1,959 research outputs found
Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
Gauged gaussian Projected Entangled Pair States are particular tensor network
constructions that describe lattice states of fermionic matter interacting with
dynamical gauge fields. We show how one can efficiently compute, using
Monte-Carlo techniques, expectation values of physical observables in that
class of states. This opens up the possibility of using tensor network
techniques to investigate lattice gauge theories in two and three spatial
dimensions
AB effect and Aharonov-Susskind charge non-superselection
We consider a particle in a coherent superposition of states with different
electric charge moving in the vicinity of a magnetic flux. Formally, it should
acquire a (gauge-dependent) AB relative phase between the charge states, even
for an incomplete loop. If measureable, such a geometric, rather than
topological, AB-phase would seem to break gauge invariance. Wick, Wightman and
Wigner argued that since (global) charge-dependent phase transformations are
physically unobservable, charge state superpositions are unphysical (`charge
superselection rule'). This would resolve the apparent paradox in a trivial
way. However, Aharonov and Susskind disputed this superselection rule: they
distinguished between such global charge-dependent transformations, and
transformations of the relative inter-charge phases of two particles, and
showed that the latter \emph{could} in principle be observable! Finally, the
paradox again disappears once we considers the `calibration' of the phase
measured by the Aharonov-Susskind phase detectors, as well as the phase of the
particle at its initial point. It turns out that such a detector can only
distinguish between the relative phases of two paths if their (oriented)
difference forms a loop around the flux
Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
Can high energy physics be simulated by low-energy, non-relativistic,
many-body systems, such as ultracold atoms? Such ultracold atomic systems lack
the type of symmetries and dynamical properties of high energy physics models:
in particular, they manifest neither local gauge invariance nor Lorentz
invariance, which are crucial properties of the quantum field theories which
are the building blocks of the standard model of elementary particles.
However, it turns out, surprisingly, that there are ways to configure atomic
system to manifest both local gauge invariance and Lorentz invariance. In
particular, local gauge invariance can arise either as an effective, low
energy, symmetry, or as an "exact" symmetry, following from the conservation
laws in atomic interactions. Hence, one could hope that such quantum simulators
may lead to new type of (table-top) experiments, that shall be used to study
various QCD phenomena, as the confinement of dynamical quarks, phase
transitions, and other effects, which are inaccessible using the currently
known computational methods.
In this report, we review the Hamiltonian formulation of lattice gauge
theories, and then describe our recent progress in constructing quantum
simulation of Abelian and non-Abelian lattice gauge theories in 1+1 and 2+1
dimensions using ultracold atoms in optical lattices.Comment: A review; 55 pages, 14 figure
Digital lattice gauge theories
We propose a general scheme for a digital construction of lattice gauge
theories with dynamical fermions. In this method, the four-body interactions
arising in models with dimensions and higher, are obtained
stroboscopically, through a sequence of two-body interactions with ancillary
degrees of freedom. This yields stronger interactions than the ones obtained
through pertubative methods, as typically done in previous proposals, and
removes an important bottleneck in the road towards experimental realizations.
The scheme applies to generic gauge theories with Lie or finite symmetry
groups, both Abelian and non-Abelian. As a concrete example, we present the
construction of a digital quantum simulator for a lattice
gauge theory with dynamical fermionic matter in dimensions, using
ultracold atoms in optical lattices, involving three atomic species,
representing the matter, gauge and auxiliary degrees of freedom, that are
separated in three different layers. By moving the ancilla atoms with a proper
sequence of steps, we show how we can obtain the desired evolution in a clean,
controlled way
Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
We suggest a method to simulate lattice compact Quantum Electrodynamics
(cQED) using ultracold atoms in optical lattices, which includes dynamical
Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of
confinement as well as 2d flux loops deformations and breaking, and to observe
Wilson-loop area-law.Comment: Includes supplementary material. Added references, minor
modification
Classification of Matrix Product States with a Local (Gauge) Symmetry
Matrix Product States (MPS) are a particular type of one dimensional tensor
network states, that have been applied to the study of numerous quantum many
body problems. One of their key features is the possibility to describe and
encode symmetries on the level of a single building block (tensor), and hence
they provide a natural playground for the study of symmetric systems. In
particular, recent works have proposed to use MPS (and higher dimensional
tensor networks) for the study of systems with local symmetry that appear in
the context of gauge theories. In this work we classify MPS which exhibit local
invariance under arbitrary gauge groups. We study the respective tensors and
their structure, revealing known constructions that follow known gauging
procedures, as well as different, other types of possible gauge invariant
states
Digital quantum simulation of lattice gauge theories in three spatial dimensions
In the present work, we propose a scheme for digital formulation of lattice
gauge theories with dynamical fermions in 3+1 dimensions. All interactions are
obtained as a stroboscopic sequence of two-body interactions with an auxiliary
system. This enables quantum simulations of lattice gauge theories where the
magnetic four-body interactions arising in two and more spatial dimensions are
obtained without the use of perturbation theory, thus resulting in stronger
interactions compared with analogue approaches. The simulation scheme is
applicable to lattice gauge theories with either compact or finite gauge
groups. The required bounds on the digitization errors in lattice gauge
theories, due to the sequential nature of the stroboscopic time evolution, are
provided. Furthermore, an implementation of a lattice gauge theory with a
non-abelian gauge group, the dihedral group , is proposed employing the
aforementioned simulation scheme using ultracold atoms in optical lattices.Comment: 38 pages, 5 figure
Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories
Tensor networks, and in particular Projected Entangled Pair States (PEPS),
are a powerful tool for the study of quantum many body physics, thanks to both
their built-in ability of classifying and studying symmetries, and the
efficient numerical calculations they allow. In this work, we introduce a way
to extend the set of symmetric PEPS in order to include local gauge invariance
and investigate lattice gauge theories with fermionic matter. To this purpose,
we provide as a case study and first example, the construction of a fermionic
PEPS, based on Gaussian schemes, invariant under both global and local U(1)
gauge transformations. The obtained states correspond to a truncated U(1)
lattice gauge theory in 2 + 1 dimensions, involving both the gauge field and
fermionic matter. For the global symmetry (pure fermionic) case, these PEPS can
be studied in terms of spinless fermions subject to a p-wave superconducting
pairing. For the local symmetry (fermions and gauge fields) case, we find
confined and deconfined phases in the pure gauge limit, and we discuss the
screening properties of the phases arising in the presence of dynamical matter
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
- …