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Register a new userPartition Functions of Strongly Correlated Electron Systems as Fermionants
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Added by
Shailesh Chandrasekharan
Publication date
2011
fields
Physics
and research's language is
English
Authors
Shailesh Chandrasekharan
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We introduce a new mathematical object, the fermionant ${mathrm{Ferm}}_N(G)$, of type $N$ of an $n times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces to the determinant. The partition function of the repulsive Hubbard model, of geometrically frustrated quantum antiferromagnets, and of Kondo lattice models can be expressed as fermionants of type N=2, which naturally incorporates infinite on-site repulsion. A computation of the fermionant in polynomial time would solve many interesting fermion sign problems.
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We present the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). The software is available from our web server at http://alps.comp-phys.org.
We reexamine the Yang-Yang-Takahashi method of deriving the thermodynamic Bethe ansatz equations which describe strongly correlated electron systems of fundamental physical interest, such as the Hubbard, $s-d$ exchange (Kondo) and Anderson models. It is shown that these equations contain some additional terms which may play an important role in the physics of the systems.
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A number of recent experiments report the low-temperature thermopower $alpha$ and specific heat coefficients $gamma=C_V/T$ of strongly correlated electron systems. Describing the charge and heat transport in a thermoelectric by transport equations, and assuming that the charge current and the heat current densities are proportional to the number density of the charge carriers, we obtain a simple mean-field relationship between $alpha$ and the entropy density $cal S$ of the charge carriers. We discuss corrections to this mean-field formula and use results obtained for the periodic Anderson and the Falicov-Kimball models to explain the concentration (chemical pressure) and temperature dependence of $alpha/gamma T$ in EuCu$_2$(Ge$_{1-x}$Si$_x$)$_2$, CePt$_{1-x}$Ni$_x$, and YbIn$_{1-x}$Ag${_x}$Cu$_4$ intermetallic compounds. % We also show, using the poor mans mapping which approximates the periodic Anderson lattice by the single impurity Anderson model, that the seemingly complicated behavior of $alpha(T)$ can be explained in simple terms and that the temperature dependence of $alpha(T)$ at each doping level is consistent with the magnetic character of 4{it f} ions.
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