Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining system Hamiltonian from eigenstate measurements without
  correlation functions   Local Hamiltonians arise naturally in physical systems. Despite its seemingly
`simple' local structure, exotic features such as nonlocal correlations and
topological orders exhibit in eigenstates of these systems. Previous studies
for recovering local Hamiltonians from measurements on an eigenstate
$|\psi\rangle$ require information of nonlocal correlation functions. In this
work, we develop an algorithm to determine local Hamiltonians from only local
measurements on $|\psi\rangle$, by reformulating the task as an unconstrained
optimization problem of certain target function of Hamiltonian parameters, with
only polynomial number of parameters in terms of system size. We also develop a
machine learning-based-method to solve the first-order gradient used in the
algorithm. Our method is tested numerically for randomly generated local
Hamiltonians and returns promising reconstruction in the desired accuracy. Our
result shed light on the fundamental question on how a single eigenstate can
encode the full system Hamiltonian, indicating a somewhat surprising answer
that only local measurements are enough without additional assumptions, for
generic cases.

14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph