SciPost Phys. 1, 011 (2016) ·
published 19 December 2016

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Building upon the onestep replica symmetry breaking formalism, duly
understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclideanspace logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the largedistance ("infrared", IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the smalldistance ("ultraviolet", UV) limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for logREMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higherorder generalizations) in terms of modelspecific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given logcorrelated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$noise.
SciPost Phys. 1, 010 (2016) ·
published 27 October 2016

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The manybody localization (MBL) transition is a quantum phase transition
involving highly excited eigenstates of a disordered quantum manybody
Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive
entanglement entropies and fluctuations) to "localized" (exhibiting arealaw
scaling of entanglement and fluctuations). The MBL transition can be driven by
the strength of disorder in a given spectral range, or by the energy density at
fixed disorder  if the system possesses a manybody mobility edge. Here we
propose to explore the latter mechanism by using "quantumquench spectroscopy",
namely via quantum quenches of variable width which prepare the state of the
system in a superposition of eigenstates of the Hamiltonian within a
controllable spectral region. Studying numerically a chain of interacting
spinless fermions in a quasiperiodic potential, we argue that this system has
a manybody mobility edge; and we show that its existence translates into a
clear dynamical transition in the time evolution immediately following a quench
in the strength of the quasiperiodic potential, as well as a transition in the
scaling properties of the quasistationary state at long times. Our results
suggest a practical scheme for the experimental observation of manybody
mobility edges using coldatom setups.
SciPost Phys. 1, 009 (2016) ·
published 27 October 2016

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We study fourpoint functions of critical percolation in two dimensions, and
more generally of the Potts model. We propose an exact ansatz for the spectrum:
an infinite, discrete and nondiagonal combination of representations of the
Virasoro algebra. Based on this ansatz, we compute fourpoint functions using a
numerical conformal bootstrap approach. The results agree with MonteCarlo
computations of connectivities of random clusters.
SciPost Phys. 1, 008 (2016) ·
published 25 October 2016

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Pumping a finite energy density into a quantum system typically leads to
`melted' states characterized by exponentiallydecaying correlations, as is the
case for finitetemperature equilibrium situations. An important exception to
this rule are states which, while being at high energy, maintain a low entropy.
Such states can interestingly still display features of quantum criticality,
especially in one dimension. Here, we consider highenergy states in
anisotropic Heisenberg quantum spin chains obtained by splitting the ground
state's magnon Fermi sea into separate pieces. Using methods based on
integrability, we provide a detailed study of static and dynamical spinspin
correlations. These carry distinctive signatures of the Fermi sea splittings,
which would be observable in eventual experimental realizations. Going further,
we employ a multicomponent TomonagaLuttinger model in order to predict the
asymptotics of static correlations. For this effective field theory, we fix all
universal exponents from energetics, and all nonuniversal correlation
prefactors using finitesize scaling of matrix elements. The correlations
obtained directly from integrability and those emerging from the Luttinger
field theory description are shown to be in extremely good correspondence, as
expected, for the large distance asymptotics, but surprisingly also for the
short distance behavior. Finally, we discuss the description of dynamical
correlations from a mobile impurity model, and clarify the relation of the
effective field theory parameters to the Bethe Ansatz solution.
SciPost Phys. 1, 003 (2016) ·
published 23 October 2016

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We study the time evolution in the transversefield Ising chain subject to
quantum quenches of finite duration, ie, a continuous change in the transverse
magnetic field over a finite time. Specifically, we consider the dynamics of
the total energy, one and twopoint correlation functions and Loschmidt echo
during and after the quench as well as their stationary behaviour at late
times. We investigate how different quench protocols affect the dynamics and
identify universal properties of the relaxation.