61 research outputs found
Lifshitz Superfluid Hydrodynamics
We construct the first order hydrodynamics of quantum critical points with
Lifshitz scaling and a spontaneously broken symmetry. The fluid is described by
a combination of two flows, a normal component that carries entropy and a
super-flow which has zero viscosity and carries no entropy. We analyze the new
transport effects allowed by the lack of boost invariance and constrain them by
the local second law of thermodynamics. Imposing time-reversal invariance, we
find eight new parity even transport coefficients. The formulation is
applicable, in general, to any superfluid/superconductor with an explicit
breaking of boost symmetry, in particular to high superconductors. We
discuss possible experimental signatures.Comment: 18 pages, 1 figure; added comments about time reversal invariance and
the choice of time direction; updated referee comments according to published
versio
Superfluid Kubo Formulas from Partition Function
Linear response theory relates hydrodynamic transport coefficients to
equilibrium retarded correlation functions of the stress-energy tensor and
global symmetry currents in terms of Kubo formulas. Some of these transport
coefficients are non-dissipative and affect the fluid dynamics at equilibrium.
We present an algebraic framework for deriving Kubo formulas for such thermal
transport coefficients by using the equilibrium partition function. We use the
framework to derive Kubo formulas for all such transport coefficients of
superfluids, as well as to rederive Kubo formulas for various normal fluid
systems.Comment: 41 pages, 4 appendixe
On Supersymmetric Lifshitz Field Theories
We consider field theories that exhibit a supersymmetric Lifshitz scaling
with two real supercharges. The theories can be formulated in the language of
stochastic quantization. We construct the free field supersymmetry algebra with
rotation singlet fermions for an even dynamical exponent in an arbitrary
dimension. We analyze the classical and quantum supersymmetric
interactions in and spacetime dimensions and reveal a supersymmetry
preserving quantum diagrammatic cancellation. Stochastic quantization indicates
that Lifshitz scale invariance is broken in the -dimensional quantum
theory.Comment: 26 page
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
Charged Complexity and the Thermofield Double State
We establish a systematic framework for studying quantum computational
complexity of Gaussian states of charged systems based on Nielsen's geometric
approach. We use this framework to examine the effect of a chemical potential
on the dynamics of complexity. As an example, we consider the complexity of a
charged thermofield double state constructed from two free massive complex
scalar fields in the presence of a chemical potential. We show that this state
factorizes between positively and negatively charged modes and demonstrate that
this fact can be used to relate it, for each momentum mode separately, to two
uncharged thermofield double states with shifted temperatures and times. We
evaluate the complexity of formation for the charged thermofield double state,
both numerically and in certain analytic expansions. We further present
numerical results for the time dependence of complexity. We compare various
aspects of these results to those obtained in holography for charged black
holes.Comment: version published in JHEP, presentation improved, results unchanged,
54 pages, 10 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
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