Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1211.0006 · Physical Review B

Oscillating terms in the Renyi entropy of Fermi gases and liquids

Brian G. Swingle, Jeremy McMinis, Norm M. Tubman

Published Jun 12, 2013• 20 citations
arXivHTMLPDF

Abstract

In this work we compute subleading oscillating terms in the Renyi entropy of Fermi gases and liquids corresponding to $2{k}_{F}$-like oscillations. Our theoretical tools are the one-dimensional formulation of Fermi liquid entanglement familiar from discussions of the logarithmic violation of the area law and quantum Monte Carlo calculations. The main result is a formula for the oscillating term for any region geometry and a spherical Fermi surface in any dimension. Specializing to two dimensions, we compare this term to numerical calculations of Renyi entropies using the correlation function method and find excellent agreement. We also compare with quantum Monte Carlo data on interacting Fermi liquids where we also find agreement up to moderate interaction strengths.

DOI
10.1103/physrevb.87.235112

Related papers

Rényi entropy, mutual information, and fluctuation properties of Fermi liquids

Brian G. Swingle

We compute the leading contribution to the ground-state R\'enyi entropy ${S}_{\ensuremath{\alpha}}$ for a region of linear size $L$ in a Fermi liquid in $d$ dimensions. The result contains a universal boundary law violating term simply related to the more familiar entanglement entropy. We also obtain a universal crossover function that smoothly interpolates between the zero-temperature result and the ordinary thermal R\'enyi entropy of a Fermi liquid. Formulas for the entanglement entropy of more complicated regions, including nonconvex and disconnected regions, are obtained from the conformal field theory formulation of Fermi surface dynamics. These results permit an evaluation of the quantum mutual information between different regions in a Fermi liquid. We also study the number fluctuations in a Fermi liquid. Taken together, these results give a reasonably complete characterization of the low-energy quantum information content of Fermi liquids.

arXiv:1007.4825•Physical Review B•Jul 12, 2012•47 citations

Renyi entropy of the interacting Fermi liquid

Jeremy McMinis, Norm M. Tubman

Entanglement properties, including the Renyi $\ensuremath{\alpha}$ entropies and scaling laws, are becoming increasingly important in condensed-matter physics because they can be used to determine physical properties and the ``fingerprint'' of quantum phases. In this work we use variational quantum Monte Carlo to compute the Renyi $\ensuremath{\alpha}$ entropies, their scaling laws, and the relationship between different $\ensuremath{\alpha}$ entropies for one of the most important phases in condensed matter, the interacting Fermi liquid. We also investigate the relationship between the scaling laws and the discontinuity in the momentum distribution at the Fermi surface. Contrary to recent theoretical predictions, we find that interactions increase the prefactor for the $\ensuremath{\alpha}$-entropy scaling laws for all particle interaction strengths and forms. We also show that a theory of these scaling laws for the interacting systems may be developed by extending the free theory to incorporate properties of the momentum distribution.

arXiv:1207.4188•Physical Review B•Feb 28, 2013•67 citations

Entanglement Entropy of the ν=1/2 Composite Fermion Non-Fermi Liquid State

Junping Shao, Eun-Ah Kim, F. D. M. Haldane +1 more

The so-called "non-Fermi liquid" behavior is very common in strongly correlated systems. However, its operational definition in terms of "what it is not" is a major obstacle for the theoretical understanding of this fascinating correlated state. Recently there has been much interest in entanglement entropy as a theoretical tool to study non-Fermi liquids. So far explicit calculations have been limited to models without direct experimental realizations. Here we focus on a two-dimensional electron fluid under magnetic field and filling fraction ν=1/2, which is believed to be a non-Fermi liquid state. Using a composite fermion wave function which captures the ν=1/2 state very accurately, we compute the second Rényi entropy using the variational Monte Carlo technique. We find the entanglement entropy scales as LlogL with the length of the boundary L as it does for free fermions, but has a prefactor twice that of free fermions.

arXiv:1403.0577•Physical Review Letters•May 22, 2015•51 citations

Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula

Ryan V. Mishmash, Olexei I. Motrunich

Quantum phases characterized by surfaces of gapless excitations are known to violate the otherwise ubiquitous boundary law of entanglement entropy in the form of a multiplicative log correction: $S\ensuremath{\sim}{L}^{d\ensuremath{-}1}logL$. Using variational Monte Carlo, we calculate the second R\'enyi entropy for a model wave function of the $\ensuremath{\nu}=1/2$ composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total R\'enyi entropy and, crucially, its contributions from the modulus and sign of the wave function on various finite-size geometries, we argue that the prefactor of the leading $L\phantom{\rule{0.16em}{0ex}}logL$ term is equivalent to that in the analogous free fermion wave function. In contrast to the recent results of Shao et al. [Phys. Rev. Lett. 114, 206402 (2015)], we thus conclude that the ``Widom formula'' holds even in this non-Fermi liquid CFL state. More generally, our results further elucidate---and place on a more quantitative footing---the relationship between nontrivial wave function sign structure and $S\ensuremath{\sim}L\phantom{\rule{0.16em}{0ex}}logL$ entanglement scaling in such highly entangled gapless phases.

arXiv:1605.08787•Physical review. B./Physical review. B•Aug 25, 2016•17 citations

Particle number fluctuations, Rényi entropy, and symmetry-resolved entanglement entropy in a two-dimensional Fermi gas from multidimensional bosonization

Mao Tian Tan, Shinsei Ryu

We revisit the computation of particle number fluctuations and the R\'enyi entanglement entropy of a two-dimensional Fermi gas using multidimensional bosonization. In particular, we compute these quantities for a circular Fermi surface and a circular entangling surface. Both quantities display a logarithmic violation of the area law, and the R\'enyi entropy agrees with the Widom conjecture. Lastly, we compute the symmetry-resolved entanglement entropy for the two-dimensional circular Fermi surface and find that, while the total entanglement entropy scales as $RlnR$, the symmetry-resolved entanglement scales as $\sqrt{RlnR}$, where $R$ is the radius of the subregion of our interest.

arXiv:1911.01451•Physical review. B./Physical review. B•Jun 29, 2020•88 citations

Aspects of quantum information in finite density field theory

Lucas Daguerre, Raimel A. Medina, Mario Solís +1 more

Abstract We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

arXiv:2011.01252•Journal of High Energy Physics•Mar 1, 2021•8 citations
In this work we compute subleading oscillating terms in the Renyi entropy of Fermi gases and liquids corresponding to 2kF2{k}_{F}2kF​-like oscillations. Our theoretical tools are the one-dimensional formulation of Fermi liquid entanglement familiar from discussions of the logarithmic violation of the area law and quantum Monte Carlo calculations. The main result is a formula for the oscillating term for any region geometry and a spherical Fermi surface in any dimension. Specializing to two dimensions, we compare this term to numerical calculations of Renyi entropies using the correlation function method and find excellent agreement. We also compare with quantum Monte Carlo data on interacting Fermi liquids where we also find agreement up to moderate interaction strengths.
We compute the leading contribution to the ground-state R\'enyi entropy ${S}_{\ensuremath{\alpha}}$ for a region of linear size LLL in a Fermi liquid in ddd dimensions. The result contains a universal boundary law violating term simply related to the more familiar entanglement entropy. We also obtain a universal crossover function that smoothly interpolates between the zero-temperature result and the ordinary thermal R\'enyi entropy of a Fermi liquid. Formulas for the entanglement entropy of more complicated regions, including nonconvex and disconnected regions, are obtained from the conformal field theory formulation of Fermi surface dynamics. These results permit an evaluation of the quantum mutual information between different regions in a Fermi liquid. We also study the number fluctuations in a Fermi liquid. Taken together, these results give a reasonably complete characterization of the low-energy quantum information content of Fermi liquids.
Entanglement properties, including the Renyi $\ensuremath{\alpha}$ entropies and scaling laws, are becoming increasingly important in condensed-matter physics because they can be used to determine physical properties and the ``fingerprint'' of quantum phases. In this work we use variational quantum Monte Carlo to compute the Renyi $\ensuremath{\alpha}$ entropies, their scaling laws, and the relationship between different $\ensuremath{\alpha}$ entropies for one of the most important phases in condensed matter, the interacting Fermi liquid. We also investigate the relationship between the scaling laws and the discontinuity in the momentum distribution at the Fermi surface. Contrary to recent theoretical predictions, we find that interactions increase the prefactor for the $\ensuremath{\alpha}$-entropy scaling laws for all particle interaction strengths and forms. We also show that a theory of these scaling laws for the interacting systems may be developed by extending the free theory to incorporate properties of the momentum distribution.
The so-called "non-Fermi liquid" behavior is very common in strongly correlated systems. However, its operational definition in terms of "what it is not" is a major obstacle for the theoretical understanding of this fascinating correlated state. Recently there has been much interest in entanglement entropy as a theoretical tool to study non-Fermi liquids. So far explicit calculations have been limited to models without direct experimental realizations. Here we focus on a two-dimensional electron fluid under magnetic field and filling fraction ν=1/2, which is believed to be a non-Fermi liquid state. Using a composite fermion wave function which captures the ν=1/2 state very accurately, we compute the second Rényi entropy using the variational Monte Carlo technique. We find the entanglement entropy scales as LlogL with the length of the boundary L as it does for free fermions, but has a prefactor twice that of free fermions.
Quantum phases characterized by surfaces of gapless excitations are known to violate the otherwise ubiquitous boundary law of entanglement entropy in the form of a multiplicative log correction: $S\ensuremath{\sim}{L}^{d\ensuremath{-}1}logL$. Using variational Monte Carlo, we calculate the second R\'enyi entropy for a model wave function of the $\ensuremath{\nu}=1/2$ composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total R\'enyi entropy and, crucially, its contributions from the modulus and sign of the wave function on various finite-size geometries, we argue that the prefactor of the leading LlogLL\phantom{\rule{0.16em}{0ex}}logLLlogL term is equivalent to that in the analogous free fermion wave function. In contrast to the recent results of Shao et al. [Phys. Rev. Lett. 114, 206402 (2015)], we thus conclude that the ``Widom formula'' holds even in this non-Fermi liquid CFL state. More generally, our results further elucidate---and place on a more quantitative footing---the relationship between nontrivial wave function sign structure and $S\ensuremath{\sim}L\phantom{\rule{0.16em}{0ex}}logL$ entanglement scaling in such highly entangled gapless phases.
We revisit the computation of particle number fluctuations and the R\'enyi entanglement entropy of a two-dimensional Fermi gas using multidimensional bosonization. In particular, we compute these quantities for a circular Fermi surface and a circular entangling surface. Both quantities display a logarithmic violation of the area law, and the R\'enyi entropy agrees with the Widom conjecture. Lastly, we compute the symmetry-resolved entanglement entropy for the two-dimensional circular Fermi surface and find that, while the total entanglement entropy scales as RlnRRlnRRlnR, the symmetry-resolved entanglement scales as RlnR\sqrt{RlnR}RlnR​, where RRR is the radius of the subregion of our interest.
Abstract We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.