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Entropy
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Entropy and Information in Quantum Many-Body Systems
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Entropy and Information in Quantum Many-Body Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (20 July 2022) | Viewed by 4504

Special Issue Editors

Prof. Dr. Zhe-Xuan Gong

E-Mail Website
Guest Editor
Colorado School of Mines, Golden, CO 80401, USA
Interests: quantum information theory; non-equilibrium dynamics in quantum many-body systems; quantum simulation with trapped ions; long-range interacting quantum systems; machine learning with quantum data
Prof. Dr. Gioacchino Massimo Palma

E-Mail Website
Guest Editor
1. Department of Physics and Chemistry-Emilio Segrè, University of Palermo, Via Archirafi 36, I-90123 Palermo, PA, Italy
2. NEST, Istituto Nanoscienze-CNR, I-56127 Pisa, PI, Italy
Interests: quantum information theory; foundations of quantum mechanics; quantum thermodynamics; atomic, molecular, and optical (AMO) physics; open quantum systems (quantum dissipation and decoherence); Bose–Einstein condensation (BEC)
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Entropy and information are playing increasingly important roles in the study of quantum many-body systems. On the one hand, the entropy of a subsystem’s quantum state, known as the entanglement entropy, identifies key properties of the quantum system related to quantum phase transitions, topological order, conformal field theory, classical simulability, etc. However, much remains unknown about entanglement entropy, such as its relation to thermodynamic entropy and its scaling with system size in various types of quantum systems. In addition, the entanglement entropy of quantum many-body systems has been connected with the entropy of black holes, leading to the onset of using quantum simulators to study black-hole physics. Experimental measurement of entanglement entropy in quantum simulators remains challenging, with scalable methods being much desired.

On the other hand, information has also become a new keyword in quantum many-body physics. For example, the speed of information propagation in quantum lattices was found to play a vital role in the classification of quantum phases, the stability of the topological order, the entanglement area laws, many-body localization, timescales for thermalization and heating, and digital quantum simulation of many-body systems. Another example is information scrambling, which quantifies how fast quantum information gets lost locally due to many-body interactions. Information scrambling is closely related to quantum chaos and high-energy physics, and there is growing interest in studying it using quantum simulation experiments. Other examples include the study of mutual information, channel capacity, and random number generators in quantum many-body systems.

This Special Issue aims to be a forum for the presentation of new results from the study of entropy and information in quantum many-body systems, with example topics listed above. Both theoretical (including computational) and experimental studies fall within the scope of this Special Issue.

Dr. Zhe-Xuan Gong
Prof. Dr. Gioacchino Massimo Palma
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • entanglement entropy
  • thermodynamic entropy
  • area laws for entropy
  • information scrambling
  • channel capacity
  • quantum speed limit for information propagation
  • random number generation
  • engineered reservoirs
  • quantum thermometry of many body systems
  • thermalization of many body systems
  • quantum thermodynamics of many body systems

Published Papers (2 papers)

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Research

28 pages, 10249 KiB  
Article
Neural-Network Quantum States for Spin-1 Systems: Spin-Basis and Parameterization Effects on Compactness of Representations
by Michael Y. Pei and Stephen R. Clark
Entropy 2021, 23(7), 879; https://doi.org/10.3390/e23070879 - 09 Jul 2021
Cited by 2 | Viewed by 2306
Abstract
Neural network quantum states (NQS) have been widely applied to spin-1/2 systems, where they have proven to be highly effective. The application to systems with larger on-site dimension, such as spin-1 or bosonic systems, has been explored less and predominantly using spin-1/2 Restricted [...] Read more.
Neural network quantum states (NQS) have been widely applied to spin-1/2 systems, where they have proven to be highly effective. The application to systems with larger on-site dimension, such as spin-1 or bosonic systems, has been explored less and predominantly using spin-1/2 Restricted Boltzmann Machines (RBMs) with a one-hot/unary encoding. Here, we propose a more direct generalization of RBMs for spin-1 that retains the key properties of the standard spin-1/2 RBM, specifically trivial product states representations, labeling freedom for the visible variables and gauge equivalence to the tensor network formulation. To test this new approach, we present variational Monte Carlo (VMC) calculations for the spin-1 anti-ferromagnetic Heisenberg (AFH) model and benchmark it against the one-hot/unary encoded RBM demonstrating that it achieves the same accuracy with substantially fewer variational parameters. Furthermore, we investigate how the hidden unit complexity of NQS depend on the local single-spin basis used. Exploiting the tensor network version of our RBM we construct an analytic NQS representation of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state in the xyz spin-1 basis using only M=2N hidden units, compared to M∼O(N2) required in the Sz basis. Additional VMC calculations provide strong evidence that the AKLT state in fact possesses an exact compact NQS representation in the xyz basis with only M=N hidden units. These insights help to further unravel how to most effectively adapt the NQS framework for more complex quantum systems. Full article
(This article belongs to the Special Issue Entropy and Information in Quantum Many-Body Systems)
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15 pages, 777 KiB  
Article
Currents in a Quantum Nanoring Controlled by Non-Classical Electromagnetic Field
by Jerzy Dajka
Entropy 2021, 23(6), 652; https://doi.org/10.3390/e23060652 - 23 May 2021
Cited by 1 | Viewed by 1301
Abstract
Quantum ring accommodating interacting spin-less fermions threaded by magnetic flux with a non-classical component added to a static, inducing persistent current, is considered. It is investigated how current flowing in the ring becomes affected by a state of non-classical flux and how Coulomb [...] Read more.
Quantum ring accommodating interacting spin-less fermions threaded by magnetic flux with a non-classical component added to a static, inducing persistent current, is considered. It is investigated how current flowing in the ring becomes affected by a state of non-classical flux and how Coulomb interaction between fermions influences entanglement of quantum ring and the driving field. In particular it is shown that in an absence of decoherence and under certain conditions fermion–fermion interaction is necessary for a ring–field entanglement to occur. Full article
(This article belongs to the Special Issue Entropy and Information in Quantum Many-Body Systems)
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