154 research outputs found
Non-equilibrium coherence dynamics of a soft boson lattice
We study the non-equilibrium evolution of the phase coherence of a
Bose-Einstein condensate (BEC) in a one dimensional optical lattice, as the
lattice is suddenly quenched from an insulating to a superfluid state. We
observe slowly damped phase coherence oscillations in the regime of large
filling factor (~100 bosons per site) at a frequency proportional to the
generalized Josephson frequency. The truncated Wigner approximation (TWA)
predicts the frequency of the observed oscillations.Comment: 10 pages. 4 figure
Oscillating fidelity susceptibility near a quantum multicritical point
We study scaling behavior of the geometric tensor
and the fidelity susceptibility
in the vicinity of a quantum multicritical point (MCP) using
the example of a transverse XY model. We show that the behavior of the
geometric tensor (and thus of ) is drastically different from
that seen near a critical point. In particular, we find that is highly
non-monotonic function of along the generic direction
when the system size is bounded between
the shorter and longer correlation lengths characterizing the MCP:
, where are the
two correlation length exponents characterizing the system. We find that the
scaling of the maxima of the components of is associated
with emergence of quasi-critical points at , related
to the proximity to the critical line of finite momentum anisotropic
transition.
This scaling is different from that in the thermodynamic limit , which is determined by the conventional critical
exponents.
We use our results to calculate the defect density following a rapid quench
starting from the MCP and show that it exerts a step-like behavior for small
quench amplitudes. Study of heat density and diagonal entropy density also show
signatures of quasi-critical points.Comment: 12 pages, 9 figure
Putting competing orders in their place near the Mott transition
We describe the localization transition of superfluids on two-dimensional
lattices into commensurate Mott insulators with average particle density p/q
(p, q relatively prime integers) per lattice site. For bosons on the square
lattice, we argue that the superfluid has at least q degenerate species of
vortices which transform under a projective representation of the square
lattice space group (a PSG). The formation of a single vortex condensate
produces the Mott insulator, which is required by the PSG to have density wave
order at wavelengths of q/n lattice sites (n integer) along the principle axes;
such a second-order transition is forbidden in the Landau-Ginzburg-Wilson
framework. We also discuss the superfluid-insulator transition in the direct
boson representation, and find that an interpretation of the quantum
criticality in terms of deconfined fractionalized bosons is only permitted at
special values of q for which a permutative representation of the PSG exists.
We argue (and demonstrate in detail in a companion paper: L. Balents et al.,
cond-mat/0409470) that our results apply essentially unchanged to electronic
systems with short-range pairing, with the PSG determined by the particle
density of Cooper pairs. We also describe the effect of static impurities in
the superfluid: the impurities locally break the degeneracy between the q
vortex species, and this induces density wave order near each vortex. We
suggest that such a theory offers an appealing rationale for the local density
of states modulations observed by Hoffman et al. (cond-mat/0201348) in STM
studies of the vortex lattice of BSCCO, and allows a unified description of the
nucleation of density wave order in zero and finite magnetic fields. We note
signatures of our theory that may be tested by future STM experiments.Comment: 35 pages, 16 figures; (v2) part II is cond-mat/0409470; (v3) added
new appendix and clarifying remarks; (v4) corrected typo
Unzipping Vortices in Type-II Superconductors
The unzipping of vortex lines using magnetic-force microscopy from extended
defects is studied theoretically. We study both the unzipping isolated vortex
from common defects, such as columnar pins and twin-planes, and the unzipping
of a vortex from a plane in the presence of other vortices. We show, using
analytic and numerical methods, that the universal properties of the unzipping
transition of a single vortex depend only on the dimensionality of the defect
in the presence and absence of disorder. For the unzipping of a vortex from a
plane populated with many vortices is shown to be very sensitive to the
properties of the vortices in the two-dimensional plane. In particular such
unzipping experiments can be used to measure the ``Luttinger liquid parameter''
of the vortices in the plane. In addition we suggest a method for measuring the
line tension of the vortex directly using the experiments.Comment: 19 pages 15 figure
Quantum Quenches in Extended Systems
We study in general the time-evolution of correlation functions in a extended
quantum system after the quench of a parameter in the hamiltonian. We show that
correlation functions in d dimensions can be extracted using methods of
boundary critical phenomena in d+1 dimensions. For d=1 this allows to use the
powerful tools of conformal field theory in the case of critical evolution.
Several results are obtained in generic dimension in the gaussian (mean-field)
approximation. These predictions are checked against the real-time evolution of
some solvable models that allows also to understand which features are valid
beyond the critical evolution.
All our findings may be explained in terms of a picture generally valid,
whereby quasiparticles, entangled over regions of the order of the correlation
length in the initial state, then propagate with a finite speed through the
system. Furthermore we show that the long-time results can be interpreted in
terms of a generalized Gibbs ensemble. We discuss some open questions and
possible future developments.Comment: 24 Pages, 4 figure
Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
The applicability of the so-called truncated Wigner approximation (-W) is
extended to multitime averages of Heisenberg field operators. This task splits
naturally in two. Firstly, what class of multitime averages the -W
approximates, and, secondly, how to proceed if the average in question does not
belong to this class. To answer the first question we develop an (in principle,
exact) path-integral approach in phase-space based on the symmetric (Weyl)
ordering of creation and annihilation operators. These techniques calculate a
new class of averages which we call time-symmetric. The -W equations emerge as
an approximation within this path-integral techniques. We then show that the
answer to the second question is associated with response properties of the
system. In fact, for two-time averages Kubo's renowned formula relating the
linear response function to two-time commutators suffices. The -W is trivially
generalised to the response properties of the system allowing one to calculate
approximate time-normally ordered two-time correlation functions with
surprising ease. The techniques we develop are demonstrated for the
Bose-Hubbard model.Comment: 20 pages, 6 figure
The Energy-dependent Checkerboard Patterns in Cuprate Superconductors
Motivated by the recent scanning tunneling microscopy (STM) experiments [J.
E. Hoffman {\it et al.}, Science {\bf 297}, 1148 (2002); K. McElroy {\it et
al.}, Nature (to be published)], we investigate the real space local density of
states (LDOS) induced by weak disorder in a d-wave superconductor. We first
present the energy dependent LDOS images around a single weak defect at several
energies, and then point out that the experimentally observed checkerboard
pattern in the LDOS could be understood as a result of quasiparticle
interferences by randomly distributed defects. It is also shown that the
checkerboard pattern oriented along to the Cu-O bonds at low energies
would transform to that oriented parallel to the Cu-O bonds at higher energies.
This result is consistent with the experiments.Comment: 3 pages, 3 figure
Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
We discuss the application of the adiabatic perturbation theory to analyze
the dynamics in various systems in the limit of slow parametric changes of the
Hamiltonian. We first consider a two-level system and give an elementary
derivation of the asymptotics of the transition probability when the tuning
parameter slowly changes in the finite range. Then we apply this perturbation
theory to many-particle systems with low energy spectrum characterized by
quasiparticle excitations. Within this approach we derive the scaling of
various quantities such as the density of generated defects, entropy and
energy. We discuss the applications of this approach to a specific situation
where the system crosses a quantum critical point. We also show the connection
between adiabatic and sudden quenches near a quantum phase transitions and
discuss the effects of quasiparticle statistics on slow and sudden quenches at
finite temperatures.Comment: 20 pages, 3 figures, contribution to "Quantum Quenching, Annealing
and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes
in Phys., Springer, Heidelberg (2009, to be published), reference correcte
Spin and charge order in the vortex lattice of the cuprates: experiment and theory
I summarize recent results, obtained with E. Demler, K. Park, A. Polkovnikov,
M. Vojta, and Y. Zhang, on spin and charge correlations near a magnetic quantum
phase transition in the cuprates. STM experiments on slightly overdoped BSCCO
(J.E. Hoffman et al., Science 295, 466 (2002)) are consistent with the
nucleation of static charge order coexisting with dynamic spin correlations
around vortices, and neutron scattering experiments have measured the magnetic
field dependence of static spin order in the underdoped regime in LSCO (B. Lake
et al., Nature 415, 299 (2002)) and LaCuO_4+y (B. Khaykovich et al., Phys. Rev.
B 66, 014528 (2002)). Our predictions provide a semi-quantitative description
of these observations, with only a single parameter measuring distance from the
quantum critical point changing with doping level. These results suggest that a
common theory of competing spin, charge and superconducting orders provides a
unified description of all the cuprates.Comment: 18 pages, 7 figures; Proceedings of the Mexican Meeting on
Mathematical and Experimental Physics, Mexico City, September 2001, to be
published by Kluwer Academic/Plenum Press; (v2) added clarifications and
updated reference
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