Lorenzo Piroli (Author), Bruno Bertini (Author), J. Ignacio Cirac (Author), Tomaž Prosen (Author)

Abstract

We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

Keywords

kvantna mehanika;nelinearna statistična mehanika;quantum mechanics;nonlinear statistical mechanics;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 536.93
COBISS: 23769347 Link will open in a new window
ISSN: 2469-9950
Views: 406
Downloads: 183
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Other data

Secondary language: Slovenian
Secondary keywords: kvantna mehanika;nelinearna statistična mehanika;
Pages: str. 094304-1-094304-16
Volume: ǂVol. ǂ101
Issue: ǂiss. ǂ9
Chronology: 2020
DOI: 10.1103/PhysRevB.101.094304
ID: 11922578