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

Quantitative theory of composite fermions in Bose-Fermi mixtures at $\nu=1$.

Ken K. W., Kun Yang

Published Nov 7, 2021• 0 citations
OpenAlex

Abstract

Composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor $\nu=1$ has been formulated by Dong and Senthil. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor $\nu=1$. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, $\nu_b = 1 -\nu_f$. This tunability enables us to study the dilute limit $\nu_b\ll 1$, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of $\nu_f\ll 1$, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.

Related papers

Quantitative theory of composite fermions in Bose-Fermi mixtures at ν=1

Ken K. W., Kun Yang

The theory of composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level, which provides the relevant degrees of freedom in the limit of strong magnetic field. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor $\ensuremath{\nu}=1$ has been formulated by Dong and Senthil [Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)]. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of a composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor $\ensuremath{\nu}=1$. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, ${\ensuremath{\nu}}_{b}=1\ensuremath{-}{\ensuremath{\nu}}_{f}$. This tunability enables us to study the dilute limit ${\ensuremath{\nu}}_{b}\ensuremath{\ll}1$, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate that gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau- Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of ${\ensuremath{\nu}}_{f}\ensuremath{\ll}1$, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.

arXiv:2111.03568•Physical review. B./Physical review. B•Jan 21, 2022•5 citations

Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Dragoljub Gočanin, Sonja Predin, Marija Dimitrijević Ćirić +2 more

Building on previous work [N. Read, Phys. Rev. B 58, 16262 (1998); Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor $\ensuremath{\nu}=1$, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and apply the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling $p$-wave pairing in the lowest Landau level, and strong coupling $p$-wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.

arXiv:2102.11313•Physical review. B./Physical review. B•Sep 23, 2021•14 citations

Lowest Landau level theory of the bosonic Jain states

Hart Goldman, T. Senthil

Quantum Hall systems offer the most familiar setting where strong interparticle interactions combine with the topology of single-particle states to yield novel phenomena. Despite our mature understanding of these systems, an open challenge has been to develop a microscopic theory capturing both their universal and nonuniversal properties, when the Hamiltonian is restricted to the noncommutative space of the lowest Landau level. Here we develop such a theory for the Jain sequence of bosonic fractional quantum Hall states at fillings $\ensuremath{\nu}=\frac{p}{p+1}$. Building on a lowest Landau level description of a parent composite Fermi liquid at $\ensuremath{\nu}=1$, we describe how to dope the system to reach the Jain states. Upon doping, the composite fermions fill noncommutative generalizations of Landau levels, and the Jain states correspond to integer composite fermion filling. Using this approach, we obtain an approximate expression for the bosonic Jain sequence gaps with no reference to any long-wavelength approximation. Furthermore, we show that the universal properties, such as Hall conductivity, are encoded in an effective noncommutative Chern-Simons theory, which is obtained on integrating out the composite fermions. This theory has the same topological content as the familiar Abelian Chern-Simons theory on commutative space.

arXiv:2110.03700•Physical review. B./Physical review. B•Feb 16, 2022•11 citations

Emergent Gauge Field in Composite-Fermion Metals: A Large-Scale Microscopic Study

Amogh Anakru, Mytraya Gattu, Ajit Coimbatore Balram +4 more

Field theories of the composite-fermion (CF) metal model it as a Fermi sea of composite fermions coupled to an emergent gauge field. Within a random phase approximation, these theories predict that the Landau damping of the gauge field resulting from its coupling to the low-energy, long-wavelength CF particle-hole excitations modifies the electrons' density-density correlation function related to the static structure factor S(q) at wave vector q. This produces a nonanalytic correction ∝q^{3}lnq to S(q) (with the magnetic length ℓ_{B}=1). Thanks to the recently developed quaternion formulation for Jain-Kamilla projection of CF wave functions, the evaluation of S(q) from the accurate microscopic theory of composite fermions has now become possible for systems containing as many as N=900 CFs, which enables a reliable determination of the small-q behavior of S(q). We study CF metals corresponding to electrons at Landau level filling factors ν=1/2 and 1/4, and for completeness, also of bosons at ν=1 and 1/3. In the q→0 limit, our microscopic calculation reveals a q^{3} term in S(q) of the CF metals rather than q^{3}lnq. This behavior is well predicted by a model of a noninteracting Fermi sea of dipolar CFs, which also obtains its coefficient accurately.

arXiv:2509.07151•Physical Review Letters•Nov 24, 2025•2 citations

Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions

Ajit Coimbatore Balram, Csaba Tőke, Jainendra K. Jain

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.

arXiv:1506.02747•Physical Review Letters•Oct 29, 2015•59 citations

Continuous transitions between composite Fermi liquid and Landau Fermi liquid: A route to fractionalized Mott insulators

Maissam Barkeshli, John McGreevy

One of the most successful theories of a non-Fermi-liquid metallic state is the composite Fermi-liquid (CFL) theory of the half-filled Landau level. In this paper, we study continuous quantum phase transitions out of the CFL state and into a Landau Fermi liquid, in the limit of no disorder and fixed particle number. This transition can be induced by tuning the bandwidth of the Landau level relative to the interaction energy, for instance through an externally applied periodic potential. We find a transition to the Landau Fermi liquid through a gapless Mott insulator with a Fermi surface of neutral fermionic excitations. In the presence of spatial symmetries, we also find a direct continuous transition between the CFL and the Landau Fermi liquid. The transitions have a number of characteristic observable signatures, including the presence of two crossover temperature scales, resistivity jumps, and vanishing compressibility. When the composite fermions are paired instead, our results imply quantum critical points between various non-Abelian topological states, including the $\ensuremath{\nu}=1/2$ Moore-Read Pfaffian [Ising $\ifmmode\times\else\texttimes\fi{}$ $U(1)$ topological order], a version of the Kitaev B phase (Ising topological order), and paired electronic superconductors. To study such transitions, we use a projective construction of the CFL, which goes beyond the conventional framework of flux attachment to include a broader set of quantum fluctuations. These considerations suggest a possible route to fractionalized Mott insulators by starting with fractional quantum Hall states and tuning the Landau-level bandwidth.

arXiv:1206.6530•Physical Review B•Aug 21, 2012•39 citations
Quantitative theory of composite fermions in Bose-Fermi mixtures at ν=1\nu=1ν=1.
Composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor ν=1\nu=1ν=1 has been formulated by Dong and Senthil. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor ν=1\nu=1ν=1. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, νb=1−νf\nu_b = 1 -\nu_fνb​=1−νf​. This tunability enables us to study the dilute limit νb≪1\nu_b\ll 1νb​≪1, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of νf≪1\nu_f\ll 1νf​≪1, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.
The theory of composite fermion provides a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level, which provides the relevant degrees of freedom in the limit of strong magnetic field. Recently a low-energy noncommutative field theory for bosons at Landau-level filling factor $\ensuremath{\nu}=1$ has been formulated by Dong and Senthil [Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)]. In the limit of long-wavelength and small-amplitude gauge fluctuation, they found it reduces to the celebrated Halperin-Lee-Read theory of a composite fermion liquid. In this work we consider a Bose-Fermi mixture at total filling factor $\ensuremath{\nu}=1$. Different from previous work, the number density of composite fermions in the mixture and corresponding Fermi momentum can be tuned by changing the filling factor of bosons, ${\ensuremath{\nu}}_{b}=1\ensuremath{-}{\ensuremath{\nu}}_{f}$. This tunability enables us to study the dilute limit ${\ensuremath{\nu}}_{b}\ensuremath{\ll}1$, which allows for a controlled and asymptotically exact calculation of the energy dispersion and effective mass of composite fermions. Furthermore, the approximation of the low-energy description by a commutative field theory is manifestly justified. Most importantly, we demonstrate that gauge fluctuations acquire a Higgs mass due to the presence of a composite boson condensate, as a result of which the system behaves like a genuine Landau- Fermi liquid. Combined with the irrelevance of four-fermion interaction in the dilute limit, we are able to obtain asymptotically exact properties of this composite fermion Fermi liquid. In the opposite limit of ${\ensuremath{\nu}}_{f}\ensuremath{\ll}1$, the Higgs mass goes to zero and we find crossover between Fermi liquid and non-Fermi liquid as temperature increases. Observing these properties either experimentally or numerically provides unambiguous evidence of not only the composite fermions and the Fermi surface they form, but also the presence of emergent gauge fields and their fluctuations due to strong correlation.
Building on previous work [N. Read, Phys. Rev. B 58, 16262 (1998); Z. Dong and T. Senthil, Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor $\ensuremath{\nu}=1$, we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and apply the Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling ppp-wave pairing in the lowest Landau level, and strong coupling ppp-wave pairing in the second Landau level that occurs in a band with nearly flat dispersion, a third power function of momentum.
Quantum Hall systems offer the most familiar setting where strong interparticle interactions combine with the topology of single-particle states to yield novel phenomena. Despite our mature understanding of these systems, an open challenge has been to develop a microscopic theory capturing both their universal and nonuniversal properties, when the Hamiltonian is restricted to the noncommutative space of the lowest Landau level. Here we develop such a theory for the Jain sequence of bosonic fractional quantum Hall states at fillings $\ensuremath{\nu}=\frac{p}{p+1}$. Building on a lowest Landau level description of a parent composite Fermi liquid at $\ensuremath{\nu}=1$, we describe how to dope the system to reach the Jain states. Upon doping, the composite fermions fill noncommutative generalizations of Landau levels, and the Jain states correspond to integer composite fermion filling. Using this approach, we obtain an approximate expression for the bosonic Jain sequence gaps with no reference to any long-wavelength approximation. Furthermore, we show that the universal properties, such as Hall conductivity, are encoded in an effective noncommutative Chern-Simons theory, which is obtained on integrating out the composite fermions. This theory has the same topological content as the familiar Abelian Chern-Simons theory on commutative space.
Field theories of the composite-fermion (CF) metal model it as a Fermi sea of composite fermions coupled to an emergent gauge field. Within a random phase approximation, these theories predict that the Landau damping of the gauge field resulting from its coupling to the low-energy, long-wavelength CF particle-hole excitations modifies the electrons' density-density correlation function related to the static structure factor S(q) at wave vector q. This produces a nonanalytic correction ∝q^{3}lnq to S(q) (with the magnetic length ℓ_{B}=1). Thanks to the recently developed quaternion formulation for Jain-Kamilla projection of CF wave functions, the evaluation of S(q) from the accurate microscopic theory of composite fermions has now become possible for systems containing as many as N=900 CFs, which enables a reliable determination of the small-q behavior of S(q). We study CF metals corresponding to electrons at Landau level filling factors ν=1/2 and 1/4, and for completeness, also of bosons at ν=1 and 1/3. In the q→0 limit, our microscopic calculation reveals a q^{3} term in S(q) of the CF metals rather than q^{3}lnq. This behavior is well predicted by a model of a noninteracting Fermi sea of dipolar CFs, which also obtains its coefficient accurately.
While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.
One of the most successful theories of a non-Fermi-liquid metallic state is the composite Fermi-liquid (CFL) theory of the half-filled Landau level. In this paper, we study continuous quantum phase transitions out of the CFL state and into a Landau Fermi liquid, in the limit of no disorder and fixed particle number. This transition can be induced by tuning the bandwidth of the Landau level relative to the interaction energy, for instance through an externally applied periodic potential. We find a transition to the Landau Fermi liquid through a gapless Mott insulator with a Fermi surface of neutral fermionic excitations. In the presence of spatial symmetries, we also find a direct continuous transition between the CFL and the Landau Fermi liquid. The transitions have a number of characteristic observable signatures, including the presence of two crossover temperature scales, resistivity jumps, and vanishing compressibility. When the composite fermions are paired instead, our results imply quantum critical points between various non-Abelian topological states, including the $\ensuremath{\nu}=1/2$ Moore-Read Pfaffian [Ising $\ifmmode\times\else\texttimes\fi{}$ U(1)U(1)U(1) topological order], a version of the Kitaev B phase (Ising topological order), and paired electronic superconductors. To study such transitions, we use a projective construction of the CFL, which goes beyond the conventional framework of flux attachment to include a broader set of quantum fluctuations. These considerations suggest a possible route to fractionalized Mott insulators by starting with fractional quantum Hall states and tuning the Landau-level bandwidth.