SciPost Phys. 1, 010 (2016) ·
published 27 October 2016
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The many-body localization (MBL) transition is a quantum phase transition
involving highly excited eigenstates of a disordered quantum many-body
Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive
entanglement entropies and fluctuations) to "localized" (exhibiting area-law
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 many-body mobility edge. Here we
propose to explore the latter mechanism by using "quantum-quench 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 quasi-periodic potential, we argue that this system has
a many-body 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 quasi-periodic potential, as well as a transition in the
scaling properties of the quasi-stationary state at long times. Our results
suggest a practical scheme for the experimental observation of many-body
mobility edges using cold-atom setups.
SciPost Phys. 1, 009 (2016) ·
published 27 October 2016
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We study four-point 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 non-diagonal combination of representations of the
Virasoro algebra. Based on this ansatz, we compute four-point functions using a
numerical conformal bootstrap approach. The results agree with Monte-Carlo
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 exponentially-decaying correlations, as is the
case for finite-temperature 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 high-energy 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 spin-spin
correlations. These carry distinctive signatures of the Fermi sea splittings,
which would be observable in eventual experimental realizations. Going further,
we employ a multi-component Tomonaga-Luttinger model in order to predict the
asymptotics of static correlations. For this effective field theory, we fix all
universal exponents from energetics, and all non-universal correlation
prefactors using finite-size 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 transverse-field 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 two-point 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.
