974 research outputs found
Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
In experimentally realistic situations, quantum systems are never perfectly
isolated and the coupling to their environment needs to be taken into account.
Often, the effect of the environment can be well approximated by a Markovian
master equation. However, solving this master equation for quantum many-body
systems, becomes exceedingly hard due to the high dimension of the Hilbert
space. Here we present an approach to the effective simulation of the dynamics
of open quantum many-body systems based on machine learning techniques. We
represent the mixed many-body quantum states with neural networks in the form
of restricted Boltzmann machines and derive a variational Monte-Carlo algorithm
for their time evolution and stationary states. We document the accuracy of the
approach with numerical examples for a dissipative spin lattice system
Reptation quantum Monte Carlo for lattice Hamiltonians with a directed-update scheme
We provide an extension to lattice systems of the reptation quantum Monte
Carlo algorithm, originally devised for continuous Hamiltonians. For systems
affected by the sign problem, a method to systematically improve upon the
so-called fixed-node approximation is also proposed. The generality of the
method, which also takes advantage of a canonical worm algorithm scheme to
measure off-diagonal observables, makes it applicable to a vast variety of
quantum systems and eases the study of their ground-state and excited-states
properties. As a case study, we investigate the quantum dynamics of the
one-dimensional Heisenberg model and we provide accurate estimates of the
ground-state energy of the two-dimensional fermionic Hubbard model
The itinerant ferromagnetic phase of the Hubbard model
Using a newly developed quantum Monte Carlo technique, we provide strong
evidence for the stability of a saturated ferromagnetic phase in the
high-density regime of the two-dimensional infinite-U Hubbard model. By
decreasing the electron density, a discontinuous transition to a paramagnetic
phase is observed, accompanied by a divergence of the susceptibility on the
paramagnetic side. This behavior, resulting from a high degeneracy among
different spin sectors, is consistent with an infinite-order phase transition.
The remarkable stability of itinerant ferromagnetism renews the hope to
describe this phenomenon within a purely kinetic mechanism and will facilitate
the validation of experimental quantum simulators with cold atoms loaded in
optical lattices
Spectral and dynamical properties of strongly correlated systems
In the first part of the Thesis we mostly concentrate on spectral properties of strongly correlated systems and on their equilibrium properties. This is accomplished by the general concept of imaginary-time dynamics which we apply to a number of different problems in which different strengths of this approach emerge.
In Chapter 1 we introduce the formalism that allows for a connection between the quantum and the classical worlds. The connection is established by means of the imaginary-time quantum evolution which, under certain circumstances, is shown to be equivalent to a classical stochastic process. It is further shown that exact static and spectral properties of correlated systems can be obtained when this mapping is feasible. The relationship between the imaginary-time dynamics in different frameworks such as the path-integral and the
perturbative one is also underlined.
In Chapter 2 we present a specific implementation of the general ideas previously presented. In particular we introduced an extension to lattice systems of the Reptation Monte Carlo algorithm [30] which benefits of a sampling scheme based on directed updates. Specific improvements over the existing methodologies consist in the unbiased evaluation of the imaginary-time path integrals for bosons and a systematic scheme to improve over the Fixed-node approximation for fermions. Applications to the Hubbard and the Heisenberg models are presented.
In Chapter 3 we demonstrate the application of the imaginary-time dynamics to the exact study of spectral properties. Subject of our attention is a highly anharmonic and correlated quantum crystal such as Helium 4 at zero temperature.[33] Concerning this system, we have obtained the first ab-initio complete phonon dispersion in good agreement with neutron spectroscopy experiments. Moreover, we have also studied the density excitations of solid
helium in a region of wave-vectors in between the collective (phonon) and the single-particle regimes, where the presence of residual coherence in the dynamics shows analogies between the highly anharmonic crystal and the superfluid phase.
In Chapter 4 we introduce a novel method, based on the imaginary-time dynamics, to obtain unbiased estimates of fermionic properties.[34] By means of this method and of a very accurate variational state, we provide strong evidence for the stability of a saturated ferromagnetic phase in the high-density regime of the two-dimensional infinite-U Hubbard model. By decreasing the electron density, we observe a discontinuous transition to a paramagnetic phase, accompanied by a divergence of the susceptibility on the paramagnetic side. This behavior, resulting from a high degeneracy among different spin sectors, is consistent with an infinite-order phase transition scenario.
In Chapter 5 the use of imaginary-time dynamics in the context of finite-temperature response functions is highlighted. As an application, we study an intriguing quantum phase featuring both glassy order and Bose-Einstein condensation. [35] We introduce and validate a model for the role of geometrical frustration in the coexistence of off-diagonal long range
order with an amorphous density profile. The exact characterization of the response of the system to an external density perturbation is what allows here to establish the existence of a spin-glass phase. The differences between such a phase and the otherwise insulating "Bose glasses" are further elucidated in the Chapter.
In the second part of the Thesis we focus our attention on the dynamics of closed systems out of equilibrium. This is accomplished by both non-stochastic exact methods for the dynamics and the introduction of a novel time-dependent Variational Monte Carlo scheme.
In Chapter 6 exact diagonalization schemes and renormalization-based methods for one-dimensional systems are introduced. We identify key phenomenological traits resulting from the many-body correlation in closed systems driven sufficiently away from equilibrium.[31]
We provide evidences that the dynamics of interacting lattice bosons away from equilibrium can be trapped into extremely long-lived inhomogeneous metastable states. The slowing down of incoherent density excitations above a threshold energy, much reminiscent of a dynamical arrest on the verge of a glass transition, is identified as the key feature of this phenomenon.
In Chapter 7 we present an extension to dynamical properties of the Variational Quantum Monte Carlo method.[32] This is accomplished by introducing a general class of time-dependent variational states which is based on the mapping of the many-body dynamics onto an instantaneous ground-state problem. The application of the method to the experimentally relevant quantum quenches of interacting bosons reveals the accuracy and the
reliability of the introduced numerical scheme. We indeed obtain for the first time a consistent variational description of the approach to the equilibrium of local observables and underline the origin of the metastability and glassy behavior previously identified.
In the very last part we draw our conclusions and show some possible paths for stimulating future research
Protected quasi-locality in quantum systems with long-range interactions
We study the out-of-equilibrium dynamics of quantum systems with long-range
interactions. Two different models describing, respectively, interacting
lattice bosons and spins are considered. Our study relies on a combined
approach based on accurate many-body numerical calculations as well as on a
quasiparticle microscopic theory. For sufficiently fast decaying long-range
potentials, we find that the quantum speed limit set by the long-range
Lieb-Robinson bounds is never attained and a purely ballistic behavior is
found. For slowly decaying potentials, a radically different scenario is
observed. In the bosonic case, a remarkable local spreading of correlations is
still observed, despite the existence of infinitely fast traveling excitations
in the system. This is in marked contrast to the spin case, where locality is
broken. We finally provide a microscopic justification of the different regimes
observed and of the origin of the protected locality in the bosonic model
Universal Superfluid Transition and Transport Properties of Two-Dimensional Dirty Bosons
We study the phase diagram of two-dimensional, interacting bosons in the
presence of a correlated disorder in continuous space, using large-scale finite
temperature quantum Monte Carlo simulations. We show that the superfluid
transition is strongly protected against disorder. It remains of the
Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the
chemical potential. Moreover, we study the transport properties in the strong
disorder regime where a zero-temperature Bose-glass phase is expected. We show
that the conductance exhibits a thermally activated behavior vanishing only at
zero temperature. Our results point towards the existence of Bose bad-metal
phase as a precursor of the Bose-glass phase
Constraints on non-local gravity from binary pulsars gravitational emission
Non-local theories of gravity are considered extended theories of gravity,
meaning that when the non-local terms are canceled out, the limit of General
Relativity (GR) is obtained. Several reasons have led us to consider this
theory with increasing interest, but primarily non-locality emerges in a
natural way as a side effect of the introduction of quantum corrections to GR,
the purpose of which was to cure the singularity problem, both at astrophysical
and cosmological level. In this paper we studied a peculiar case of the so
called Deser-Woodard theory consisting in the addition of a non-local term to
the Hilbert-Einstein lagrangian, and we derived for the first time contraints
on the dimensionaless non-local parameter A by exploiting the predicted
gravitational wave emission in three binary pulsars, namely PSR J1012+5307, PSR
J0348+0432 and PSR $J1738+0333. We discovered that the instantaneous flux
strongly depends on A and that the best constraints (0.12 < A < 0.16) come from
PSR J1012+5307, for which the GR prediction is outside the observational
ranges. However, since for PSR J1012 + 5307 scintillation is suspected, as
emerged in a recent census by LOFAR, corruptions in pulsar timing could be
hidden. We finally comment on the usability and reliability of this type of
test for extended theories of gravity
Learning hard quantum distributions with variational autoencoders
Studying general quantum many-body systems is one of the major challenges in
modern physics because it requires an amount of computational resources that
scales exponentially with the size of the system.Simulating the evolution of a
state, or even storing its description, rapidly becomes intractable for exact
classical algorithms. Recently, machine learning techniques, in the form of
restricted Boltzmann machines, have been proposed as a way to efficiently
represent certain quantum states with applications in state tomography and
ground state estimation. Here, we introduce a new representation of states
based on variational autoencoders. Variational autoencoders are a type of
generative model in the form of a neural network. We probe the power of this
representation by encoding probability distributions associated with states
from different classes. Our simulations show that deep networks give a better
representation for states that are hard to sample from, while providing no
benefit for random states. This suggests that the probability distributions
associated to hard quantum states might have a compositional structure that can
be exploited by layered neural networks. Specifically, we consider the
learnability of a class of quantum states introduced by Fefferman and Umans.
Such states are provably hard to sample for classical computers, but not for
quantum ones, under plausible computational complexity assumptions. The good
level of compression achieved for hard states suggests these methods can be
suitable for characterising states of the size expected in first generation
quantum hardware.Comment: v2: 9 pages, 3 figures, journal version with major edits with respect
to v1 (rewriting of section "hard and easy quantum states", extended
discussion on comparison with tensor networks
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