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/0407151 · Physical Review B

Role of nonmagnetic disorder on the stability of the U(1) spin liquid: A renormalization group study

Ki‐Seok Kim

Published Oct 14, 2004• 14 citations
arXivHTMLPDF

Abstract

Recently, Hermele et al. claimed that the infrared (IR) fixed point of noncompact ${\mathrm{QED}}_{3}$ is stable against instanton excitations in the limit of large flavors of massless Dirac fermions [M. Hermele et al., cond-mat/0404751, Phys. Rev. B (to be published October 2004)]. We investigate an effect of nonmagnetic disorder on the deconfined quantum critical phase dubbed $U(1)$ spin liquid $(U1\mathrm{SL})$ in the context of quantum antiferromagnet. In the case of weak disorder the IR fixed point remains stable against the presence of both the instanton excitations and nonmagnetic disorder and thus the $U1\mathrm{SL}$ is sustained. In the case of strong disorder the IR fixed point becomes unstable against the disorder and the Anderson localization is expected to occur. We argue that in this case deconfinement of spinons does not occur since the Dirac fermion becomes massive owing to the localization.

DOI
10.1103/physrevb.70.140405

Related papers

Deconfinement in the presence of a Fermi surface

Ki‐Seok Kim

U(1) gauge theory of nonrelativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions $({\mathrm{QED}}_{3})$ by [Hermele et al.Phys. Rev. B 70, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ [the coupling strength between nonrelativistic fermions and U(1) gauge fields] reveals that the conductivity $\ensuremath{\sigma}$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in ${\mathrm{QED}}_{3}$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the nonrelativistic fermions at the charged fixed point. As a result a critical field theory of nonrelativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point.

arXiv:cond-mat/0502652•Physical Review B•Dec 7, 2005•18 citations

Stability of U(1) spin liquids in two dimensions

Michael Hermele, T. Senthil, Matthew P. A. Fisher +3 more

We establish that spin liquids described in terms of gapless fermionic (Dirac) spinons and gapless $U(1)$ gauge fluctuations can be stable in two dimensions, at least when the physical $SU(2)$ spin symmetry is generalized to $SU(N)$. Equivalently, we show that compact ${\mathrm{QED}}_{3}$ has a deconfined phase for a large number of fermion fields, in the sense that monopole fluctuations can be irrelevant at low energies. A precise characterization is provided by an emergent global topological $U(1)$ symmetry corresponding to the conservation of gauge flux. Beginning with an $SU(N)$ generalization of the $S=1∕2$ square-lattice Heisenberg antiferromagnet, we consider the $\ensuremath{\pi}$-flux spin liquid and, via a systematic analysis of all operators, show that there are no relevant perturbations (in the renormalization-group sense) about the large-$N$ spin-liquid fixed point, which is thus a stable phase. We provide a further illustration of this conclusion with an approximate renormalization-group calculation that treats the gapless fermions and the monopoles on an equal footing. This approach directly points out some of the flaws in the erroneous ``screening'' argument for the relevance of monopoles in compact ${\mathrm{QED}}_{3}$.

arXiv:cond-mat/0404751•Physical Review B•Dec 30, 2004•317 citations

Quantum Electrodynamics in 2+1 Dimensions, Confinement, and the Stability of U(1) Spin Liquids

Flavio S. Nogueira, Hagen M. Kleinert

Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.

arXiv:cond-mat/0501022•Physical Review Letters•Oct 20, 2005•34 citations

Destabilization of U(1) Dirac spin liquids on two-dimensional nonbipartite lattices by quenched disorder

Santanu Dey

The stability of the Dirac spin liquid on two-dimensional lattices has long been debated. It was recently demonstrated [Nat. Commun. 10, 4254 (2019) and Phys. Rev. B 93, 144411 (2016)] that the staggered $\ensuremath{\pi}$-flux Dirac spin-liquid phase on the nonbipartite triangular lattice may be stable in the clean limit. However, quenched disorder plays a crucial role in determining whether such a phase is experimentally viable. For SU(2) spin systems, the effective zero-temperature low-energy description of Dirac spin liquids in $(2+1)$ dimensions is given by the compact quantum electrodynamics $({\mathrm{cQED}}_{2+1})$ which admits monopoles. It is already known that generic quenched random perturbations to the noncompact version of ${\mathrm{QED}}_{2+1}$ (where monopoles are absent) lead to strong-coupling instabilities. In this paper we study ${\mathrm{cQED}}_{2+1}$ in the presence of a class of time-reversal invariant quenched disorder perturbations. We show that in this model, random non-Abelian vector potentials make the symmetry-allowed monopole operators more relevant. The disorder-induced underscreening of monopoles, thus, generically makes the gapless spin-liquid phase fragile.

arXiv:2008.12307•Physical review. B./Physical review. B•Dec 30, 2020•3 citations

Critical behavior of the QED3 -Gross-Neveu model: Duality and deconfined criticality

Lukas Janssen, Yin-Chen He

We study the critical properties of the ${\mathrm{QED}}_{3}$-Gross-Neveu model with $2N$ flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For $N=1$, this theory has recently been suggested to be dual to the SU(2) noncompact ${\mathrm{CP}}^{1}$ model that describes the deconfined phase transition between the N\'eel antiferromagnet and the valence bond solid on the square lattice. For $N=2$, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-$1/2$ systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the ${\mathrm{QED}}_{3}$-Gross-Neveu model for all values of $N$. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain ${\mathrm{QED}}_{3}$ (without scalar-field coupling) unstable at low values of $N$. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter $\ensuremath{\epsilon}=4\ensuremath{-}D$. We compute the scalar-field anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, the correlation-length exponent $\ensuremath{\nu}$, as well as the scaling dimension of the flavor-symmetry-breaking bilinear $\overline{\ensuremath{\psi}}{\ensuremath{\sigma}}^{z}\ensuremath{\psi}$ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.

arXiv:1708.02256•Physical review. B./Physical review. B•Nov 8, 2017•46 citations

Spin-Peierls instability of the U(1) Dirac spin liquid

Urban F. P. Seifert, Josef Willsher, Markus Drescher +2 more

A complicating factor in the realization and observation of quantum spin liquids in materials is the ubiquitous presence of other degrees of freedom, in particular lattice distortion modes (phonons). These provide additional routes for relieving magnetic frustration, thereby possibly destabilizing spin-liquid ground states. In this work, we focus on triangular-lattice Heisenberg antiferromagnets, where recent numerical evidence suggests the presence of an extended U(1) Dirac spin liquid phase which is described by compact quantum electrodynamics in 2+1 dimensions (QED$_3$), featuring gapless spinons and monopoles as gauge excitations, and believed to flow to a strongly-coupled fixed point with conformal symmetry. Using complementary perturbation theory and scaling arguments, we show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) 12-site valence-bond solid state. We support our theoretical analysis with state-of-the-art density matrix renormalization group simulations. Away from the limit of static distortions, we demonstrate that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable, and show that the monopole-lattice coupling leads to softening of the phonon in analogy to the Kohn anomaly. We discuss the applicability of our results to similar systems, in particular the Dirac spin liquid on the Kagome lattice.

arXiv:2307.12295•Jul 23, 2023•3 citations
Recently, Hermele et al. claimed that the infrared (IR) fixed point of noncompact QED3{\mathrm{QED}}_{3}QED3​ is stable against instanton excitations in the limit of large flavors of massless Dirac fermions [M. Hermele et al., cond-mat/0404751, Phys. Rev. B (to be published October 2004)]. We investigate an effect of nonmagnetic disorder on the deconfined quantum critical phase dubbed U(1)U(1)U(1) spin liquid (U1SL)(U1\mathrm{SL})(U1SL) in the context of quantum antiferromagnet. In the case of weak disorder the IR fixed point remains stable against the presence of both the instanton excitations and nonmagnetic disorder and thus the U1SLU1\mathrm{SL}U1SL is sustained. In the case of strong disorder the IR fixed point becomes unstable against the disorder and the Anderson localization is expected to occur. We argue that in this case deconfinement of spinons does not occur since the Dirac fermion becomes massive owing to the localization.
U(1) gauge theory of nonrelativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions (QED3)({\mathrm{QED}}_{3})(QED3​) by [Hermele et al.Phys. Rev. B 70, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge eee [the coupling strength between nonrelativistic fermions and U(1) gauge fields] reveals that the conductivity $\ensuremath{\sigma}$ of fermions near the Fermi surface plays the same role as the flavor number NNN of massless Dirac fermions in QED3{\mathrm{QED}}_{3}QED3​. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the nonrelativistic fermions at the charged fixed point. As a result a critical field theory of nonrelativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point.
We establish that spin liquids described in terms of gapless fermionic (Dirac) spinons and gapless U(1)U(1)U(1) gauge fluctuations can be stable in two dimensions, at least when the physical SU(2)SU(2)SU(2) spin symmetry is generalized to SU(N)SU(N)SU(N). Equivalently, we show that compact QED3{\mathrm{QED}}_{3}QED3​ has a deconfined phase for a large number of fermion fields, in the sense that monopole fluctuations can be irrelevant at low energies. A precise characterization is provided by an emergent global topological U(1)U(1)U(1) symmetry corresponding to the conservation of gauge flux. Beginning with an SU(N)SU(N)SU(N) generalization of the S=1∕2S=1∕2S=1∕2 square-lattice Heisenberg antiferromagnet, we consider the $\ensuremath{\pi}$-flux spin liquid and, via a systematic analysis of all operators, show that there are no relevant perturbations (in the renormalization-group sense) about the large-NNN spin-liquid fixed point, which is thus a stable phase. We provide a further illustration of this conclusion with an approximate renormalization-group calculation that treats the gapless fermions and the monopoles on an equal footing. This approach directly points out some of the flaws in the erroneous ``screening'' argument for the relevance of monopoles in compact QED3{\mathrm{QED}}_{3}QED3​.
Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.
The stability of the Dirac spin liquid on two-dimensional lattices has long been debated. It was recently demonstrated [Nat. Commun. 10, 4254 (2019) and Phys. Rev. B 93, 144411 (2016)] that the staggered $\ensuremath{\pi}$-flux Dirac spin-liquid phase on the nonbipartite triangular lattice may be stable in the clean limit. However, quenched disorder plays a crucial role in determining whether such a phase is experimentally viable. For SU(2) spin systems, the effective zero-temperature low-energy description of Dirac spin liquids in (2+1)(2+1)(2+1) dimensions is given by the compact quantum electrodynamics (cQED2+1)({\mathrm{cQED}}_{2+1})(cQED2+1​) which admits monopoles. It is already known that generic quenched random perturbations to the noncompact version of QED2+1{\mathrm{QED}}_{2+1}QED2+1​ (where monopoles are absent) lead to strong-coupling instabilities. In this paper we study cQED2+1{\mathrm{cQED}}_{2+1}cQED2+1​ in the presence of a class of time-reversal invariant quenched disorder perturbations. We show that in this model, random non-Abelian vector potentials make the symmetry-allowed monopole operators more relevant. The disorder-induced underscreening of monopoles, thus, generically makes the gapless spin-liquid phase fragile.
We study the critical properties of the QED3{\mathrm{QED}}_{3}QED3​-Gross-Neveu model with 2N2N2N flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For N=1N=1N=1, this theory has recently been suggested to be dual to the SU(2) noncompact CP1{\mathrm{CP}}^{1}CP1 model that describes the deconfined phase transition between the N\'eel antiferromagnet and the valence bond solid on the square lattice. For N=2N=2N=2, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-1/21/21/2 systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED3{\mathrm{QED}}_{3}QED3​-Gross-Neveu model for all values of NNN. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED3{\mathrm{QED}}_{3}QED3​ (without scalar-field coupling) unstable at low values of NNN. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter $\ensuremath{\epsilon}=4\ensuremath{-}D$. We compute the scalar-field anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, the correlation-length exponent $\ensuremath{\nu}$, as well as the scaling dimension of the flavor-symmetry-breaking bilinear $\overline{\ensuremath{\psi}}{\ensuremath{\sigma}}^{z}\ensuremath{\psi}$ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.
A complicating factor in the realization and observation of quantum spin liquids in materials is the ubiquitous presence of other degrees of freedom, in particular lattice distortion modes (phonons). These provide additional routes for relieving magnetic frustration, thereby possibly destabilizing spin-liquid ground states. In this work, we focus on triangular-lattice Heisenberg antiferromagnets, where recent numerical evidence suggests the presence of an extended U(1) Dirac spin liquid phase which is described by compact quantum electrodynamics in 2+1 dimensions (QED3_33​), featuring gapless spinons and monopoles as gauge excitations, and believed to flow to a strongly-coupled fixed point with conformal symmetry. Using complementary perturbation theory and scaling arguments, we show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) 12-site valence-bond solid state. We support our theoretical analysis with state-of-the-art density matrix renormalization group simulations. Away from the limit of static distortions, we demonstrate that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable, and show that the monopole-lattice coupling leads to softening of the phonon in analogy to the Kohn anomaly. We discuss the applicability of our results to similar systems, in particular the Dirac spin liquid on the Kagome lattice.