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:hep-th/9811109 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction

Ivan Andrić, Velimir Bardek, Larisa Jonke

Published Apr 23, 1999• 8 citations
arXivHTMLPDF

Abstract

We consider the large-$N$ Chern-Simons theory for attractive bosonic matter (Jackiw-Pi model) in the Hamiltonian collective-field approach based on the $1/N$ expansion. We show that the dynamics of low-lying density excitations around the ground-state vortex configuration is equivalent to that of the Sutherland model. The correspondence between the Chern-Simons coupling constant $\ensuremath{\lambda}$ and the Calogero-Sutherland statistical parameter ${\ensuremath{\lambda}}_{s}$ signals some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.

DOI
10.1103/physrevd.59.107702

Related papers

Calogero-Sutherland Hamiltonian from anyonic density excitations

Ivan Andrić, Larisa Jonke, Velimir Bardek

We consider a large-N hard-core anyonic system in the Hamiltonian, collective -field approach based on the 1/N expansion. We show that the dynamics of density excitations around the ground-state semiclassical configuration is governed by the Calogero or by the Sutherland Hamiltonian, depending on the symmetry of the underlying static-soliton configuration. The relationship between the anyonic statistical parameter \\l and the Calogero-Sutherland parameter \\l_c signalizes some sort of Fermi-Bose transmutation accompanying the dimensional reduction of the anyonic problem.

•Jan 1, 1995•0 citations

Vortices of the Chern-Simons theory in the collective field approach

Ivan Andrić, Velimir Bardek

We formulate a collective field approach to a planar nonrelativistic system of bosons interacting via the Chern-Simons interaction. Adding the attractive $\ensuremath{\delta}$ potential this system can be solved and the vortex soliton appears. The ground state of this system is scale and inversion invariant. In the harmonic well this system is not stable against the creation of vortices. Leading and next to leading terms in the $\frac{1}{N}$ expansion of the ground-state energy are calculated.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jun 15, 1993•2 citations

Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern–Simons theory*

Fei Ye, P. A. Marchetti, Zhixun Su +1 more

Abstract The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern–Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.

arXiv:1708.02791•Journal of Physics A Mathematical and Theoretical•Aug 8, 2017•4 citations

Quantum dynamics of the effective field theory of the Calogero-Sutherland model

Federico L. Bottesi, Guillermo R. Zemba

We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry algebra, and not by diagonalization of the hamiltonian, which is given in terms of fields that carry representations of the W 1 + ∞ algebra (representing the incompressibility of the Fermi sea). Nevertheless, the role of the effective hamiltonian of the theory is to establish a specific dynamics, which deserves further consideration. We show that the time evolution of the (chiral or antichiral) density field is given by the quantum Benjamin-Ono equation, in agreement with previous results obtained from the alternative description of the continuous limit of the model, based on quantum hydrodynamics. In this study, all calculations are performed at the quantum operator level, without making any assumption on the semiclassical limit of the fields and their equations of motion. This result may be considered as a reliable indication of the equivalence between the quantum field theoretic and quantum hydrodynamical formulations of the effective theories of the model. A one-dimensional quantum compressible fluid that includes both chiralities is the physical picture that emerges for the continuous limit of the Calogero-Sutherland model. • The chiral density field of the Calogero-Sutherland EFT satisfies a quantum Benjamin-Ono equation. • Agrees with quantum hydrodynamics results by Abanov and Wiegmann, extending their validity to quantum fields themselves. • Findings could be of interest to the QFT community, with new tools to deal with time non-locality within the realm of CFT. • Equivalence between the EFT and the hydrodynamic formulations of the thermodynamic limit of the Calogero-Sutherland model is supported.

arXiv:2404.10011•Nuclear Physics B•Feb 7, 2025•2 citations

Chiral sound waves from a gauge theory of 1D generalized statistics

Silvio Rabello

A topological gauge field theory in one spatial dimension is studied, with the gauge fields as generators of two commuting U(1) Kauc-Moody algebras. Coupling of these gauge fields to nonrelativistic bosonic matter fields, produces a statistical transmutation of the later, as in the Chern-Simons theory in two dimensions. The sound waves of the model are investigated and proven to be chiral bosonic excitations, with the same spectrum as the density fluctuations of the Luttinger model.

arXiv:cond-mat/9604040•Apr 6, 1996•0 citations

Chern-Simons superconductors and their instabilities

Rui Wang, Baigeng Wang, Tigran Sedrakyan

Two-dimensional quantum antiferromagnets host rich physics, including long-range ordering, high-${T}_{c}$ superconductivity, quantum spin-liquid behavior, topological ordering, a variety of other exotic phases, and quantum criticalities. Frustrating perturbations in antiferromagnets may give rise to strong quantum fluctuations, challenging the theoretical understanding of the many-body ground state. Here we develop a method to describe the quantum antiferromagnets using fermionic degrees of freedom. The method is based on a formally exact mapping between spin-exchange models and theories describing fermionic matter with the emergent $\text{U}(1)$ Chern-Simons gauge field. For the planar N\'eel state, this mapping self-consistently generates the Chern-Simons superconductor mean-field ground state of introduced spinless fermions. We systematically compare the Chern-Simons superconductor state with the planar N\'eel state at the level of collective modes as well as order parameters. We reveal qualitative and quantitative correspondences between these two states. We demonstrate that such a construction using the fractionalized excitations and Chern-Simons gauge field can not only describe the N\'eel order, but can also be applied to study quantum spin liquids. Furthermore, we show that the confinement-deconfinement transitions from the N\'eel order to quantum spin liquids are signaled and characterized by the instabilities of Chern-Simons superconductors, driven by strong frustration. The results suggest observing and classifying the descendants of antiferromagnets, including other ordered states and unconventional superconductors, as well as emergent quantum spin liquids.

arXiv:2010.10067•Physical review. B./Physical review. B•Feb 4, 2022•14 citations
We consider the large-NNN Chern-Simons theory for attractive bosonic matter (Jackiw-Pi model) in the Hamiltonian collective-field approach based on the 1/N1/N1/N expansion. We show that the dynamics of low-lying density excitations around the ground-state vortex configuration is equivalent to that of the Sutherland model. The correspondence between the Chern-Simons coupling constant \ensuremathλ\ensuremath{\lambda}\ensuremathλ and the Calogero-Sutherland statistical parameter \ensuremathλs{\ensuremath{\lambda}}_{s}\ensuremathλs​ signals some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.
We consider a large-N hard-core anyonic system in the Hamiltonian, collective -field approach based on the 1/N expansion. We show that the dynamics of density excitations around the ground-state semiclassical configuration is governed by the Calogero or by the Sutherland Hamiltonian, depending on the symmetry of the underlying static-soliton configuration. The relationship between the anyonic statistical parameter \\l and the Calogero-Sutherland parameter \\l_c signalizes some sort of Fermi-Bose transmutation accompanying the dimensional reduction of the anyonic problem.
We formulate a collective field approach to a planar nonrelativistic system of bosons interacting via the Chern-Simons interaction. Adding the attractive $\ensuremath{\delta}$ potential this system can be solved and the vortex soliton appears. The ground state of this system is scale and inversion invariant. In the harmonic well this system is not stable against the creation of vortices. Leading and next to leading terms in the 1N\frac{1}{N}N1​ expansion of the ground-state energy are calculated.
Abstract The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern–Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.
We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry algebra, and not by diagonalization of the hamiltonian, which is given in terms of fields that carry representations of the W 1 + ∞ algebra (representing the incompressibility of the Fermi sea). Nevertheless, the role of the effective hamiltonian of the theory is to establish a specific dynamics, which deserves further consideration. We show that the time evolution of the (chiral or antichiral) density field is given by the quantum Benjamin-Ono equation, in agreement with previous results obtained from the alternative description of the continuous limit of the model, based on quantum hydrodynamics. In this study, all calculations are performed at the quantum operator level, without making any assumption on the semiclassical limit of the fields and their equations of motion. This result may be considered as a reliable indication of the equivalence between the quantum field theoretic and quantum hydrodynamical formulations of the effective theories of the model. A one-dimensional quantum compressible fluid that includes both chiralities is the physical picture that emerges for the continuous limit of the Calogero-Sutherland model. • The chiral density field of the Calogero-Sutherland EFT satisfies a quantum Benjamin-Ono equation. • Agrees with quantum hydrodynamics results by Abanov and Wiegmann, extending their validity to quantum fields themselves. • Findings could be of interest to the QFT community, with new tools to deal with time non-locality within the realm of CFT. • Equivalence between the EFT and the hydrodynamic formulations of the thermodynamic limit of the Calogero-Sutherland model is supported.
Two-dimensional quantum antiferromagnets host rich physics, including long-range ordering, high-Tc{T}_{c}Tc​ superconductivity, quantum spin-liquid behavior, topological ordering, a variety of other exotic phases, and quantum criticalities. Frustrating perturbations in antiferromagnets may give rise to strong quantum fluctuations, challenging the theoretical understanding of the many-body ground state. Here we develop a method to describe the quantum antiferromagnets using fermionic degrees of freedom. The method is based on a formally exact mapping between spin-exchange models and theories describing fermionic matter with the emergent U(1)\text{U}(1)U(1) Chern-Simons gauge field. For the planar N\'eel state, this mapping self-consistently generates the Chern-Simons superconductor mean-field ground state of introduced spinless fermions. We systematically compare the Chern-Simons superconductor state with the planar N\'eel state at the level of collective modes as well as order parameters. We reveal qualitative and quantitative correspondences between these two states. We demonstrate that such a construction using the fractionalized excitations and Chern-Simons gauge field can not only describe the N\'eel order, but can also be applied to study quantum spin liquids. Furthermore, we show that the confinement-deconfinement transitions from the N\'eel order to quantum spin liquids are signaled and characterized by the instabilities of Chern-Simons superconductors, driven by strong frustration. The results suggest observing and classifying the descendants of antiferromagnets, including other ordered states and unconventional superconductors, as well as emergent quantum spin liquids.