2,274 research outputs found
Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
We discuss recently introduced numerical linked-cluster (NLC) algorithms that
allow one to obtain temperature-dependent properties of quantum lattice models,
in the thermodynamic limit, from exact diagonalization of finite clusters. We
present studies of thermodynamic observables for spin models on square,
triangular, and kagome lattices. Results for several choices of clusters and
extrapolations methods, that accelerate the convergence of NLC, are presented.
We also include a comparison of NLC results with those obtained from exact
analytical expressions (where available), high-temperature expansions (HTE),
exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo
simulations.For many models and properties NLC results are substantially more
accurate than HTE and ED.Comment: 14 pages, 16 figures, as publishe
Numerical Linked-Cluster Approach to Quantum Lattice Models
We present a novel algorithm that allows one to obtain temperature dependent
properties of quantum lattice models in the thermodynamic limit from exact
diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach
provides a systematic framework to assess finite-size effects and is valid for
any quantum lattice model. Unlike high temperature expansions (HTE), which have
a finite radius of convergence in inverse temperature, these calculations are
accurate at all temperatures provided the range of correlations is finite. We
illustrate the power of our approach studying spin models on {\it kagom\'e},
triangular, and square lattices.Comment: 4 pages, 5 figures, published versio
Linked cluster expansions for open quantum systems on a lattice
We propose a generalization of the linked-cluster expansions to study
driven-dissipative quantum lattice models, directly accessing the thermodynamic
limit of the system. Our method leads to the evaluation of the desired
extensive property onto small connected clusters of a given size and topology.
We first test this approach on the isotropic spin-1/2 Hamiltonian in two
dimensions, where each spin is coupled to an independent environment that
induces incoherent spin flips. Then we apply it to the study of an anisotropic
model displaying a dissipative phase transition from a magnetically ordered to
a disordered phase. By means of a Pad\'e analysis on the series expansions for
the average magnetization, we provide a viable route to locate the phase
transition and to extrapolate the critical exponent for the magnetic
susceptibility.Comment: 10 pages, 5 figure
Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
We discuss the application of a recently introduced numerical linked-cluster
(NLC) algorithm to strongly correlated itinerant models. In particular, we
present a study of thermodynamic observables: chemical potential, entropy,
specific heat, and uniform susceptibility for the t-J model on the square
lattice, with J/t=0.5 and 0.3. Our NLC results are compared with those obtained
from high-temperature expansions (HTE) and the finite-temperature Lanczos
method (FTLM). We show that there is a sizeable window in temperature where NLC
results converge without extrapolations whereas HTE diverges. Upon
extrapolations, the overall agreement between NLC, HTE, and FTLM is excellent
in some cases down to 0.25t. At intermediate temperatures NLC results are
better controlled than other methods, making it easier to judge the convergence
and numerical accuracy of the method.Comment: 7 pages, 12 figures, as publishe
Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice
We study the Heisenberg model on the pinwheel distorted kagome lattice as
observed in the material Rb_2Cu_3SnF_12. Experimentally relevant thermodynamic
properties at finite temperatures are computed utilizing numerical
linked-cluster expansions. We also develop a Lanczos-based, zero-temperature,
numerical linked cluster expansion to study the approach of the pinwheel
distorted lattice to the uniform kagome-lattice Heisenberg model. We find
strong evidence for a phase transition before the uniform limit is reached,
implying that the ground state of the kagome-lattice Heisenberg model is likely
not pinwheel dimerized and is stable to finite pinwheel-dimerizing
perturbations.Comment: 6 pages, 6 figures, 1 tabl
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