Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories
The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their technological exploitation . A central question in open quantum systems concerns the fate of quantum correlat...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2024
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| Online Access: | https://hdl.handle.net/10356/173546 |
| _version_ | 1811681377822703616 |
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| author | Verstraelen, Wouter Huybrechts, Dolf Roscilde, Tommaso Wouters, Michiel |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Verstraelen, Wouter Huybrechts, Dolf Roscilde, Tommaso Wouters, Michiel |
| author_sort | Verstraelen, Wouter |
| collection | NTU |
| description | The study of quantum many-body physics in Liouvillian open quantum systems
becomes increasingly important with the recent progress in experimental control
on dissipative systems and their technological exploitation . A central
question in open quantum systems concerns the fate of quantum correlations, and
the possibility of controlling them by engineering the competition between the
Hamiltonian dynamics and the coupling to a bath. Such a question is challenging
from a theoretical point of view, as numerical methods faithfully accounting
for quantum correlations are either relying on exact diagonalization, limiting
drastically the sizes that can be treated; or on approximations on the range or
strength of quantum correlations, associated to the choice of a specific Ansatz
for the density matrix. In this work we propose a new method to treat open
quantum-spin lattices, based on stochastic quantum trajectories for the
solution of the open-system dynamics. Along each trajectory, the hierarchy of
equations of motion for many-point spin-spin correlators is truncated to a
given finite order, assuming that multivariate $k$-th order cumulants vanish
for $k$ exceeding a cutoff $k_c$. This allows tracking the evolution of quantum
spin-spin correlations up to order $k_c$ for all length scales. We validate
this approach in the paradigmatic case of the phase transitions of the
dissipative 2D XYZ lattice, subject to spontaneous decay. We convincingly
assess the existence of steady-state phase transitions from paramagnetic to
ferromagnetic, and back to paramagnetic, upon increasing one of the Hamiltonian
couplings; as well as their classical Ising nature. Moreover, the approach
allows us to show the presence of significant quantum correlations in the
vicinity of the dissipative critical point, and to unveil the presence of spin
squeezing, a tight lower bound to the quantum Fisher information. |
| first_indexed | 2024-10-01T03:39:59Z |
| format | Journal Article |
| id | ntu-10356/173546 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:39:59Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1735462024-02-19T15:34:47Z Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories Verstraelen, Wouter Huybrechts, Dolf Roscilde, Tommaso Wouters, Michiel School of Physical and Mathematical Sciences Physics Equations of Motion Fisher Information Matrix The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their technological exploitation . A central question in open quantum systems concerns the fate of quantum correlations, and the possibility of controlling them by engineering the competition between the Hamiltonian dynamics and the coupling to a bath. Such a question is challenging from a theoretical point of view, as numerical methods faithfully accounting for quantum correlations are either relying on exact diagonalization, limiting drastically the sizes that can be treated; or on approximations on the range or strength of quantum correlations, associated to the choice of a specific Ansatz for the density matrix. In this work we propose a new method to treat open quantum-spin lattices, based on stochastic quantum trajectories for the solution of the open-system dynamics. Along each trajectory, the hierarchy of equations of motion for many-point spin-spin correlators is truncated to a given finite order, assuming that multivariate $k$-th order cumulants vanish for $k$ exceeding a cutoff $k_c$. This allows tracking the evolution of quantum spin-spin correlations up to order $k_c$ for all length scales. We validate this approach in the paradigmatic case of the phase transitions of the dissipative 2D XYZ lattice, subject to spontaneous decay. We convincingly assess the existence of steady-state phase transitions from paramagnetic to ferromagnetic, and back to paramagnetic, upon increasing one of the Hamiltonian couplings; as well as their classical Ising nature. Moreover, the approach allows us to show the presence of significant quantum correlations in the vicinity of the dissipative critical point, and to unveil the presence of spin squeezing, a tight lower bound to the quantum Fisher information. Ministry of Education (MOE) Published version This work is supported by UAntwerpen/DOCPRO/34878. W.V. gratefully acknowledges support from the Singapore Ministry of Education Tier 2 Grant No. MOET2EP50121-0020. D.H. and T.R. gratefully acknowledge the support of ANR (‘EELS’ project) and QuantERA (‘MAQS’ project). Part of the computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government department EWI. 2024-02-13T07:36:27Z 2024-02-13T07:36:27Z 2023 Journal Article Verstraelen, W., Huybrechts, D., Roscilde, T. & Wouters, M. (2023). Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories. PRX Quantum, 4(3), 030304-1-030304-28. https://dx.doi.org/10.1103/PRXQuantum.4.030304 2691-3399 https://hdl.handle.net/10356/173546 10.1103/PRXQuantum.4.030304 2-s2.0-85167872481 3 4 030304-1 030304-28 en MOET2EP50121-0020 PRX Quantum © 2023 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. application/pdf |
| spellingShingle | Physics Equations of Motion Fisher Information Matrix Verstraelen, Wouter Huybrechts, Dolf Roscilde, Tommaso Wouters, Michiel Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories |
| title | Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories |
| title_full | Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories |
| title_fullStr | Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories |
| title_full_unstemmed | Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories |
| title_short | Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories |
| title_sort | quantum and classical correlations in open quantum spin lattices via truncated cumulant trajectories |
| topic | Physics Equations of Motion Fisher Information Matrix |
| url | https://hdl.handle.net/10356/173546 |
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