Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetries and boundary conditions with a twist   Interest in finite-size systems has risen in the last decades, due to the
focus on nanotechnological applications and because they are convenient for
numerical treatment that can subsequently be extrapolated to infinite lattices.
Independently of the envisioned application, special attention must be given to
boundary condition, which may or may not preserve the symmetry of the infinite
lattice. Here we present a detailed study of the compatibility between boundary
conditions and conservation laws. The conflict between open boundary conditions
and momentum conservation is well understood, but we examine other symmetries,
as well: we discuss gauge invariance, inversion, spin, and particle-hole
symmetry and their compatibility with open, periodic, and twisted boundary
conditions. We develop the reasoning in the framework of the one-dimensional
half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries.
Our discussion includes analytical and numerical results. Our analytical survey
shows that boundary conditions break one or more symmetries of the
infinite-lattice Hamiltonian. The exception is twisted boundary condition with
the special torsion $\Theta=\pi L/2$, where $L$ is the lattice size. Our
numerical results for the ground-state energy at half-filling and the energy
gap for $L=2$--$7$ show how the breaking of symmetry affects the convergence to
the $L\to\infty$ limit. We compare the computed energies and gaps with the
exact results for the infinite lattice drawn from the Bethe-Ansatz solution.
The deviations are boundary-condition dependent. The special torsion yields
more rapid convergence than open or periodic boundary conditions. For sizes as
small as $L=7$, the numerical results for twisted condition are very close to
the $L\to\infty$ limit. We also discuss the ground-state electronic density and
magnetization at half filling under the three boundary conditions.

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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn