A general introduction to the non-zero temperature dynamic and transport properties of low-dimensional systems near a quantum phase transition shall be presented. Basic results will be reviewed in the context of experiments on the spin-ladder compounds. Recent large N computations (M. Vojta and S. Sachdev, Phys. Rev. Lett. 83), 3916 (1999) on an extended t-J model motivate a global scenario of the quantum phases and transitions in the high temperature superconductors, and connections will be made to numerous experiments. A universal theory (S. Sachdev, C. Buragohain, and M. Vojta, Science, in press; M. Vojta, C. Buragohain, and S. Sachdev, cond-mat/9912020) of quantum impurities in spin-gap antiferromagnets near a magnetic ordering transition will be compared quantitatively to experiments on Zn doped Y Ba_2 Cu_3 O_7 (Fong et al.), Phys. Rev. Lett. 82, 1939 (1999)
[T7.002] Universal critical temperature in bilayer quantum
magnets
Matthias Troyer (Theoretische Physik, ETH Zürich)
Recent algorithmic advances in quantum Monte Carlo
simulations for quantum lattice models and the availability
of massively parallel computers led to a breakthrough in the
simulation of quantum phase transitions in magnetic systems.
We can now simulate large systems with high accuracy,
similar to what has been possible for classical systems for
more than a decade. This allows to perform detailed
numerical simulations of quantum critical systems and to
obtain accurate values for universal critical exponents and
universal amplitudes. In this talk I will discuss the
effects of a magnetic field on the properties of a quantum
critival two-dimensional Heisenberg bilayer model. This
system shows a canted antiferromagnetic phase with a
Kosterlitz Thouless phase transitions at a finite
temperature T_KT. In the vicinity of the quantum
critical point, the order vanishes at a
temperatureT_KT=\kappa H, where H is the magnetic
field and \kappa is a universal number. I present quantum
Monte Carlo simulations which support the universality of
\kappa and determine its value. This allows experimental
tests of an intrinsically quantum-mechanical universal
quantity, which is not also a property of a higher
dimensional classical critical point. I will discuss the
relation of this model to recent experiments on double layer
quantum Hall systems, which may have a ground state with
canted antiferromagnetic order.
[T7.003] Advances in quantum Monte Carlo for quantum critical systems
Anders Sandvik (Department of Physics, University of Illinois at Urbana-Champaign)
During the past few years, there has been significant
progress in efficient quantum Monte Carlo methods for
certain classes of spin systems and other lattice many-body
problems. Cluster updates have been developed that speed up
the sampling by several orders of magnitude, and schemes to
avoid the systematic errors of the traditionally used
Trotter decomposition have been deviced. Thanks to these
developments, quantum critical phenomena (for systems where
there are no sign problems) can now be investigated to a
level of accuracy approaching classical simulation studies.
I will discuss an approach to quantum simulations which is
particularly efficient for (unfrustrated) S=1/2 Heisenberg
models; the stochastic series expansion (SSE) method
incorporating a cluster update for sampling the power series
expansion of exp(-\beta H) to all contributing orders [A.
W. Sandvik, Phys. Rev. B 59 R14157 (1999)]. I will
also discuss high-precision calculations using the SSE
algorithm for the Heisenberg antiferromagnet on a bilayer.
This model can be tuned through a quantum critical point by
varying the ratio of the inter-plane (J_\perp) to in-plane
interaction (J), and has been very useful for testing
predictions for quantum critical behavior in two-dimensional
antiferromagnets. I will discuss finite-size scaling of
ground state data, as well as the finite-temperature quantum
critical behavior.
[T7.004] Meron-Cluster Simulation of Phase Transitions in Strongly Interacting Fermionic Systems.
Shailesh Chandrasekharan (Department of Physics, Duke University)
We present a general strategy to solve the notorious fermion
sign problem using cluster algorithms. A configuration of
fermion world-lines is decomposed into oriented clusters.
Flipping a cluster generates new fermion world-lines and may
change the fermion permutation sign. It is always possible
to construct clusters such that the effect of a cluster flip
on the fermion sign is independent of the orientation of
other clusters. A cluster whose flip changes the fermion
sign is called a meron. A class of strongly interacting
fermionic systems can be shown to describe a gas of clusters
in the zero-meron sector with positive definite weights and
can be simulated using a meron-cluster algorithm. We present
some results from the study of phase transitions in such
models.
[T7.005] Quantum percolation, infinite-randomness fixed points, and the random transverse-field Ising model
David A. Huse (Princeton U.)
The low energy properties of a many-body quantum system with quenched randomness may be governed by a renormalization-group (RG) fixed point where the renormalized randomness is either (i) zero, (ii) finite and nonzero, or (iii) infinite. The case of infinite randomness is where the local interactions or other coupling constants have a probability distribution that is arbitrarily broad on a logarithmic scale. In this limit controlled RG calculations can be done by integrating out the highest-energy degrees of freedom and treating their effects on the lower-energy modes perturbatively. We (Motrunich, et al., cond-mat/9906322, Phys. Rev. B 1/1/2000) have found that the quantum critical point of the random transverse-field Ising model is governed by such an infinite-randomness fixed point for all physical dimensionalities, d. This is the first nontrivial such fixed point found for d>1. The infinite randomness at low energy means the phase transition is also a novel type of quantum percolation transition. Could a similar scenario apply to other interesting, but currently poorly-understood, quantum phase transitions? Infinite randomness also makes frustration irrelevant, so the same fixed point governs the quantum critical point of the spin-glass and the unfrustrated ferromagnet. Related work on dynamical and transport properties of systems governed by infinite-randomness fixed points will be presented Thurs. afternoon in an invited talk by K. Damle.