Abstract
The emergence of random eigenstates of quantum many-body systems in integrable-chaos transitions is the underlying mechanism of thermalization for these quantum systems. We use fidelity and modulus fidelity to measure the randomness of eigenstates in quantum many-body systems. Analytic results of modulus fidelity between random vectors are obtained to be a judge for the degree of randomness. Unlike fidelity, which just refers to a kind of criterion of necessity, modulus fidelity can measure the degree of randomness in eigenstates of a one-dimension (1D) hard-core boson system and identifies the integrable-chaos transition in this system.
Highlights
Thermalization is a basic assumption in equilibrium statistical physics, in general it is approached in real material
We investigated the randomness of eigenstates of a quantum many-body system by using the quantities, fidelity and modulus fidelity
To identify the randomness in eigenstates of a quantum many-body system in the integrable–chaos transition, we used modulus fidelity to measure the closeness between eigenstates of quantum many-body system and random vectors
Summary
Thermalization is a basic assumption in equilibrium statistical physics, in general it is approached in real material. Eigenstate thermalization hypothesis (ETH) [9,10,11] has been conjectured so that in generic quantum many-body systems, thermalization occurs at individual energy eigenstates, which means that the expectation value of an few-body observable on one eigenstate equals to its microcanonical ensemble average. ETH indicates that the expectation value of an observable on one enenrgy eigenstate is close to its neighbors in generic quantum many-body systems. We will study how randomness emergences in the integrable-chaos transition in quantum many-body systems. For this purpose, two quantities, fidelity and modulus fidelity, are used.
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