Correlations, Spectra and Entanglement Transitions in Ensembles of Matrix Product States

• URL: http://arxiv.org/abs/2412.14261v2
• Date: Fri, 17 Jan 2025 09:50:10 GMT
• Title: Correlations, Spectra and Entanglement Transitions in Ensembles of Matrix Product States
• Authors: Hugo Lóio, Guillaume Cecile, Sarang Gopalakrishnan, Guglielmo Lami, Jacopo De Nardis,
• Abstract summary: We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $chi$. In all cases, we analyze the spectra of the MPS transfer matrices and relate them to the spreading of mutual information in the MPS state. We show the existence of a measurement-induced entanglement transition (MIPT) in MPS ensembles, with the averaged dimension of the transfer matrix's null space serving as the effective order parameter.
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• Abstract: We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential unitary circuits, (ii) random brickwork unitary circuits, and (iii) circuits involving both unitaries and projective measurements. In all cases, we analyze the spectra of the MPS transfer matrices and relate them to the spreading of mutual information in the MPS state. We demonstrate how different features of the spectral density correspond to distinct types of circuits, revealing that these MPS ensembles retain crucial physical information about the underlying microscopic dynamics. Notably, in the presence of quantum monitoring, we show the existence of a measurement-induced entanglement transition (MIPT) in MPS ensembles, with the averaged dimension of the transfer matrix's null space serving as the effective order parameter.

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