89 research outputs found
Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics
Nanoscale physics and dynamical mean field theory have both generated
increased interest in complex quantum impurity problems and so have focused
attention on the need for flexible quantum impurity solvers. Here we
demonstrate that the mapping of single quantum impurity problems onto
spin-chains can be exploited to yield a powerful and extremely flexible
impurity solver. We implement this cluster algorithm explicitly for the
Anderson and Kondo Hamiltonians, and illustrate its use in the ``mesoscopic
Kondo problem''. To study universal Kondo physics, a large ratio between the
effective bandwidth and the temperature is required; our
cluster algorithm treats the mesoscopic fluctuations exactly while being able
to approach the large limit with ease. We emphasize that the
flexibility of our method allows it to tackle a wide variety of quantum
impurity problems; thus, it may also be relevant to the dynamical mean field
theory of lattice problems.Comment: 4 pages, 3 figure
Superconductivity and antiferromagnetism in a hard-core boson spin-1 model in two dimensions
A model of hard-core bosons and spin-1 sites with single-ion anisotropy is
proposed to approximately describe hole pairs moving in a background of
singlets and triplets with the aim of exploring the relationship between
superconductivity and antiferromagnetism. The properties of this model at zero
temperature were investigated using quantum Monte Carlo techniques. The most
important feature found is the suppression of superconductivity, as long range
coherence of preformed pairs, due to the presence of both antiferromagnetism
and excitations. Indications of charge ordered and other phases are
also discussed.Comment: One figure, one reference, adde
Universal scaling at field-induced magnetic phase transitions
We study field-induced magnetic order in cubic lattices of dimers with
antiferromagnetic Heisenberg interactions. The thermal critical exponents at
the quantum phase transition from a spin liquid to a magnetically ordered phase
are determined from Stochastic Series Expansion Quantum Monte Carlo
simulations. These exponents are independent of the interdimer coupling ratios,
and converge to the value obtained by considering the transition as a
Bose-Einstein condensation of magnons, alpha_(BEC) = 1.5. The scaling results
are of direct relevance to the spin-dimer systems TlCuCl_3 and KCuCl_3, and
explain the broad range of exponents reported for field-induced ordering
transitions.Comment: 4 pages, 4 eps-figure
Accessing the dynamics of large many-particle systems using Stochastic Series Expansion
The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC)
technique working directly in the imaginary time continuum and thus avoiding
"Trotter discretization" errors. Using a non-local "operator-loop update" it
allows treating large quantum mechanical systems of many thousand sites. In
this paper we first give a comprehensive review on SSE and present benchmark
calculations of SSE's scaling behavior with system size and inverse
temperature, and compare it to the loop algorithm, whose scaling is known to be
one of the best of all QMC methods. Finally we introduce a new and efficient
algorithm to measure Green's functions and thus dynamical properties within
SSE.Comment: 11 RevTeX pages including 7 figures and 5 table
SO(5) Theory of Antiferromagnetism and Superconductivity
Antiferromagnetism and superconductivity are both fundamental and common
states of matter. In many strongly correlated systems, including the high Tc
cuprates, the heavy fermion compounds and the organic superconductors, they
occur next to each other in the phase diagram and influence each other's
physical properties. The SO(5) theory unifies these two basic states of matter
by a symmetry principle and describes their rich phenomenology through a single
low energy effective model. In this paper, we review the framework of the SO(5)
theory, and its detailed comparison with numerical and experimental results.Comment: Review article. 81 page
Universal SSE algorithm for Heisenberg model and Bose Hubbard model with interaction
We propose universal SSE method for simulation of Heisenberg model with
arbitrary spin and Bose Hubbard model with interaction. We report on the first
calculations of soft-core bosons with interaction by the SSE method. Moreover
we develop a simple procedure for increase efficiency of the algorithm. From
calculation of integrated autocorrelation times we conclude that the method is
efficient for both models and essentially eliminates the critical slowing down
problem.Comment: 6 pages, 5 figure
Directed geometrical worm algorithm applied to the quantum rotor model
We discuss the implementation of a directed geometrical worm algorithm for
the study of quantum link-current models. In this algorithm Monte Carlo updates
are made through the biased reptation of a worm through the lattice. A directed
algorithm is an algorithm where, during the construction of the worm, the
probability for erasing the immediately preceding part of the worm, when adding
a new part,is minimal. We introduce a simple numerical procedure for minimizing
this probability. The procedure only depends on appropriately defined local
probabilities and should be generally applicable. Furthermore we show how
correlation functions, C(r,tau) can be straightforwardly obtained from the
probability of a worm to reach a site (r,tau) away from its starting point
independent of whether or not a directed version of the algorithm is used.
Detailed analytical proofs of the validity of the Monte Carlo algorithms are
presented for both the directed and un-directed geometrical worm algorithms.
Results for auto-correlation times and Green functions are presented for the
quantum rotor model.Comment: 11 pages, 9 figures, v2 : Additional results and data calculated at
an incorrect chemical potential replaced. Conclusions unchange
Quantum Monte Carlo with Directed Loops
We introduce the concept of directed loops in stochastic series expansion and
path integral quantum Monte Carlo methods. Using the detailed balance rules for
directed loops, we show that it is possible to smoothly connect generally
applicable simulation schemes (in which it is necessary to include
back-tracking processes in the loop construction) to more restricted loop
algorithms that can be constructed only for a limited range of Hamiltonians
(where back-tracking can be avoided). The "algorithmic discontinuities" between
general and special points (or regions) in parameter space can hence be
eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg
antiferromagnet in an external magnetic field. We show that directed loop
simulations are very efficient for the full range of magnetic fields (zero to
the saturation point) and anisotropies. In particular for weak fields and
anisotropies, the autocorrelations are significantly reduced relative to those
of previous approaches. The back-tracking probability vanishes continuously as
the isotropic Heisenberg point is approached. For the XY-model, we show that
back-tracking can be avoided for all fields extending up to the saturation
field. The method is hence particularly efficient in this case. We use directed
loop simulations to study the magnetization process in the 2D Heisenberg model
at very low temperatures. For LxL lattices with L up to 64, we utilize the
step-structure in the magnetization curve to extract gaps between different
spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the
transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +-
0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in
algorithmic phase diagram corrected, to appear in Phys. Rev.
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