30 research outputs found
Neural-Network Quantum States, String-Bond States, and Chiral Topological States
Neural-Network Quantum States have been recently introduced as an Ansatz for
describing the wave function of quantum many-body systems. We show that there
are strong connections between Neural-Network Quantum States in the form of
Restricted Boltzmann Machines and some classes of Tensor-Network states in
arbitrary dimensions. In particular we demonstrate that short-range Restricted
Boltzmann Machines are Entangled Plaquette States, while fully connected
Restricted Boltzmann Machines are String-Bond States with a nonlocal geometry
and low bond dimension. These results shed light on the underlying architecture
of Restricted Boltzmann Machines and their efficiency at representing many-body
quantum states. String-Bond States also provide a generic way of enhancing the
power of Neural-Network Quantum States and a natural generalization to systems
with larger local Hilbert space. We compare the advantages and drawbacks of
these different classes of states and present a method to combine them
together. This allows us to benefit from both the entanglement structure of
Tensor Networks and the efficiency of Neural-Network Quantum States into a
single Ansatz capable of targeting the wave function of strongly correlated
systems. While it remains a challenge to describe states with chiral
topological order using traditional Tensor Networks, we show that
Neural-Network Quantum States and their String-Bond States extension can
describe a lattice Fractional Quantum Hall state exactly. In addition, we
provide numerical evidence that Neural-Network Quantum States can approximate a
chiral spin liquid with better accuracy than Entangled Plaquette States and
local String-Bond States. Our results demonstrate the efficiency of neural
networks to describe complex quantum wave functions and pave the way towards
the use of String-Bond States as a tool in more traditional machine-learning
applications.Comment: 15 pages, 7 figure
Construction of spin models displaying quantum criticality from quantum field theory
We provide a method for constructing finite temperature states of
one-dimensional spin chains displaying quantum criticality. These models are
constructed using correlators of products of quantum fields and have an
analytical purification. Their properties can be investigated by Monte-Carlo
simulations, which enable us to study the low-temperature phase diagram and to
show that it displays a region of quantum criticality. The mixed states
obtained are shown to be close to the thermal state of a simple nearest
neighbour Hamiltonian.Comment: 10 pages, 6 figure
Lattice effects on Laughlin wave functions and parent Hamiltonians
We investigate lattice effects on wave functions that are lattice analogues
of bosonic and fermionic Laughlin wave functions with number of particles per
flux in the Landau levels. These wave functions are defined
analytically on lattices with particles per lattice site, where may
be different than . We give numerical evidence that these states have the
same topological properties as the corresponding continuum Laughlin states for
different values of and for different fillings . These states define,
in particular, particle-hole symmetric lattice Fractional Quantum Hall states
when the lattice is half-filled. On the square lattice it is observed that for
this particle-hole symmetric state displays the topological
properties of the continuum Laughlin state at filling fraction , while
for larger there is a transition towards long-range ordered
anti-ferromagnets. This effect does not persist if the lattice is deformed from
a square to a triangular lattice, or on the Kagome lattice, in which case the
topological properties of the state are recovered. We then show that changing
the number of particles while keeping the expression of these wave functions
identical gives rise to edge states that have the same correlations in the bulk
as the reference lattice Laughlin states but a different density at the edge.
We derive an exact parent Hamiltonian for which all these edge states are
ground states with different number of particles. In addition this Hamiltonian
admits the reference lattice Laughlin state as its unique ground state of
filling factor . Parent Hamiltonians are also derived for the lattice
Laughlin states at other fillings of the lattice, when or
and when also at half-filling.Comment: 18 pages, 15 figure
String Derived Exophobic SU(6)xSU(2) GUTs
With the apparent discovery of the Higgs boson, the Standard Model has been
confirmed as the theory accounting for all sub-atomic phenomena. This
observation lends further credence to the perturbative unification in Grand
Unified Theories (GUTs) and string theories. The free fermionic formalism
yielded fertile ground for the construction of quasi--realistic
heterotic--string models, which correspond to toroidal Z2xZ2 orbifold
compactifications. In this paper we study a new class of heterotic-string
models in which the GUT group is SU(6)xSU(2) at the string level. We use our
recently developed fishing algorithm to extract an example of a three
generation SU(6)xSU(2) GUT model. We explore the phenomenology of the model and
show that it contains the required symmetry breaking Higgs representations. We
show that the model admits flat directions that produce a Yukawa coupling for a
single family. The novel feature of the SU(6)xSU(2) string GUT models is that
they produce an additional family universal anomaly free U(1)symmetry that may
remain unbroken below the string scale. The massless spectrum of the model is
free of exotic states.Comment: 20 pages. Standard LaTe
NetKet: A machine learning toolkit for many-body quantum systems
We introduce NetKet, a comprehensive open source framework for the study of many-body quantum systems using machine learning techniques. The framework is built around a general and flexible implementation of neural-network quantum states, which are used as a variational ansatz for quantum wavefunctions. NetKet provides algorithms for several key tasks in quantum many-body physics and quantum technology, namely quantum state tomography, supervised learning from wavefunction data, and ground state searches for a wide range of customizable lattice models. Our aim is to provide a common platform for open research and to stimulate the collaborative development of computational methods at the interface of machine learning and many-body physics