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

Physical review. B, Condensed matter

Mean-field theory of the chiral spin state

Yu-Liang Liu

Published Feb 1, 1992• 0 citations
Publisher

Abstract

Using the mean-field method, we study some properties of the chiral spin state and give its ground-state wave function under finite doping. We find that as the mass m of the spin fermion increases, the chiral spin state has a Kosterlitz-Thouless-type phase transition, and prove that the chiral spin state in external electromagnetic fields is an incompressible spin liquid with a finite gap which derives from the topological term. As considering the condensation of the hole bosons, we find the chiral spin state goes into a superconducting phase and has two finite gaps.

DOI
10.1103/physrevb.45.2327

Related papers

Schwinger-boson mean-field study of the spin- 1/2 J1−J2−Jχ model in the honeycomb lattice: Thermal Hall signature

Rohit Mukherjee, Ritajit Kundu, Avinash Singh +1 more

We theoretically investigate, within Schwinger-boson mean-field theory, the transition from a gapped ${\mathbb{Z}}_{2}$ quantum spin liquid, in a ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg spin-$\frac{1}{2}$ system in a honeycomb lattice, to a chiral ${\mathbb{Z}}_{2}$ spin-liquid phase under the presence of time-reversal symmetry-breaking scalar chiral interaction (with amplitude ${J}_{\ensuremath{\chi}}$). We numerically obtain a phase diagram of this ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{\ensuremath{\chi}}$ system, where different ground states are distinguished based on the gap and the nature of excitation spectrum, topological invariant of the excitations, the nature of spin-spin correlation, and the symmetries of the mean-field parameters. The chiral ${\mathbb{Z}}_{2}$ state is characterized by the nontrivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to a large thermal Hall coefficient.

arXiv:2108.08801•Physical review. B./Physical review. B•Apr 11, 2023•3 citations

Mean-field theory of spin-liquid states with finite energy gap and topological orders

Xiao-Gang Wen

The mean-field theory of a T- and P-symmetric spin-liquid state is developed. The quasiparticle excitations in the spin-liquid state are shown to be spin-1/2 neutral fermions (the spinons) and charge e spinless bosons (the holons). The spin-liquid state is shown to be characterized by a nontrivial topological order. Although our discussions are based on the mean-field theory, the concept of the topological order and the associated universal properties (e.g., the quantum number of the quasiparticles) are expected to be valid beyond the mean-field theory. We also discuss the dynamical stability of the mean-field theory.

Physical review. B, Condensed matter•Aug 1, 1991•627 citations

Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

Kirill Plekhanov, Ivana Vasić, Alexandru Petrescu +4 more

Recently, the frustrated XY model for spins 1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

arXiv:1707.07037•Physical Review Letters•Apr 10, 2018•17 citations

Spin gap in doped ladder systems

Lorenzo Campos Venuti

A proper theoretical description of doped antiferromagnets is until now an unresolved issue. In this work we study chain and ladder systems, and in particularly we focus on the physically most interesting two leg ladder. Our starting point is the Spin Fermion model in which an antiferromagnetic background of localized spins interacts with mobile holes via a rotation invariant Kondo-like term. The interesting region of the phase diagram is that close to the Mott-insulator transition where the doping delta is zero. At zero doping in fact the system is an insulator and the spins organize themselves in a spin liquid, a rotational invariant state characterized by a finite correlation length and an energy gap (a spin gap) above the ground state. Such a state is also the ground state of a field theory, the non linear sigma model (NLsigmaM) which is recognized as the low energy effective theory for antiferromagnetic spin ladder. The first question we answer is how such a spin state evolves as one moves off from the Mott phase by increasing the doping. Integrating out the fermions in our model we obtain an effective theory for the spins which we are able to evaluate in the continuum limit. The effective theory is again a NLsigmaM with coupling constants which depend on the concentration of dopant holes. In contrast to existing mean field calculation our theory predicts a lowering of the spin gap with doping and a consequent increase in the correlation length. Indeed a lowering of the spin gap due to doping is also observed in numerical simulation and on NMR experiments on $Sr14-xCaxCu24O41 with which we obtain very good agreement. Secondly we concentrated on the behavior of the fermions. The general paradigm of interacting fermions in one dimension is that of the Luttinger Liquid characterized by bosonic excitations and spin charge separation. By generalizing our approach we are able to access the one particle fermion propagator as a quantity averaged over the NLsigmaM which controls the spin background. We see that in the limit of zero doping the quasiparticle weight Z is non-zero in a neighborhood of the Fermi energy. This in turn implies that the Luttinger liquid parameter Krho goes to one as the doping delta goes to zero as was first argued by Schulz. Our stronger result allows us to assert that in the very low doping regime the fermions constitute a Fermi liquid.

•Jan 1, 2004•0 citations

Chirality quantum phase transition in the Dirac oscillator

A. Bermúdez, Miguel Angel Martin-Delgado, Alfredo Luis

We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition, which can be fully characterized. We obtain analytical expressions for the energy gap, order parameter, and canonical quantum fluctuations across the critical point. Moreover, we also discuss the effect of this phase transition on the statistics of the chiral bosonic ensemble, where its super- or sub-Poissonian nature can be controlled by means of external parameters. Finally, we study the entanglement properties between the degrees of freedom in the relativistic ground state, where an interesting transition between a biseparable and a genuinely tripartite entangled state occurs.

arXiv:0802.0577•Physical Review A•Jun 11, 2008•112 citations

Thermodynamic-Limit Evidence for Chiral Superconductivity Induced by Doping Chiral Topological Phases

Sen Niu, D. N. Sheng, Yang Peng

The emergence of superconductivity from doping strongly correlated chiral topological phases in purely repulsive two-dimensional fermionic systems is a problem of broad and fundamental interest. However, existing numerical evidence has been limited to finite-size studies, and direct thermodynamic-limit evidence for superconducting long-range order has remained lacking. Here we provide such evidence for chiral superconductivity in the triangular Hofstadter-Hubbard model by advancing a simplex tensor-network approach that simultaneously captures superconducting long-range order and chiral topological order in the presence of intrinsic charge fluctuations, a capability that has remained challenging for previous two-dimensional approaches. We show that a broad intermediate-$U$ chiral spin liquid is separated from the weak-$U$ Chern insulator by a Mott transition, together forming undoped parent chiral topological states. Upon hole doping, we identify a uniform chiral superconducting state in the infinite system, characterized by a finite complex pairing order parameter. The pairing field exhibits an almost universal phase winding over a broad interaction-doping regime, with a distinct pocket of opposite winding near the Mott criticality. In addition, the entanglement spectrum retains the chiral structure of the parent topological phases while developing additional low-energy branches upon doping. These results establish that chiral superconductivity emerges robustly from doped chiral topological phases.

arXiv:2512.21503•Dec 25, 2025•0 citations
Using the mean-field method, we study some properties of the chiral spin state and give its ground-state wave function under finite doping. We find that as the mass m of the spin fermion increases, the chiral spin state has a Kosterlitz-Thouless-type phase transition, and prove that the chiral spin state in external electromagnetic fields is an incompressible spin liquid with a finite gap which derives from the topological term. As considering the condensation of the hole bosons, we find the chiral spin state goes into a superconducting phase and has two finite gaps.
We theoretically investigate, within Schwinger-boson mean-field theory, the transition from a gapped Z2{\mathbb{Z}}_{2}Z2​ quantum spin liquid, in a ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg spin-12\frac{1}{2}21​ system in a honeycomb lattice, to a chiral Z2{\mathbb{Z}}_{2}Z2​ spin-liquid phase under the presence of time-reversal symmetry-breaking scalar chiral interaction (with amplitude ${J}_{\ensuremath{\chi}}$). We numerically obtain a phase diagram of this ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{\ensuremath{\chi}}$ system, where different ground states are distinguished based on the gap and the nature of excitation spectrum, topological invariant of the excitations, the nature of spin-spin correlation, and the symmetries of the mean-field parameters. The chiral Z2{\mathbb{Z}}_{2}Z2​ state is characterized by the nontrivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to a large thermal Hall coefficient.
The mean-field theory of a T- and P-symmetric spin-liquid state is developed. The quasiparticle excitations in the spin-liquid state are shown to be spin-1/2 neutral fermions (the spinons) and charge e spinless bosons (the holons). The spin-liquid state is shown to be characterized by a nontrivial topological order. Although our discussions are based on the mean-field theory, the concept of the topological order and the associated universal properties (e.g., the quantum number of the quasiparticles) are expected to be valid beyond the mean-field theory. We also discuss the dynamical stability of the mean-field theory.
Recently, the frustrated XY model for spins 1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).
A proper theoretical description of doped antiferromagnets is until now an unresolved issue. In this work we study chain and ladder systems, and in particularly we focus on the physically most interesting two leg ladder. Our starting point is the Spin Fermion model in which an antiferromagnetic background of localized spins interacts with mobile holes via a rotation invariant Kondo-like term. The interesting region of the phase diagram is that close to the Mott-insulator transition where the doping delta is zero. At zero doping in fact the system is an insulator and the spins organize themselves in a spin liquid, a rotational invariant state characterized by a finite correlation length and an energy gap (a spin gap) above the ground state. Such a state is also the ground state of a field theory, the non linear sigma model (NLsigmaM) which is recognized as the low energy effective theory for antiferromagnetic spin ladder. The first question we answer is how such a spin state evolves as one moves off from the Mott phase by increasing the doping. Integrating out the fermions in our model we obtain an effective theory for the spins which we are able to evaluate in the continuum limit. The effective theory is again a NLsigmaM with coupling constants which depend on the concentration of dopant holes. In contrast to existing mean field calculation our theory predicts a lowering of the spin gap with doping and a consequent increase in the correlation length. Indeed a lowering of the spin gap due to doping is also observed in numerical simulation and on NMR experiments on $Sr14-xCaxCu24O41 with which we obtain very good agreement. Secondly we concentrated on the behavior of the fermions. The general paradigm of interacting fermions in one dimension is that of the Luttinger Liquid characterized by bosonic excitations and spin charge separation. By generalizing our approach we are able to access the one particle fermion propagator as a quantity averaged over the NLsigmaM which controls the spin background. We see that in the limit of zero doping the quasiparticle weight Z is non-zero in a neighborhood of the Fermi energy. This in turn implies that the Luttinger liquid parameter Krho goes to one as the doping delta goes to zero as was first argued by Schulz. Our stronger result allows us to assert that in the very low doping regime the fermions constitute a Fermi liquid.
We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition, which can be fully characterized. We obtain analytical expressions for the energy gap, order parameter, and canonical quantum fluctuations across the critical point. Moreover, we also discuss the effect of this phase transition on the statistics of the chiral bosonic ensemble, where its super- or sub-Poissonian nature can be controlled by means of external parameters. Finally, we study the entanglement properties between the degrees of freedom in the relativistic ground state, where an interesting transition between a biseparable and a genuinely tripartite entangled state occurs.
The emergence of superconductivity from doping strongly correlated chiral topological phases in purely repulsive two-dimensional fermionic systems is a problem of broad and fundamental interest. However, existing numerical evidence has been limited to finite-size studies, and direct thermodynamic-limit evidence for superconducting long-range order has remained lacking. Here we provide such evidence for chiral superconductivity in the triangular Hofstadter-Hubbard model by advancing a simplex tensor-network approach that simultaneously captures superconducting long-range order and chiral topological order in the presence of intrinsic charge fluctuations, a capability that has remained challenging for previous two-dimensional approaches. We show that a broad intermediate-UUU chiral spin liquid is separated from the weak-UUU Chern insulator by a Mott transition, together forming undoped parent chiral topological states. Upon hole doping, we identify a uniform chiral superconducting state in the infinite system, characterized by a finite complex pairing order parameter. The pairing field exhibits an almost universal phase winding over a broad interaction-doping regime, with a distinct pocket of opposite winding near the Mott criticality. In addition, the entanglement spectrum retains the chiral structure of the parent topological phases while developing additional low-energy branches upon doping. These results establish that chiral superconductivity emerges robustly from doped chiral topological phases.