323 research outputs found
Lattice Gauge Tensor Networks
We present a unified framework to describe lattice gauge theories by means of
tensor networks: this framework is efficient as it exploits the high amount of
local symmetry content native of these systems describing only the gauge
invariant subspace. Compared to a standard tensor network description, the
gauge invariant one allows to speed-up real and imaginary time evolution of a
factor that is up to the square of the dimension of the link variable. The
gauge invariant tensor network description is based on the quantum link
formulation, a compact and intuitive formulation for gauge theories on the
lattice, and it is alternative to and can be combined with the global symmetric
tensor network description. We present some paradigmatic examples that show how
this architecture might be used to describe the physics of condensed matter and
high-energy physics systems. Finally, we present a cellular automata analysis
which estimates the gauge invariant Hilbert space dimension as a function of
the number of lattice sites and that might guide the search for effective
simplified models of complex theories.Comment: 28 pages, 9 figure
Physics Without Physics: The Power of Information-theoretical Principles
David Finkelstein was very fond of the new information-theoretic paradigm of
physics advocated by John Archibald Wheeler and Richard Feynman. Only recently,
however, the paradigm has concretely shown its full power, with the derivation
of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et
al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev.
A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al.,
Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from
informational principles. The paradigm has opened for the first time the
possibility of avoiding physical primitives in the axioms of the physical
theory, allowing a refoundation of the whole physics over logically solid
grounds. In addition to such methodological value, the new
information-theoretic derivation of quantum field theory is particularly
interesting for establishing a theoretical framework for quantum gravity, with
the idea of obtaining gravity itself as emergent from the quantum information
processing, as also suggested by the role played by information in the
holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev.
Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory
is derived without using mechanical primitives, including space-time, special
relativity, Hamiltonians, and quantization rules. The theory is simply provided
by the simplest quantum algorithm encompassing a countable set of quantum
systems whose network of interactions satisfies the three following simple
principles: homogeneity, locality, and isotropy. The inherent discrete nature
of the informational derivation leads to an extension of quantum field theory
in terms of a quantum cellular automata and quantum walks. A simple heuristic
argument sets the scale to the Planck one, and the observed regime is that of
small wavevectors ...Comment: 34 pages, 8 figures. Paper for in memoriam of David Finkelstei
Universal gauge-invariant cellular automata
Gauge symmetries play a fundamental role in Physics, as they provide a
mathematical justification for the fundamental forces. Usually, one starts from
a non-interactive theory which governs `matter', and features a global
symmetry. One then extends the theory so as make the global symmetry into a
local one (a.k.a gauge-invariance). We formalise a discrete counterpart of this
process, known as gauge extension, within the Computer Science framework of
Cellular Automata (CA). We prove that the CA which admit a relative gauge
extension are exactly the globally symmetric ones (a.k.a the colour-blind). We
prove that any CA admits a non-relative gauge extension. Both constructions
yield universal gauge-invariant CA, but the latter allows for a first example
where the gauge extension mediates interactions within the initial CA
Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks
Gauge invariance is one of the more important concepts in physics. We discuss
this concept in connection with the unitary evolution of discrete-time quantum
walks in one and two spatial dimensions, when they include the interaction with
synthetic, external electromagnetic fields. One introduces this interaction as
additional phases that play the role of gauge fields. Here, we present a way to
incorporate those phases, which differs from previous works. Our proposal
allows the discrete derivatives, that appear under a gauge transformation, to
treat time and space on the same footing, in a way which is similar to standard
lattice gauge theories. By considering two steps of the evolution, we define a
density current which is gauge invariant and conserved. In the continuum limit,
the dynamics of the particle, under a suitable choice of the parameters,
becomes the Dirac equation, and the conserved current satisfies the
corresponding conservation equation
Universal Gauge-Invariant Cellular Automata
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs "matter", and features a global symmetry. One then extends the theory so as make the global symmetry into a local one (a.k.a gauge-invariance). We formalise a discrete counterpart of this process, known as gauge extension, within the Computer Science framework of Cellular Automata (CA). We prove that the CA which admit a relative gauge extension are exactly the globally symmetric ones (a.k.a the colour-blind). We prove that any CA admits a non-relative gauge extension. Both constructions yield universal gauge-invariant CA, but the latter allows for a first example where the gauge extension mediates interactions within the initial CA
Quantum cellular automata and free quantum field theory
In a series of recent papers it has been shown how free quantum field theory
can be derived without using mechanical primitives (including space-time,
special relativity, quantization rules, etc.), but only considering the easiest
quantum algorithm encompassing a countable set of quantum systems whose network
of interactions satisfies the simple principles of unitarity, homogeneity,
locality, and isotropy. This has opened the route to extending the axiomatic
information-theoretic derivation of the quantum theory of abstract systems to
include quantum field theory. The inherent discrete nature of the informational
axiomatization leads to an extension of quantum field theory to a quantum
cellular automata theory, where the usual field theory is recovered in a regime
where the discrete structure of the automata cannot be probed. A simple
heuristic argument sets the scale of discreteness to the Planck scale, and the
customary physical regime where discreteness is not visible is the relativistic
one of small wavevectors. In this paper we provide a thorough derivation from
principles that in the most general case the graph of the quantum cellular
automaton is the Cayley graph of a finitely presented group, and showing how
for the case corresponding to Euclidean emergent space (where the group resorts
to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics
in the relativistic limit. We conclude with some perspectives towards the more
general scenario of non-linear automata for interacting quantum field theory.Comment: 10 pages, 2 figures, revtex style. arXiv admin note: substantial text
overlap with arXiv:1601.0483
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