Daniel Ranard — Page 2

arXiv2019

Target Space Entanglement Entropy

We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen sub-algebra of observables $\mathcal{A}$. The entanglement entropy is calculated as the entropy of the density matrix restricted to $\mathcal{A}$. As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra $\mathcal{A}$ is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting.

hep-th↗

arXiv2019

Determining a local Hamiltonian from a single eigenstate

We ask whether the knowledge of a single eigenstate of a local Hamiltonian is sufficient to uniquely determine the Hamiltonian. We present evidence that the answer is "yes" for generic local Hamiltonians, given either the ground state or an excited eigenstate. In fact, knowing only the two-point equal-time correlation functions of local observables with respect to the eigenstate should generically be sufficient to exactly recover the Hamiltonian for finite-size systems, with numerical algorithms that run in a time that is polynomial in the system size. We also investigate the large-system limit, the sensitivity of the reconstruction to error, and the case when correlation functions are only known for observables on a fixed sub-region. Numerical demonstrations support the results for finite one-dimensional spin chains (though caution must be taken when extrapolating to infinite-size systems in higher dimensions). For the purpose of our analysis, we define the "$k$-correlation spectrum" of a state, which reveals properties of local correlations in the state and may be of independent interest.

quant-ph↗