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Inhomogeneous matrix product ansatz and exact steady states of boundary-driven spin chains at large dissipation
ID
Popkov, Vladislav
(
Author
),
ID
Prosen, Tomaž
(
Author
),
ID
Zadnik, Lenart
(
Author
)
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https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.042122
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Abstract
We find novel site-dependent Lax operators in terms of which we demonstrate exact solvability of a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, with jump operators polarizing the boundary spins in arbitrary directions. We write the corresponding nonequilibrium steady state using an inhomogeneous matrix product ansatz, where the constituent matrices satisfy a simple set of linear recurrence relations. Although these matrices can be embedded into an infinite-dimensional auxiliary space, we have verified that they cannot be simultaneously put into a tridiagonal form, not even in the case of axially symmetric (XXZ) bulk interactions and general nonlongitudinal boundary dissipation. We expect our results to have further fundamental applications for the construction of nonlocal integrals of motion for the open XYZ model with arbitrary boundary fields, or the eight-vertex model.
Language:
English
Keywords:
statistical physics
,
open quantum systems
,
quantum spin chains
Typology:
1.01 - Original Scientific Article
Organization:
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Author Accepted Manuscript
Year:
2020
Number of pages:
Str. 042122-1-042122-10
Numbering:
Vol. 101, iss. 4
PID:
20.500.12556/RUL-117817
UDC:
530.145
ISSN on article:
2470-0045
DOI:
10.1103/PhysRevE.101.042122
COBISS.SI-ID:
23761667
Publication date in RUL:
28.07.2020
Views:
1062
Downloads:
693
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Record is a part of a journal
Title:
Physical review
Shortened title:
Phys. rev., E
Publisher:
American Physical Society
ISSN:
2470-0045
COBISS.SI-ID:
2048366611
Secondary language
Language:
Slovenian
Keywords:
statistična fizika
,
odprti kvantni sistemi
,
kvantne spinske verige
Projects
Funder:
EC - European Commission
Funding programme:
H2020
Project number:
694544
Name:
Open Many-body Non-Equilibrium Systems
Acronym:
OMNES
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0402
Name:
Matematična fizika
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