SciPost Phys. 6, 057 (2019) ·
published 10 May 2019

· pdf
We study the edge behavior of inhomogeneous onedimensional quantum systems,
such as LiebLiniger models in traps or spin chains in spatially varying
magnetic fields. For free systems these fall into several universality classes,
the most generic one being governed by the TracyWidom distribution. We
investigate in this paper the effect of interactions. Using semiclassical
arguments, we show that since the density vanishes to leading order, the strong
interactions in the bulk are renormalized to zero at the edge, which simply
explains the survival of TracyWidom scaling in general. For integrable
systems, it is possible to push this argument further, and determine exactly
the remaining length scale which controls the variance of the edge
distribution. This analytical prediction is checked numerically, with excellent
agreement. We also study numerically the edge scaling at fronts generated by
quantum quenches, which provide new universality classes awaiting theoretical
explanation.
Jérôme Dubail, JeanMarie Stéphan, Pasquale Calabrese
SciPost Phys. 3, 019 (2017) ·
published 6 September 2017

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The lightcone spreading of entanglement and correlation is a fundamental and
ubiquitous feature of homogeneous extended quantum systems. Here we point out
that a class of inhomogenous Luttinger liquids (those with a uniform Luttinger
parameter $K$) at low energy display the universal phenomenon of curved light
cones: gapless excitations propagate along the geodesics of the metric
$ds^2=dx^2+v(x)^2 d\tau^2$, with $v(x)$ being the calculable spatial dependent
velocity induced by the inhomogeneity. We confirm our findings with explicit
analytic and numerical calculations both in and outofequilibrium for a
TonksGirardeau gas in a harmonic potential and in lattice systems with
artificially tuned hamiltonian density.
Jérôme Dubail, JeanMarie Stéphan, Jacopo Viti, Pasquale Calabrese
SciPost Phys. 2, 002 (2017) ·
published 13 February 2017

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Conformal field theory (CFT) has been extremely successful in describing
largescale universal effects in onedimensional (1D) systems at quantum
critical points. Unfortunately, its applicability in condensed matter physics
has been limited to situations in which the bulk is uniform because CFT
describes lowenergy excitations around some energy scale, taken to be constant
throughout the system. However, in many experimental contexts, such as quantum
gases in trapping potentials and in several outofequilibrium situations,
systems are strongly inhomogeneous. We show here that the powerful CFT methods
can be extended to deal with such 1D situations, providing a few concrete
examples for noninteracting Fermi gases. The system's inhomogeneity enters the
field theory action through parameters that vary with position; in particular,
the metric itself varies, resulting in a CFT in curved space. This approach
allows us to derive exact formulas for entanglement entropies which were not
known by other means.
Dr Stéphan: "We thank the referee for his/h..."
in Report on Conformal Field Theory for Inhomogeneous Onedimensional Quantum Systems: the Example of NonInteracting Fermi Gases