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Han LP, Zou J, Li H, Shao B. Quantum Information Scrambling in Non-Markovian Open Quantum System. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1532. [PMID: 36359623 PMCID: PMC9689867 DOI: 10.3390/e24111532] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/18/2022] [Revised: 10/17/2022] [Accepted: 10/21/2022] [Indexed: 06/16/2023]
Abstract
In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.
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Affiliation(s)
- Li-Ping Han
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
- School of Science, Tianjin University of Technology, Tianjin 300384, China
| | - Jian Zou
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Hai Li
- School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai 264005, China
| | - Bin Shao
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
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Bulchandani VB, Karrasch C, Moore JE. Superdiffusive transport of energy in one-dimensional metals. Proc Natl Acad Sci U S A 2020; 117:12713-12718. [PMID: 32457150 PMCID: PMC7293602 DOI: 10.1073/pnas.1916213117] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic one-dimensional metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We argue that the expansion of energy when such a nonintegrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix-product-state calculations on a specific perturbed spinless fermion chain. Different metals will have different scaling exponents and shapes in their energy spreading, but the superdiffusive behavior is stable and should be visible in time-resolved experiments.
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Affiliation(s)
- Vir B Bulchandani
- Department of Physics, University of California, Berkeley, CA 94720;
| | - Christoph Karrasch
- Institut für Mathematische Physik, Technische Universität Braunschweig, 38106 Braunschweig, Germany
| | - Joel E Moore
- Department of Physics, University of California, Berkeley, CA 94720
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
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Mierzejewski M, Vidmar L. Quantitative Impact of Integrals of Motion on the Eigenstate Thermalization Hypothesis. PHYSICAL REVIEW LETTERS 2020; 124:040603. [PMID: 32058771 DOI: 10.1103/physrevlett.124.040603] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2019] [Revised: 11/26/2019] [Indexed: 06/10/2023]
Abstract
Even though the eigenstate thermalization hypothesis (ETH) may be introduced as an extension of the random matrix theory, physical Hamiltonians and observables differ from random operators. One of the challenges is to embed local integrals of motion (LIOMs) within the ETH. Here we make steps towards a unified treatment of the ETH in integrable and nonintegrable models with translational invariance. Specifically, we focus on the impact of LIOMs on the fluctuations and structure of the diagonal matrix elements of local observables. We first show that nonvanishing fluctuations entail the presence of LIOMs. Then we introduce a generic protocol to construct observables, subtracted by their projections on LIOMs as well as products of LIOMs. The protocol systematically reduces fluctuations and/or the structure of the diagonal matrix elements. We verify our arguments by numerical results for integrable and nonintegrable models.
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Affiliation(s)
- Marcin Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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Palmero M, Xu X, Guo C, Poletti D. Thermalization with detailed-balanced two-site Lindblad dissipators. Phys Rev E 2019; 100:022111. [PMID: 31574662 DOI: 10.1103/physreve.100.022111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/10/2023]
Abstract
The use of two-site Lindblad dissipators to generate thermal states and study heat transport was raised to prominence by Prosen and Žnidarič [J. Stat. Mech. (2009) P020351742-546810.1088/1742-5468/2009/02/P02035]. Here we propose a variant of this method based on detailed balance of internal levels of the two-site Hamiltonian and characterize its performance. We study the thermalization profile in the chain, the effective temperatures achieved by different single- and two-site observables, and we also investigate the decay of two-time correlations. We find that at a large enough temperature, the steady state approaches closely a thermal state, with a relative error below 1% for the inverse temperature estimated from different observables.
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Affiliation(s)
- Mikel Palmero
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Xiansong Xu
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Chu Guo
- Zhengzhou Information Science and Technology Institute, Zhengzhou 450004, China
| | - Dario Poletti
- Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- Engineering Product Development, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
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Buča B, Prosen T. Charge and spin current statistics of the open Hubbard model with weak coupling to the environment. Phys Rev E 2017; 95:052141. [PMID: 28618579 DOI: 10.1103/physreve.95.052141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Indexed: 06/07/2023]
Abstract
Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.067201] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the XXZ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.
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Affiliation(s)
- Berislav Buča
- Department of Medical Physics and Biophysics, University of Split School of Medicine, 21000 Split, Croatia
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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Santos JP, Landi GT. Microscopic theory of a nonequilibrium open bosonic chain. Phys Rev E 2016; 94:062143. [PMID: 28085332 DOI: 10.1103/physreve.94.062143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Indexed: 06/06/2023]
Abstract
Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.
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Affiliation(s)
- Jader P Santos
- Universidade Federal do ABC, 09210-580 Santo André, Brazil
| | - Gabriel T Landi
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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Guimarães PH, Landi GT, de Oliveira MJ. Nonequilibrium quantum chains under multisite Lindblad baths. Phys Rev E 2016; 94:032139. [PMID: 27739825 DOI: 10.1103/physreve.94.032139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2016] [Indexed: 06/06/2023]
Abstract
We study a quantum XX chain coupled to two heat reservoirs that act on multiple sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators, which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formulas for all steady-state properties of the system. We compute both the particle or magnetization current and the energy current, both of which are found to have the structure of Landauer's formula. We also obtain exact formulas for the Onsager coefficients. All properties are found to differ substantially from those of a single-site bath. In particular, we find a strong dependence on the intensity of the bath couplings. In the weak-coupling regime, we show that the Onsager reciprocal relations are satisfied.
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Affiliation(s)
- Pedro H Guimarães
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | | | - Mario J de Oliveira
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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