Locally Accurate Tensor Networks for Thermal States and Time Evolution

Tensor-network methods are routinely used in approximating various equilibrium and nonequilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximat...
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Autor*in:	Álvaro M. Alhambra [verfasserIn] J. Ignacio Cirac [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Übergeordnetes Werk:	In: PRX Quantum - American Physical Society, 2021, 2(2021), 4, p 040331
Übergeordnetes Werk:	volume:2 ; year:2021 ; number:4, p 040331

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DOI / URN:	10.1103/PRXQuantum.2.040331

Katalog-ID:	DOAJ015323862

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callnumber-first	Q - Science
author	Álvaro M. Alhambra
spellingShingle	Álvaro M. Alhambra misc QC1-999 misc QA76.75-76.765 misc Physics misc Computer software Locally Accurate Tensor Networks for Thermal States and Time Evolution
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topic_title	QC1-999 QA76.75-76.765 Locally Accurate Tensor Networks for Thermal States and Time Evolution
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title	Locally Accurate Tensor Networks for Thermal States and Time Evolution
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title_full	Locally Accurate Tensor Networks for Thermal States and Time Evolution
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title_sort	locally accurate tensor networks for thermal states and time evolution
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title_auth	Locally Accurate Tensor Networks for Thermal States and Time Evolution
abstract	Tensor-network methods are routinely used in approximating various equilibrium and nonequilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximations to thermal states and time evolution demand a bond dimension growing with system size. To address this problem, we construct projected entangled-pair operators that approximate, for all local observables, (i) their thermal expectation values and (ii) their Heisenberg time evolution. The bond dimension required does not depend on system size, but only on the temperature or time. We also show how these can be used to approximate thermal correlation functions and expectation values in quantum quenches.
abstractGer	Tensor-network methods are routinely used in approximating various equilibrium and nonequilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximations to thermal states and time evolution demand a bond dimension growing with system size. To address this problem, we construct projected entangled-pair operators that approximate, for all local observables, (i) their thermal expectation values and (ii) their Heisenberg time evolution. The bond dimension required does not depend on system size, but only on the temperature or time. We also show how these can be used to approximate thermal correlation functions and expectation values in quantum quenches.
abstract_unstemmed	Tensor-network methods are routinely used in approximating various equilibrium and nonequilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximations to thermal states and time evolution demand a bond dimension growing with system size. To address this problem, we construct projected entangled-pair operators that approximate, for all local observables, (i) their thermal expectation values and (ii) their Heisenberg time evolution. The bond dimension required does not depend on system size, but only on the temperature or time. We also show how these can be used to approximate thermal correlation functions and expectation values in quantum quenches.
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title_short	Locally Accurate Tensor Networks for Thermal States and Time Evolution
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