The spectrum of local random Hamiltonians

Abstract

The spectrum of a local random Hamiltonian can be represented generically by the so-called $\epsilon$-free convolution of its local terms' probability distributions. We establish an isomorphism between the set of $\epsilon$-noncrossing partitions and permutations to study its spectrum. Moreover, we derive some lower and upper bounds for the largest eigenvalue of the Hamiltonian.

arXiv comment22 pages

References in corpus (13)

• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Learning a local Hamiltonian from local measurements
• Bounds on Information Propagation in Disordered Quantum Spin Chains
• Non-Gaussian Non-Hermitean Random Matrix Theory: phase transitions and addition formalism
• Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices
• Dynamical Localization in Disordered Quantum Spin Systems
• Convergence to equilibrium under a random Hamiltonian
• Generic Local Hamiltonians are Gapless
• Density of States of Quantum Spin Systems from Isotropic Entanglement
• Many-body systems with random spatially local interactions
• Epsilon-noncrossing partitions and cumulants in free probability
• Hamiltonian Dynamics of a Sum of Interacting Random Matrices
• Matrix models for $\epsilon$-free independence

Cited by in corpus (1)

• Energy dynamics in a class of local random matrix Hamiltonians