Connection between low energy effective Hamiltonians and energy level statistics

Abstract

We study the level statistics of a non-integrable one dimensional interacting fermionic system characterized by the GOE distribution. We calculate numerically on a finite size system the level spacing distribution $P(s)$ and the Dyson-Mehta ${\Delta }_3$ correlation. We observe that its low energy spectrum follows rather the Poisson distribution, characteristic of an integrable system, consistent with the fact that the low energy excitations of this system are described by the Luttinger model. We propose this Random Matrix Theory analysis as a probe for the existence and integrability of low energy effective Hamiltonians for strongly correlated systems.

REVTEX, 5 postscript figures at the end of the file

References in corpus (1)

• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian

Cited by in corpus (19)

• Strong and weak thermalization of infinite non-integrable quantum systems
• Quantum Quenches, Thermalization and Many-Body Localization
• Evidence for ideal insulating/conducting state in a 1D integrable system
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• The Quantum Inverse Scattering Method for Hubbard-like Models
• Quantum Chaos in the Bose-Hubbard model
• Crossover from Poisson to Wigner-Dyson Level Statistics in Spin Chains with Integrability Breaking
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
• Incoherent transport induced by a single static impurity in a Heisenberg chain
• Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Interacting systems and wormholes
• Many-body localization and thermalization in the full probability distribution function of observables
• Shallow Coulomb Gap and Weak Level-Level Correlations in a Deeply Insulating Electron System with Interactions
• Parametric Excitation of a 1D Gas in Integrable and Nonintegrable Cases
• Superconductivity in the Extended Hubbard Model with More Than Nearest-Neighbour Contributions
• Extended Aharonov-Bohm period analysis of strongly correlated electron systems
• Absence of thermalisation in a Fermi liquid