14 research outputs found
Towards Complexity for Quantum Field Theory States
We investigate notions of complexity of states in continuous quantum-many
body systems. We focus on Gaussian states which include ground states of free
quantum field theories and their approximations encountered in the context of
the continuous version of Multiscale Entanglement Renormalization Ansatz. Our
proposal for quantifying state complexity is based on the Fubini-Study metric.
It leads to counting the number of applications of each gate (infinitesimal
generator) in the transformation, subject to a state-dependent metric. We
minimize the defined complexity with respect to momentum preserving quadratic
generators which form algebras. On the manifold of
Gaussian states generated by these operations the Fubini-Study metric
factorizes into hyperbolic planes with minimal complexity circuits reducing to
known geodesics. Despite working with quantum field theories far outside the
regime where Einstein gravity duals exist, we find striking similarities
between our results and holographic complexity proposals.Comment: 6+7 pages, 6 appendices, 2 figures; v2: references added;
acknowledgments expanded; appendix F added, reviewing similarities and
differences with hep-th/1707.08570; v3: version published in PR
On the Time Dependence of Holographic Complexity
We evaluate the full time dependence of holographic complexity in various
eternal black hole backgrounds using both the complexity=action (CA) and the
complexity=volume (CV) conjectures. We conclude using the CV conjecture that
the rate of change of complexity is a monotonically increasing function of
time, which saturates from below to a positive constant in the late time limit.
Using the CA conjecture for uncharged black holes, the holographic complexity
remains constant for an initial period, then briefly decreases but quickly
begins to increase. As observed previously, at late times, the rate of growth
of the complexity approaches a constant, which may be associated with Lloyd's
bound on the rate of computation. However, we find that this late time limit is
approached from above, thus violating the bound. Adding a charge to the eternal
black holes washes out the early time behaviour, i.e., complexity immediately
begins increasing with sufficient charge, but the late time behaviour is
essentially the same as in the neutral case. We also evaluate the complexity of
formation for charged black holes and find that it is divergent for extremal
black holes, implying that the states at finite chemical potential and zero
temperature are infinitely more complex than their finite temperature
counterparts.Comment: 52+31 pages, 30 figure
On the Time Dependence of Holographic Complexity
We evaluate the full time dependence of holographic complexity in various
eternal black hole backgrounds using both the complexity=action (CA) and the
complexity=volume (CV) conjectures. We conclude using the CV conjecture that
the rate of change of complexity is a monotonically increasing function of
time, which saturates from below to a positive constant in the late time limit.
Using the CA conjecture for uncharged black holes, the holographic complexity
remains constant for an initial period, then briefly decreases but quickly
begins to increase. As observed previously, at late times, the rate of growth
of the complexity approaches a constant, which may be associated with Lloyd's
bound on the rate of computation. However, we find that this late time limit is
approached from above, thus violating the bound. Adding a charge to the eternal
black holes washes out the early time behaviour, i.e., complexity immediately
begins increasing with sufficient charge, but the late time behaviour is
essentially the same as in the neutral case. We also evaluate the complexity of
formation for charged black holes and find that it is divergent for extremal
black holes, implying that the states at finite chemical potential and zero
temperature are infinitely more complex than their finite temperature
counterparts.Comment: 52+31 pages, 30 figure
Holographic Complexity in Vaidya Spacetimes II
In this second part of the study initiated in arxiv:1804.07410, we
investigate holographic complexity for eternal black hole backgrounds perturbed
by shock waves, with both the complexityaction (CA) and complexityvolume
(CV) proposals. In particular, we consider Vaidya geometries describing a thin
shell of null fluid with arbitrary energy falling in from one of the boundaries
of a two-sided AdS-Schwarzschild spacetime. We demonstrate how known properties
of complexity, such as the switchback effect for light shocks, as well as
analogous properties for heavy ones, are imprinted in the complexity of
formation and in the full time evolution of complexity. Following our
discussion in arxiv:1804.07410, we find that in order to obtain the expected
properties of the complexity, the inclusion of a particular counterterm on the
null boundaries of the Wheeler-DeWitt patch is required for the CA proposal.Comment: 83+38 pages, 34 figure