to ideas of
typicality and concentration of measure.Comment: 27 pages, final versio
Efficient and feasible state tomography of quantum many-body systems
We present a novel method to perform quantum state tomography for
many-particle systems which are particularly suitable for estimating states in
lattice systems such as of ultra-cold atoms in optical lattices. We show that
the need for measuring a tomographically complete set of observables can be
overcome by letting the state evolve under some suitably chosen random circuits
followed by the measurement of a single observable. We generalize known results
about the approximation of unitary 2-designs, i.e., certain classes of random
unitary matrices, by random quantum circuits and connect our findings to the
theory of quantum compressed sensing. We show that for ultra-cold atoms in
optical lattices established techniques like optical super-lattices, laser
speckles, and time-of-flight measurements are sufficient to perform fully
certified, assumption-free tomography. Combining our approach with tensor
network methods - in particular the theory of matrix-product states - we
identify situations where the effort of reconstruction is even constant in the
number of lattice sites, allowing in principle to perform tomography on
large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing
that no single-site addressing is needed at any stage of the scheme when
implemented in optical lattice system
Entanglement and correlation functions following a local quench: a conformal field theory approach
We show that the dynamics resulting from preparing a one-dimensional quantum
system in the ground state of two decoupled parts, then joined together and
left to evolve unitarily with a translational invariant Hamiltonian (a local
quench), can be described by means of quantum field theory. In the case when
the corresponding theory is conformal, we study the evolution of the
entanglement entropy for different bi-partitions of the line. We also consider
the behavior of one- and two-point correlation functions. All our findings may
be explained in terms of a picture, that we believe to be valid more generally,
whereby quasiparticles emitted from the joining point at the initial time
propagate semiclassically through the system.Comment: 19 pages, 4 figures, v2 typos corrected and refs adde
Quantum Quenches in Extended Systems
We study in general the time-evolution of correlation functions in a extended
quantum system after the quench of a parameter in the hamiltonian. We show that
correlation functions in d dimensions can be extracted using methods of
boundary critical phenomena in d+1 dimensions. For d=1 this allows to use the
powerful tools of conformal field theory in the case of critical evolution.
Several results are obtained in generic dimension in the gaussian (mean-field)
approximation. These predictions are checked against the real-time evolution of
some solvable models that allows also to understand which features are valid
beyond the critical evolution.
All our findings may be explained in terms of a picture generally valid,
whereby quasiparticles, entangled over regions of the order of the correlation
length in the initial state, then propagate with a finite speed through the
system. Furthermore we show that the long-time results can be interpreted in
terms of a generalized Gibbs ensemble. We discuss some open questions and
possible future developments.Comment: 24 Pages, 4 figure
Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
We present a new class of tensor network states that are specifically
designed to capture the electron correlation of a molecule of arbitrary
structure. In this ansatz, the electronic wave function is represented by a
Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient
reduction of the number of variational parameters by breaking down the
complexity of the high-dimensional coefficient tensor of a
full-configuration-interaction (FCI) wave function. We demonstrate that CGTN
states approximate ground states of molecules accurately by comparison of the
CGTN and FCI expansion coefficients. The CGTN parametrization is not biased
towards any reference configuration in contrast to many standard quantum
chemical methods. This feature allows one to obtain accurate relative energies
between CGTN states which is central to molecular physics and chemistry. We
discuss the implications for quantum chemistry and focus on the spin-state
problem. Our CGTN approach is applied to the energy splitting of states of
different spin for methylene and the strongly correlated ozone molecule at a
transition state structure. The parameters of the tensor network ansatz are
variationally optimized by means of a parallel-tempering Monte Carlo algorithm
Ground states of unfrustrated spin Hamiltonians satisfy an area law
We show that ground states of unfrustrated quantum spin-1/2 systems on
general lattices satisfy an entanglement area law, provided that the
Hamiltonian can be decomposed into nearest-neighbor interaction terms which
have entangled excited states. The ground state manifold can be efficiently
described as the image of a low-dimensional subspace of low Schmidt measure,
under an efficiently contractible tree-tensor network. This structure gives
rise to the possibility of efficiently simulating the complete ground space
(which is in general degenerate). We briefly discuss "non-generic" cases,
including highly degenerate interactions with product eigenbases, using a
relationship to percolation theory. We finally assess the possibility of using
such tree tensor networks to simulate almost frustration-free spin models.Comment: 14 pages, 4 figures, small corrections, added a referenc
Entanglement Entropy dynamics in Heisenberg chains
By means of the time-dependent density matrix renormalization group algorithm
we study the zero-temperature dynamics of the Von Neumann entropy of a block of
spins in a Heisenberg chain after a sudden quench in the anisotropy parameter.
In the absence of any disorder the block entropy increases linearly with time
and then saturates. We analyze the velocity of propagation of the entanglement
as a function of the initial and final anisotropies and compare, wherever
possible, our results with those obtained by means of Conformal Field Theory.
In the disordered case we find a slower (logarithmic) evolution which may
signals the onset of entanglement localization.Comment: 15 pages, 9 figure
Can One Trust Quantum Simulators?
Various fundamental phenomena of strongly-correlated quantum systems such as
high- superconductivity, the fractional quantum-Hall effect, and quark
confinement are still awaiting a universally accepted explanation. The main
obstacle is the computational complexity of solving even the most simplified
theoretical models that are designed to capture the relevant quantum
correlations of the many-body system of interest. In his seminal 1982 paper
[Int. J. Theor. Phys. 21, 467], Richard Feynman suggested that such models
might be solved by "simulation" with a new type of computer whose constituent
parts are effectively governed by a desired quantum many-body dynamics.
Measurements on this engineered machine, now known as a "quantum simulator,"
would reveal some unknown or difficult to compute properties of a model of
interest. We argue that a useful quantum simulator must satisfy four
conditions: relevance, controllability, reliability, and efficiency. We review
the current state of the art of digital and analog quantum simulators. Whereas
so far the majority of the focus, both theoretically and experimentally, has
been on controllability of relevant models, we emphasize here the need for a
careful analysis of reliability and efficiency in the presence of
imperfections. We discuss how disorder and noise can impact these conditions,
and illustrate our concerns with novel numerical simulations of a paradigmatic
example: a disordered quantum spin chain governed by the Ising model in a
transverse magnetic field. We find that disorder can decrease the reliability
of an analog quantum simulator of this model, although large errors in local
observables are introduced only for strong levels of disorder. We conclude that
the answer to the question "Can we trust quantum simulators?" is... to some
extent.Comment: 20 pages. Minor changes with respect to version 2 (some additional
explanations, added references...
Temperature changes when adiabatically ramping up an optical lattice
When atoms are loaded into an optical lattice, the process of gradually
turning on the lattice is almost adiabatic. In this paper we investigate how
the temperature changes when going from the gapless superfluid phase to the
gapped Mott phase along isentropic lines. To do so we calculate the entropy in
the single-band Bose-Hubbard model for various densities, interaction strengths
and temperatures in one and two dimensions for homogeneous and trapped systems.
Our theory is able to reproduce the experimentally observed visibilities and
therefore strongly supports that current experiments remain in the quantum
regime for all considered lattice depths with low temperatures and minimal
heating.Comment: 18 pages, 24 figur
Entanglement negativity after a global quantum quench
We study the time evolution of the logarithmic negativity after a global quantum quench. In a 1+1-dimensional conformal invariant field theory, we consider the negativity between two intervals which can be either adjacent or disjoint. We show that the negativity follows the quasi-particle interpretation for the spreading of entanglement. We check and generalise our findings with a systematic analysis of the negativity after a quantum quench in the harmonic chain, highlighting two peculiar lattice effects: the late birth and the sudden death of entanglement