Generalized quantum microcanonical ensemble from random matrix product states

Abstract

We propose a tensor network algorithm for the efficient sampling of quantum pure states belonging to a generalized microcanonical ensemble. The algorithm consists in an adaptation of the power method to a recently introduced ensemble of random matrix product states. The microcanonical ensemble that we consider is characterized by the fact that the participating energy eigenstates are not required to have identical statistical weight. To test the method we apply it to the Heisenberg model with an external magnetic field, and we find that the magnetization curves, due to the microcanonical constraint, are qualitatively different from those obtained in the canonical ensemble. Possible future applications include the study of isolated quantum systems evolving after a quantum quench.

7 pages, 4 figures

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• Thermal Pure Quantum Matrix Product States Recovering a Volume Law Entanglement
• Pure state thermodynamics with matrix product states
• Purity of thermal mixed quantum states
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
• Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
• Sample complexity of matrix product states at finite temperature
• Stalled response near thermal equilibrium in periodically driven systems