Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the local equivalence between the canonical and the microcanonical
  distributions for quantum spin systems   We study a quantum spin system on the $d$-dimensional hypercubic lattice
$\Lambda$ with $N=L^d$ sites with periodic boundary conditions. We take an
arbitrary translation invariant short-ranged Hamiltonian. For this system, we
consider both the canonical ensemble with inverse temperature $\beta_0$ and the
microcanonical ensemble with the corresponding energy $U_N(\beta_0)$. For an
arbitrary self-adjoint operator $\hat{A}$ whose support is contained in a
hypercubic block $B$ inside $\Lambda$, we prove that the expectation values of
$\hat{A}$ with respect to these two ensembles are close to each other for large
$N$ provided that $\beta_0$ is sufficiently small and the number of sites in
$B$ is $o(N^{1/2})$. This establishes the equivalence of ensembles on the level
of local states in a large but finite system. The result is essentially that of
Brandao and Cramer (here restricted to the case of the canonical and the
microcanonical ensembles), but we prove improved estimates in an elementary
manner. We also review and prove standard results on the thermodynamic limits
of thermodynamic functions and the equivalence of ensembles in terms of
thermodynamic functions. The present paper assumes only elementary knowledge on
quantum statistical mechanics and quantum spin systems.

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The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an