3,608 research outputs found
Quantum critical dynamics of the two-dimensional Bose gas
The dilute, two-dimensional Bose gas exhibits a novel regime of relaxational
dynamics in the regime k_B T > |\mu| where T is the absolute temperature and
\mu is the chemical potential. This may also be interpreted as the quantum
criticality of the zero density quantum critical point at \mu=0. We present a
theory for this dynamics, to leading order in 1/\ln (\Lambda/ (k_B T)), where
\Lambda is a high energy cutoff. Although pairwise interactions between the
bosons are weak at low energy scales, the collective dynamics are strongly
coupled even when \ln (\Lambda/T) is large. We argue that the strong-coupling
effects can be isolated in an effective classical model, which is then solved
numerically. Applications to experiments on the gap-closing transition of spin
gap antiferromagnets in an applied field are presented.Comment: 9 pages, 10 figure
Quantum criticality of a Bose gas in an optical lattice near the Mott transition
We derive the equation of state of bosons in an optical lattice in the
framework of the Bose-Hubbard model. Near the density-driven Mott transition,
the expression of the pressure P({\mu},T) versus chemical potential and
temperature is similar to that of a dilute Bose gas but with renormalized mass
m^* and scattering length a^*. m^* is the mass of the elementary excitations at
the quantum critical point governing the transition from the superfluid phase
to the Mott insulating phase, while a^* is related to their effective
interaction at low energy. We use a nonperturbative renormalization-group
approach to compute these parameters as a function of the ratio t/U between
hopping amplitude and on-site repulsion.Comment: v1) 4 pages, 6 figures. v2) Significant rewriting (new title) with
more emphasis on the quantum critical behavior near the Mott transitio
Spin dynamics across the superfluid-insulator transition of spinful bosons
Bosons with non-zero spin exhibit a rich variety of superfluid and insulating
phases. Most phases support coherent spin oscillations, which have been the
focus of numerous recent experiments. These spin oscillations are Rabi
oscillations between discrete levels deep in the insulator, while deep in the
superfluid they can be oscillations in the orientation of a spinful condensate.
We describe the evolution of spin oscillations across the superfluid-insulator
quantum phase transition. For transitions with an order parameter carrying
spin, the damping of such oscillations is determined by the scaling dimension
of the composite spin operator. For transitions with a spinless order parameter
and gapped spin excitations, we demonstrate that the damping is determined by
an associated quantum impurity problem of a localized spin excitation
interacting with the bulk critical modes. We present a renormalization group
analysis of the quantum impurity problem, and discuss the relationship of our
results to experiments on ultracold atoms in optical lattices.Comment: 43 pages (single-column format), 8 figures; v2: corrected discussion
of fixed points in Section V
Metallic spin glasses
Recent work on the zero temperature phases and phase transitions of strongly
random electronic system is reviewed. The transition between the spin glass and
quantum paramagnet is examined, for both metallic and insulating systems.
Insight gained from the solution of infinite range models leads to a quantum
field theory for the transition between a metallic quantum paramagnetic and a
metallic spin glass. The finite temperature phase diagram is described and
crossover functions are computed in mean field theory. A study of fluctuations
about mean field leads to the formulation of scaling hypotheses.Comment: Contribution to the Proceedings of the ITP Santa Barbara conference
on Non-Fermi liquids, 25 pages, requires IOP style file
Many-body spin interactions and the ground state of a dense Rydberg lattice gas
We study a one-dimensional atomic lattice gas in which Rydberg atoms are
excited by a laser and whose external dynamics is frozen. We identify a
parameter regime in which the Hamiltonian is well-approximated by a spin
Hamiltonian with quasi-local many-body interactions which possesses an exact
analytic ground state solution. This state is a superposition of all states of
the system that are compatible with an interaction induced constraint weighted
by a fugacity. We perform a detailed analysis of this state which exhibits a
cross-over between a paramagnetic phase with short-ranged correlations and a
crystal. This study also leads us to a class of spin models with many-body
interactions that permit an analytic ground state solution
Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model
Motivated by the indication of a new critical theory for the spin-1/2
Heisenberg model with a spatially staggered anisotropy on the square lattice as
suggested in \cite{Wenzel08}, we re-investigate the phase transition of this
model induced by dimerization using first principle Monte Carlo simulations. We
focus on studying the finite-size scaling of and ,
where stands for the spatial box size used in the simulations and
with is the spin-stiffness in the -direction.
Remarkably, while we do observe a large correction to scaling for the
observable as proposed in \cite{Fritz11}, the data for
exhibit a good scaling behavior without any indication of a large
correction. As a consequence, we are able to obtain a numerical value for the
critical exponent which is consistent with the known O(3) result with
moderate computational effort. Specifically, the numerical value of we
determine by fitting the data points of to their expected scaling
form is given by , which agrees quantitatively with the most
accurate known Monte Carlo O(3) result . Finally, while we can
also obtain a result of from the observable second Binder ratio
which is consistent with , the uncertainty of calculated
from is more than twice as large as that of determined from
.Comment: 7 figures, 1 table; brief repor
Dissipation effects in random transverse-field Ising chains
We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the
zero-temperature quantum phase transition in the random transverse-field Ising
chain by means of an (asymptotically exact) analytical strong-disorder
renormalization-group approach. We find that Ohmic damping destabilizes the
infinite-randomness critical point and the associated quantum Griffiths
singularities of the dissipationless system. The quantum dynamics of large
magnetic clusters freezes completely which destroys the sharp phase transition
by smearing. The effects of sub-Ohmic dissipation are similar and also lead to
a smeared transition. In contrast, super-Ohmic damping is an irrelevant
perturbation; the critical behavior is thus identical to that of the
dissipationless system. We discuss the resulting phase diagrams, the behavior
of various observables, and the implications to higher dimensions and
experiments.Comment: 18 pages, 3 figures; (v2) minor changes, published versio
Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
We present a strong-coupling expansion of the Bose-Hubbard model which
describes both the superfluid and the Mott phases of ultracold bosonic atoms in
an optical lattice. By performing two successive Hubbard-Stratonovich
transformations of the intersite hopping term, we derive an effective action
which provides a suitable starting point to study the strong-coupling limit of
the Bose-Hubbard model. This action can be analyzed by taking into account
Gaussian fluctuations about the mean-field approximation as in the Bogoliubov
theory of the weakly interacting Bose gas. In the Mott phase, we reproduce
results of previous mean-field theories and also calculate the momentum
distribution function. In the superfluid phase, we find a gapless spectrum and
compare our results with the Bogoliubov theory.Comment: 8 pages, 6 figures; (v2) Two references adde
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