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:cond-mat/0504541

Deconfined Quantum Criticality at the Quantum Phase Transition from Antiferromagnetism to Algebraic Spin Liquid

Ki‐Seok Kim

Published Apr 21, 2005• 0 citations
arXivHTMLPDF

Abstract

We investigate the quantum phase transition from antiferromagnetism ($AF$) to algebraic spin liquid ($ASL$). {\it We propose that spin 1/2 fermionic spinons in the $ASL$ fractionalize into spin 1/2 bosonic spinons and spinless fermions at the quantum critical point ($QCP$) between the $AF$ and the $ASL$}. Condensation of the bosonic spinons leads to the $AF$, where the condensed bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are also confined to make antiferromagnons as elementary excitations in the $AF$. {\it Approaching the $QCP$ from the $AF$, spin 1 critical antiferromagnetic fluctuations are expected to break up into spin 1/2 critical bosonic spinons. Then, these bosonic spinons hybridize with spin 1/2 fermionic spinons, making spinless fermions}. As a result the fermionic spinons decay into the bosonic spinons and the spinless fermions. But, the spinless fermions are confined and thus, only the bosonic spinons emerge at the $QCP$. This coincides with the recent studies of {\it deconfined quantum criticality}\cite{Laughlin_deconfinement,Senthil_deconfinement,Kim1,Ichinose_de confinement}. When the bosonic spinons are gapped, the $ASL$ is realized. The bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are deconfined to describe the $ASL$.

DOI
10.48550/arxiv.cond-mat/0504541

Related papers

Deconfined quantum criticality in the two-dimensional Kondo lattice model

Ki‐Seok Kim

We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.

arXiv:cond-mat/0505230•Physical Review B•Oct 28, 2005•4 citations

Existence of fermion zero modes and deconfinement of spinons in quantum antiferromagnetism resulting from algebraic spin liquid

Ki‐Seok Kim

We investigate the quantum antiferromagnetism arising from algebraic spin liquid via spontaneous chiral symmetry breaking. We claim that in the antiferromagnet massive Dirac spinons can appear to make a broad continuum spectrum at high energies in inelastic neutron scattering. The mechanism of spinon deconfinement results from the existence of fermion zero modes in single monopole potentials. N\'eel vectors can make a hedgehog configuration around a magnetic monopole of compact U(1) gauge fields. Remarkably, in the monopole composite potential the Dirac fermion is shown to have a zero mode. The emergence of the fermion zero mode forbids the condensation of monopoles, resulting in deconfinement of Dirac spinons in the quantum antiferromagnet.

arXiv:cond-mat/0503458•Physical Review B•Dec 1, 2005•9 citations

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Xiao Yan Xu, Yang Qi, Long Zhang +3 more

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics.However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here we show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations.One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations.By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases.The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality.In particular, for four flavors N f ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.

arXiv:1807.07574•Physical Review X•May 2, 2019•98 citations

Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State

Alex Thomson, Subir Sachdev A

Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP 1 theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry.Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z 2 topological order possibly intertwined with discrete broken global symmetries.We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in π flux in each square lattice plaquette.Fluctuations about this π-flux state are described by (2 þ 1)-dimensional quantum chromodynamics (QCD 3 ) with a SU(2) gauge group and N f ¼ 2 flavors of massless Dirac fermions.It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017).]that this QCD 3 theory describes the Néel-VBS quantum phase transition.We introduce adjoint Higgs fields in QCD 3 and obtain fermionic dual descriptions of the phases with Z 2 topological order obtained earlier using the bosonic CP 1 theory.We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state.The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.

arXiv:1708.04626•Physical Review X•Jan 24, 2018•33 citations

Kagome spin liquid: a deconfined critical phase driven by $U(1)$ gauge fluctuation

Yin-Chen He, Yohei Fuji, Subhro Bhattacharjee

We investigate the nature of quantum spin liquid (QSL) phase of the spin-$1/2$ nearest-neighbor XXZ antiferromagnet on the kagome lattice. Recent numerical calculations suggest that such a kagome spin liquid is insensitive to the XXZ anisotropy and is adjacent to a chiral spin liquid phase. Reformulating the problem in terms of a $U(1)$ lattice gauge theory with dynamical bosonic spinons, we propose that the kagome spin liquid can be understood as a deconfined critical phase extended by the $U(1)$ gauge fluctuation from a deconfined critical point between a symmetry-protected topological phase and a superfluid phase. Crucially, the stability of this QSL is ensured by the gauge fluctuation and hence our description necessarily falls beyond the conventional mean-field constructions of QSLs. Our work also makes an interesting connection between the critical spin liquid, deconfined criticality, symmetry protected topological phase and topological order.

arXiv:1512.05381•Dec 16, 2015•9 citations

Deconfined criticality and a gapless Z 2 spin liquid in the square-lattice antiferromagnet

Henry Shackleton, Alex Thomson, Subir Sachdev A

The theory for the vanishing of N\'eel order in the spin $S=1/2$ square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable ${\mathbb{Z}}_{2}$ spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the `$\ensuremath{\pi}$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless ${\mathbb{Z}}_{2}$ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z\ensuremath{\ne}1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing ${J}_{2}/{J}_{1}$: N\'eel, gapless ${\mathbb{Z}}_{2}$ spin liquid, and valence bond solid.

arXiv:2104.09537•Physical review. B./Physical review. B•Jul 6, 2021•27 citations
We investigate the quantum phase transition from antiferromagnetism (AFAFAF) to algebraic spin liquid (ASLASLASL). {\it We propose that spin 1/2 fermionic spinons in the ASLASLASL fractionalize into spin 1/2 bosonic spinons and spinless fermions at the quantum critical point (QCPQCPQCP) between the AFAFAF and the ASLASLASL}. Condensation of the bosonic spinons leads to the AFAFAF, where the condensed bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are also confined to make antiferromagnons as elementary excitations in the AFAFAF. {\it Approaching the QCPQCPQCP from the AFAFAF, spin 1 critical antiferromagnetic fluctuations are expected to break up into spin 1/2 critical bosonic spinons. Then, these bosonic spinons hybridize with spin 1/2 fermionic spinons, making spinless fermions}. As a result the fermionic spinons decay into the bosonic spinons and the spinless fermions. But, the spinless fermions are confined and thus, only the bosonic spinons emerge at the QCPQCPQCP. This coincides with the recent studies of {\it deconfined quantum criticality}\cite{Laughlin_deconfinement,Senthil_deconfinement,Kim1,Ichinose_de confinement}. When the bosonic spinons are gapped, the ASLASLASL is realized. The bosonic spinons are confined with the spinless fermions to form the fermionic spinons. These fermionic spinons are deconfined to describe the ASLASLASL.
We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.
We investigate the quantum antiferromagnetism arising from algebraic spin liquid via spontaneous chiral symmetry breaking. We claim that in the antiferromagnet massive Dirac spinons can appear to make a broad continuum spectrum at high energies in inelastic neutron scattering. The mechanism of spinon deconfinement results from the existence of fermion zero modes in single monopole potentials. N\'eel vectors can make a hedgehog configuration around a magnetic monopole of compact U(1) gauge fields. Remarkably, in the monopole composite potential the Dirac fermion is shown to have a zero mode. The emergence of the fermion zero mode forbids the condensation of monopoles, resulting in deconfinement of Dirac spinons in the quantum antiferromagnet.
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics.However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here we show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations.One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations.By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases.The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality.In particular, for four flavors N f ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.
Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP 1 theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry.Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z 2 topological order possibly intertwined with discrete broken global symmetries.We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in π flux in each square lattice plaquette.Fluctuations about this π-flux state are described by (2 þ 1)-dimensional quantum chromodynamics (QCD 3 ) with a SU(2) gauge group and N f ¼ 2 flavors of massless Dirac fermions.It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017).]that this QCD 3 theory describes the Néel-VBS quantum phase transition.We introduce adjoint Higgs fields in QCD 3 and obtain fermionic dual descriptions of the phases with Z 2 topological order obtained earlier using the bosonic CP 1 theory.We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state.The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.
Kagome spin liquid: a deconfined critical phase driven by U(1)U(1)U(1) gauge fluctuation
We investigate the nature of quantum spin liquid (QSL) phase of the spin-1/21/21/2 nearest-neighbor XXZ antiferromagnet on the kagome lattice. Recent numerical calculations suggest that such a kagome spin liquid is insensitive to the XXZ anisotropy and is adjacent to a chiral spin liquid phase. Reformulating the problem in terms of a U(1)U(1)U(1) lattice gauge theory with dynamical bosonic spinons, we propose that the kagome spin liquid can be understood as a deconfined critical phase extended by the U(1)U(1)U(1) gauge fluctuation from a deconfined critical point between a symmetry-protected topological phase and a superfluid phase. Crucially, the stability of this QSL is ensured by the gauge fluctuation and hence our description necessarily falls beyond the conventional mean-field constructions of QSLs. Our work also makes an interesting connection between the critical spin liquid, deconfined criticality, symmetry protected topological phase and topological order.
The theory for the vanishing of N\'eel order in the spin S=1/2S=1/2S=1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z2{\mathbb{Z}}_{2}Z2​ spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the `$\ensuremath{\pi}$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z\ensuremath{\ne}1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J2/J1{J}_{2}/{J}_{1}J2​/J1​: N\'eel, gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid, and valence bond solid.