Related papers: Determining a local Hamiltonian from a single eige…
We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with mean field interaction. This mathematically verifies the observation made in [L.Santos and…
The notion of capacity of entanglement is the quantum information theoretic counterpart of the heat capacity which is defined as the second cumulant of the entanglement spectrum. Given any bipartite pure state, we can define the capacity of…
Reconstructing Hamiltonians from local measurements is key to enabling reliable quantum simulation: both validating the implemented model, and identifying any left-over terms with sufficient precision is a problem of increasing importance.…
Identifying the nature of interactions in a quantum system is essential in understanding any physical phenomena. Acquiring information on the Hamiltonian can be a tough challenge in many-body systems because it generally requires access to…
We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond…
Understanding the extreme sensitivity of the eigenvalues of non-Hermitian Hamiltonians to the boundary conditions is of great importance when analyzing non-Hermitian systems, as it appears generically and is intimately connected to the skin…
Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from…
We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding…
We establish multiple interrelated, fundamental results in quantum many-body systems that can have long-range interactions. For a sufficiently long quantum spin chain, we first show that if the multi-spin interactions in the Hamiltonian…
We describe a general method to identify exact, local parent Hamiltonians for trial states like quantum Hall or spin liquid states, which we have used extensively during the past decade. It can be used to identify exact parent Hamiltonians,…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
We study the conditions for obtaining maximally multipartite entangled states (MMES) as non-degenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits…
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. These Hamiltonians, say $K_{1}$ and $K_{2}$, result to be…
Recent numerical advances in the field of strongly correlated electron systems allow the calculation of the entanglement spectrum and entropies for interacting fermionic systems. An explicit determination of the entanglement (modular)…
We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy…
We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds…
We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between…
Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly…
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…
Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under…