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Fisher information approach to nonequilibrium phase transitions in a quantum XXZ spin chain with boundary noise
ID
Marzolino, Ugo
(
Author
),
ID
Prosen, Tomaž
(
Author
)
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MD5: E74552767CC91F042E2A30CCBA99D859
PID:
20.500.12556/rul/4bb65e8c-c241-4005-9c4d-fec99c0111a5
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https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.104402
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Abstract
We investigated quantum critical behaviors in the nonequilibrium steady state of a XXZ spin chain with boundary Markovian noise using Fisher information. The latter represents the distance between two infinitesimally close states, and its superextensive size scaling witnesses a critical behavior due to a phase transition since all the interaction terms are extensive. Perturbatively, in the noise strength, we found superextensive Fisher information at anisotropy |Δ|⩽1 and irrational $\frac{\arccos\Delta}{\pi}$ irrespective of the order of two noncommuting limits, i.e., the thermodynamic limit and the limit of sending $\frac{\arccos\Delta}{\pi}$ to an irrational number via a sequence of rational approximants. From this result we argue the existence of a nonequilibrium quantum phase transition with a critical phase |Δ|⩽1. From the nonsuperextensivity of the Fisher information of reduced states, we infer that this nonequilibrium quantum phase transition does not have local order parameters but has nonlocal ones, at least at|Δ|=1. In the nonperturbative regime for the noise strength, we numerically computed the reduced Fisher information which lower bounds the full-state Fisher information and is superextensive only at |Δ|=1. From the latter result, we derived local order parameters at |Δ|=1 in the nonperturbative case. The existence of critical behavior witnessed by the Fisher information in the phase |Δ|<1 is still an open problem. The Fisher information also represents the best sensitivity for any estimation of the control parameter, in our case the anisotropy Δ, and its superextensivity implies enhanced estimation precision which is also highly robust in the presence of a critical phase.
Language:
English
Keywords:
quantum mechanics
,
spin models
,
quantum chains
,
phase transitions
,
nonequilibrium statistical mechanics
Typology:
1.01 - Original Scientific Article
Organization:
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Author Accepted Manuscript
Publisher:
American Physical Society
Year:
2017
Number of pages:
Str. 104402-1-104402-10
Numbering:
Vol. 96, iss. 10
PID:
20.500.12556/RUL-100087
UDC:
530.145
ISSN on article:
2469-9950
DOI:
10.1103/PhysRevB.96.104402
COBISS.SI-ID:
3179108
Copyright:
American Physical Society
Publication date in RUL:
05.03.2018
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1553
Downloads:
891
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Record is a part of a journal
Title:
Physical review
Publisher:
American Physical Society
ISSN:
2469-9950
COBISS.SI-ID:
2997348
Secondary language
Language:
Slovenian
Keywords:
kvantna mehanika
,
spinski modeli
,
kvantne verige
,
fazni prehodi
,
neravnovesna statistična mehnaika
Projects
Funder:
EC - European Commission
Funding programme:
H2020
Project number:
694544
Name:
Open many-body non-equilibrium systems
Acronym:
OMNES
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