5,967 research outputs found
The Kernel Polynomial Method
Efficient and stable algorithms for the calculation of spectral quantities
and correlation functions are some of the key tools in computational condensed
matter physics. In this article we review basic properties and recent
developments of Chebyshev expansion based algorithms and the Kernel Polynomial
Method. Characterized by a resource consumption that scales linearly with the
problem dimension these methods enjoyed growing popularity over the last decade
and found broad application not only in physics. Representative examples from
the fields of disordered systems, strongly correlated electrons,
electron-phonon interaction, and quantum spin systems we discuss in detail. In
addition, we illustrate how the Kernel Polynomial Method is successfully
embedded into other numerical techniques, such as Cluster Perturbation Theory
or Monte Carlo simulation.Comment: 32 pages, 17 figs; revised versio
QCD Thermodynamics from the Lattice
We review the current methods and results of lattice simulations of quantum
chromodynamics at nonzero temperatures and densities. The review is intended to
introduce the subject to interested nonspecialists and beginners. It includes a
brief overview of lattice gauge theory, a discussion of the determination of
the crossover temperature, the QCD phase diagram at zero and nonzero densities,
the equation of state, some in-medium properties of hadrons including
charmonium, and some plasma transport coefficients.Comment: 74 pp. 31 figs. To appear in the European Physical Journal A and
Advances in Physics of Particles and Nuclei. Added references, corrected
typos, and updated the discussion of the thermal heavy quark/antiquark
potential. Added and updated references. Final versio
Cold atom simulation of interacting relativistic quantum field theories
We demonstrate that Dirac fermions self-interacting or coupled to dynamic
scalar fields can emerge in the low energy sector of designed bosonic and
fermionic cold atom systems. We illustrate this with two examples defined in
two spacetime dimensions. The first one is the self-interacting Thirring model.
The second one is a model of Dirac fermions coupled to a dynamic scalar field
that gives rise to the Gross-Neveu model. The proposed cold atom experiments
can be used to probe spectral or correlation properties of interacting quantum
field theories thereby presenting an alternative to lattice gauge theory
simulations.Comment: 5 pages, 3 figues, Phys. Rev. Lett. versio
Few-qubit quantum-classical simulation of strongly correlated lattice fermions
We study a proof-of-principle example of the recently proposed hybrid
quantum-classical simulation of strongly correlated fermion models in the
thermodynamic limit. In a "two-site" dynamical mean-field theory (DMFT)
approach we reduce the Hubbard model to an effective impurity model subject to
self-consistency conditions. The resulting minimal two-site representation of
the non-linear hybrid setup involves four qubits implementing the impurity
problem, plus an ancilla qubit on which all measurements are performed. We
outline a possible implementation with superconducting circuits feasible with
near-future technology.Comment: 20 pages, 10 figure
Exact Chiral Symmetry on the Lattice
Developments during the last eight years have refuted the folklore that
chiral symmetries cannot be preserved on the lattice. The mechanism that
permits chiral symmetry to coexist with the lattice is quite general and may
work in Nature as well. The reconciliation between chiral symmetry and the
lattice is likely to revolutionize the field of numerical QCD.Comment: 30 pages, LaTeX, reference adde
A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
We extend a standard stochastic theory to study open quantum systems coupled
to generic quantum environments including the three fundamental classes of
noninteracting particles: bosons, fermions and spins. In this unified
stochastic approach, the generalized stochastic Liouville equation (SLE)
formally captures the exact quantum dissipations when noise variables with
appropriate statistics for different bath models are applied. Anharmonic
effects of a non-Gaussian bath are precisely encoded in the bath multi-time
correlation functions that noise variables have to satisfy. Staring from the
SLE, we devise a family of generalized hierarchical equations by averaging out
the noise variables and expand bath multi-time correlation functions in a
complete basis of orthonormal functions. The general hiearchical equations
constitute systems of linear equations that provide numerically exact
simulations of quantum dynamics. For bosonic bath models, our general
hierarchical equation of motion reduces exactly to an extended version of
hierarchical equation of motion which allows efficient simulation for arbitrary
spectral densities and temperature regimes. Similar efficiency and exibility
can be achieved for the fermionic bath models within our formalism. The spin
bath models can be simulated with two complementary approaches in the presetn
formalism. (I) They can be viewed as an example of non-Gaussian bath models and
be directly handled with the general hierarchical equation approach given their
multi-time correlation functions. (II) Alterantively, each bath spin can be
first mapped onto a pair of fermions and be treated as fermionic environments
within the present formalism.Comment: 31 pages, 2 figure
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