69 research outputs found
Enhancement of Spin Susceptibility near Charge-Ordering Transition in a Two-Dimensional Extended Hubbard Model
Based on the non-skeleton diagrammatic expansion satisfying the
compressibility and spin-susceptibility sum rules, we investigate static charge
and spin responses in a two-dimensional extended Hubbard model with the
nearest-neighbor Coulomb repulsion in the vicinity of its charge-ordering
transition point. In this expansion, we can calculate approximate charge and
spin response functions by systematic inclusion of vertex corrections, from
which we obtain the uniform susceptibility equal to the so-called q-limit of
the response function and the second-order transition point as a divergent
point in the same response function at some finite wave-number vector. It is
shown that the reentrant charge-ordering transition, which has already been
observed in the random-phase approximation (RPA), remains to take place even
though the vertex corrections are included beyond the RPA. As a prominent
effect of the vertex corrections, we find that the uniform spin susceptibility
is enhanced due to charge fluctuations developing toward the charge-ordering
transition. We give a qualitative comparison of this enhanced spin
susceptibility with the experimental results on the quasi-two-dimensional
organic conductors, together with its explanation in the Landau's Fermi-liquid
theory.Comment: 24 pages, 8 figure
Sparse Modeling in Quantum Many-Body Problems
This review paper describes the basic concept and technical details of sparse modeling and its applications to quantum many-body problems. Sparse modeling refers to methodologies for finding a small number of relevant parameters that well explain a given dataset. This concept reminds us physics, where the goal is to find a small number of physical laws that are hidden behind complicated phenomena. Sparse modeling extends the target of physics from natural phenomena to data, and may be interpreted as “physics for data”. The first half of this review introduces sparse modeling for physicists. It is assumed that readers have physics background but no expertise in data science. The second half reviews applications. Matsubara Green’s function, which plays a central role in descriptions of correlated systems, has been found to be sparse, meaning that it contains little information. This leads to (i) a new method for solving the ill-conditioned inverse problem for analytical continuation, and (ii) a highly compact representation of Matsubara Green’s function, which enables efficient calculations for quantum many-body systems
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