Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle

Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fi...

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Main Authors: Huan-Qiang Zhou, Qian-Qian Shi, Yan-Wei Dai
Format: Article
Language:English
Published: MDPI AG 2022-09-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/24/9/1306
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author Huan-Qiang Zhou
Qian-Qian Shi
Yan-Wei Dai
author_facet Huan-Qiang Zhou
Qian-Qian Shi
Yan-Wei Dai
author_sort Huan-Qiang Zhou
collection DOAJ
description Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XYZ model, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.
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spelling doaj.art-c8edb240e5a245a8bc7b7371898fc6002023-11-23T16:09:26ZengMDPI AGEntropy1099-43002022-09-01249130610.3390/e24091306Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s PrincipleHuan-Qiang Zhou0Qian-Qian Shi1Yan-Wei Dai2Centre for Modern Physics, Chongqing University, Chongqing 400044, ChinaCentre for Modern Physics, Chongqing University, Chongqing 400044, ChinaCentre for Modern Physics, Chongqing University, Chongqing 400044, ChinaFidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XYZ model, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.https://www.mdpi.com/1099-4300/24/9/1306quantum critical phenomenatensor network algorithmssymmetry-breaking ordertopological orderan analogue of Landauer’s principleanalogues of the four thermodynamic laws
spellingShingle Huan-Qiang Zhou
Qian-Qian Shi
Yan-Wei Dai
Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
Entropy
quantum critical phenomena
tensor network algorithms
symmetry-breaking order
topological order
an analogue of Landauer’s principle
analogues of the four thermodynamic laws
title Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
title_full Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
title_fullStr Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
title_full_unstemmed Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
title_short Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
title_sort fidelity mechanics analogues of the four thermodynamic laws and landauer s principle
topic quantum critical phenomena
tensor network algorithms
symmetry-breaking order
topological order
an analogue of Landauer’s principle
analogues of the four thermodynamic laws
url https://www.mdpi.com/1099-4300/24/9/1306
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