Entanglement growth in diffusive systems

Abstract

Entanglement helps in understanding diverse phenomena, going from quantifying complexity to classifying phases of matter. Here we study the influence of conservation laws on entanglement growth. Focusing on systems with U(1) symmetry, i.e., conservation of charge or magnetization, that exhibits diffusive dynamics, we theoretically predict the growth of entanglement, as quantified by the Rényi entropy, in lattice systems in any spatial dimension d and for any local Hilbert space dimension q (qudits). We find that the growth depends both on d and q, and is in generic case first linear in time, similarly as for systems without any conservation laws. Exception to this rule are chains of 2-level systems where the dependence is a square-root of time at all times. Predictions are numerically verified by simulations of diffusive Clifford circuits with upto ~ 10$^5$ qubits. Such efficiently simulable circuits should be a useful tool for other many-body problems.

Keywords

kvantna mehanika;prepletenost;statistična mehanika;fizika kondenzirane snovi;quantum mechanics;entanglement;statistical mechanics;condensed matter physics;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	530.145
COBISS:	17689859
ISSN:	2399-3650
Views:	310
Downloads:	86
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	kvantna mehanika;prepletenost;statistična mehanika;fizika kondenzirane snovi;
Type (COBISS):	Article
Pages:	9 str.
Volume:	ǂVol. ǂ3
Issue:	ǂart. no. ǂ100
Chronology:	Jun. 2020
DOI:	10.1038/s42005-020-0366-7
ID:	13153729