850 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
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
Quantum Field as a quantum cellular automaton: the Dirac free evolution in one dimension
We present a quantum cellular automaton model in one space-dimension which
has the Dirac equation as emergent. This model, a discrete-time and causal
unitary evolution of a lattice of quantum systems, is derived from the
assumptions of homogeneity, parity and time-reversal invariance. The comparison
between the automaton and the Dirac evolutions is rigorously set as a
discrimination problem between unitary channels. We derive an exact lower bound
for the probability of error in the discrimination as an explicit function of
the mass, the number and the momentum of the particles, and the duration of the
evolution. Computing this bound with experimentally achievable values, we see
that in that regime the QCA model cannot be discriminated from the usual Dirac
evolution. Finally, we show that the evolution of one-particle states with
narrow-band in momentum can be effi- ciently simulated by a dispersive
differential equation for any regime. This analysis allows for a comparison
with the dynamics of wave-packets as it is described by the usual Dirac
equation. This paper is a first step in exploring the idea that quantum field
theory could be grounded on a more fundamental quantum cellular automaton model
and that physical dynamics could emerge from quantum information processing. In
this framework, the discretization is a central ingredient and not only a tool
for performing non-perturbative calculation as in lattice gauge theory. The
automaton model, endowed with a precise notion of local observables and a full
probabilistic interpretation, could lead to a coherent unification of an
hypothetical discrete Planck scale with the usual Fermi scale of high-energy
physics.Comment: 21 pages, 4 figure
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
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
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