Random Matrix Theory of the Isospectral twirling

Abstract

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.

Submission to SciPost

References in corpus (34)

• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• Black holes as mirrors: quantum information in random subsystems
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Measuring Quantum Coherence with Entanglement
• Dynamics of Loschmidt echoes and fidelity decay
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Evenly distributed unitaries: on the structure of unitary designs
• Aspects of generic entanglement
• Typicality for Generalized Microcanonical Ensembles
• Chaos, Complexity, and Random Matrices
• Introduction to Random Matrices - Theory and Practice
• Loschmidt Echo
• Performance bound for quantum absorption refrigerators
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Jarzynski-like equality for the out-of-time-ordered correlator
• Entangling power of the quantum baker's map
• Optimizing quantum process tomography with unitary 2-designs
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Generalization of von Neumann's Approach to Thermalization
• Scrambling and Complexity in Phase Space
• Unitary designs from statistical mechanics in random quantum circuits
• The Clifford group fails gracefully to be a unitary 4-design
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Quantum Chaos and the Correspondence Principle
• How complex is the quantum motion?
• Conditional Mutual Information of Bipartite Unitaries and Scrambling
• Black Holes, Entanglement and Random Matrices
• Efficient algorithm for multi-qudit twirling for ensemble quantum computation
• Higher-order level spacings in random matrix theory based on Wigner's conjecture
• Universal scrambling in gapless quantum spin chains
• Nonperturbative theory of power spectrum in complex systems
• Power spectrum and form factor in random diagonal matrices and integrable billiards
• Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian Geometry