Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals

A system with charge conservation and lattice translation symmetry has a well-defined filling ν, which is a real number representing the average charge per unit cell. We show that if ν is fractional (i.e., not an integer), this imposes very strong constraints on the low-energy theory of the system a...

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Autores principales:	Dominic V. Else, Ryan Thorngren, T. Senthil
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/430887a5269d4d44847dcba9800bc48e
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spelling	oai:doaj.org-article:430887a5269d4d44847dcba9800bc48e2021-12-02T14:25:40ZNon-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals10.1103/PhysRevX.11.0210052160-3308https://doaj.org/article/430887a5269d4d44847dcba9800bc48e2021-04-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021005http://doi.org/10.1103/PhysRevX.11.021005https://doaj.org/toc/2160-3308A system with charge conservation and lattice translation symmetry has a well-defined filling ν, which is a real number representing the average charge per unit cell. We show that if ν is fractional (i.e., not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems. The most powerful constraint comes about if ν is continuously tunable (i.e., the system is charge compressible), in which case, we show that the low-energy theory must have a very large emergent symmetry group—larger than any compact Lie group. An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved. We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics. We call a system with this property an ersatz Fermi liquid. We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttinger’s theorem (which is thus extended to a large class of non-Fermi liquids) and periodic “quantum oscillations” in the response to an applied magnetic field. We also establish versions of Luttinger’s theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators. Our work makes a connection between filling constraints and the theory of symmetry-protected topological phases, in particular through the concept of “’t Hooft anomalies.”Dominic V. ElseRyan ThorngrenT. SenthilAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021005 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Dominic V. Else Ryan Thorngren T. Senthil Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals
description	A system with charge conservation and lattice translation symmetry has a well-defined filling ν, which is a real number representing the average charge per unit cell. We show that if ν is fractional (i.e., not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems. The most powerful constraint comes about if ν is continuously tunable (i.e., the system is charge compressible), in which case, we show that the low-energy theory must have a very large emergent symmetry group—larger than any compact Lie group. An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved. We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics. We call a system with this property an ersatz Fermi liquid. We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttinger’s theorem (which is thus extended to a large class of non-Fermi liquids) and periodic “quantum oscillations” in the response to an applied magnetic field. We also establish versions of Luttinger’s theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators. Our work makes a connection between filling constraints and the theory of symmetry-protected topological phases, in particular through the concept of “’t Hooft anomalies.”
format	article
author	Dominic V. Else Ryan Thorngren T. Senthil
author_facet	Dominic V. Else Ryan Thorngren T. Senthil
author_sort	Dominic V. Else
title	Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals
title_short	Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals
title_full	Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals
title_fullStr	Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals
title_full_unstemmed	Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals
title_sort	non-fermi liquids as ersatz fermi liquids: general constraints on compressible metals
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/430887a5269d4d44847dcba9800bc48e
work_keys_str_mv	AT dominicvelse nonfermiliquidsasersatzfermiliquidsgeneralconstraintsoncompressiblemetals AT ryanthorngren nonfermiliquidsasersatzfermiliquidsgeneralconstraintsoncompressiblemetals AT tsenthil nonfermiliquidsasersatzfermiliquidsgeneralconstraintsoncompressiblemetals
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Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals

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