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:1703.01308 · Physical review. B./Physical review. B

Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice

Dimitri Pimenov, Matthias Punk

Published May 25, 2017• 6 citations
arXivHTMLPDF

Abstract

We propose field theories for a deconfined quantum critical point in SU(3) antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three-sublattice color-ordered phase and a trimerized SU(3) singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the SU(2) N\'eel---valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled $C{P}^{2}$ models and we study its fixed point structure using a functional renormalization group approach in a suitable large $N$ limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the $C{P}^{N}$ model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized SU(3) singlet phase.

DOI
10.1103/physrevb.95.184427

Related papers

Deconfined quantum critical point on the triangular lattice

Chao‐Ming Jian, Alex Thomson, Alex Rasmussen +2 more

In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard ``$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$'' noncollinear antiferromagnetic order (or the so-called ${120}^{\ensuremath{\circ}}$ state) and the ``$\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$'' valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the ``intertwinement'' between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ antiferromagnetic order and the $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the ${N}_{f}=4$ quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/${Z}_{4}$ symmetry only at the critical point. The aforementioned topological term is also naturally derived from the ${N}_{f}=4$ QED. We also point out that physics around this DQCP is analogous to the boundary of a $3d$ bosonic symmetry- protected topological state with only on-site symmetries.

arXiv:1710.04668•Physical review. B./Physical review. B•May 10, 2018•43 citations

One-dimensional model for deconfined criticality with Z 3 × Z 3 symmetry

Brenden Roberts, Shenghan Jiang, Olexei I. Motrunich

We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a ${\mathbb{Z}}_{3}$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with ${\mathbb{Z}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{3}$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of $SU(3)$-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a ${\mathbb{Z}}_{3}$ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order and is part of a family of deconfined quantum critical points described by walking of renormalization group flows.

arXiv:2010.07917•Physical review. B./Physical review. B•Apr 21, 2021•19 citations

Spin-Peierls instability of deconfined quantum critical points

David Hofmeier, Josef Willsher, Urban F. P. Seifert +1 more

Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-$\frac{1}{2}$ quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and N\'eel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.

arXiv:2406.12729•Physical review. B./Physical review. B•Sep 13, 2024•3 citations

Impurity spin texture at the critical point between Néel-ordered and valence-bond-solid states in two-dimensional SU(3) quantum antiferromagnets

Argha Banerjee, Kedar Damle, Fabien Alet

We study the impurity physics at a continuous quantum phase transition from an SU(3) symmetric N\'eel-ordered state to a valence-bond-solid state that breaks lattice symmetries, using quantum Monte Carlo techniques. This continuous transition is expected to be an example of ``deconfined criticality'' in an SU(3) symmetric system. We find that the spin-texture induced by a missing-spin defect at the transition takes on a finite-size scaling form consistent with expectations from standard scaling arguments at a scale-invariant quantum critical point, albeit with significant subleading power-law finite size corrections that we analyze in detail. Together with recently found logarithmic violations of scaling at similar continuous transitions in the SU(2) case, our results provide indirect evidence of the existence of operators that become marginal as $N$ is reduced to $2$ in the field theoretical description of these deconfined critical points.

arXiv:1012.3691•Physical Review B•Jun 7, 2011•22 citations

Quantum criticality and deconfinement in phase transitions between valence bond solids

Ashvin Vishwanath, Leon Balents, T. Senthil

We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transition between two such VBS phases is studied. In some cases, an interesting second-order transition controlled by a fixed line with varying critical exponents is found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gapped spin-$1∕2$ spinon excitations emerge right at the transition. The low-energy physics of this critical point (up to marginally irrelevant interactions) contains just a free quadratically dispersing ``photon.'' The phase structure on one side of this continuous transition is very intricate, consisting of a series of infinitely closely spaced further transitions in a ``devil's staircase'' form. Analogies with previous examples of deconfined quantum criticality are emphasized. Closely related transitions in single layer systems are explored. These are second order only at some multicritical points. The solvable Rokshar-Kivelson point of quantum dimer models of single layer systems is found to correspond to a nongeneric multicritical point.

arXiv:cond-mat/0311085•Physical Review B•Jun 30, 2004•141 citations

Deconfined Quantum Critical Point: A Review of Progress

Yi Cui, Rong Yu, Weiqiang Yu

Abstract Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu2(BO3)2, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a Néel antiferromagnetic phase. Remarkably, SrCu2(BO3)2 has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the Néel state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.

arXiv:2504.10027•Chinese Physics Letters•Mar 19, 2025•11 citations
We propose field theories for a deconfined quantum critical point in SU(3) antiferromagnets on the triangular lattice. In particular we consider the continuous transition between a magnetic, three-sublattice color-ordered phase and a trimerized SU(3) singlet phase. Starting from the magnetically ordered state we derive a critical theory in terms of fractional bosonic degrees of freedom, in close analogy to the well-developed description of the SU(2) N'eel---valence bond solid (VBS) transition on the square lattice. Our critical theory consists of three coupled CP2C{P}^{2}CP2 models and we study its fixed point structure using a functional renormalization group approach in a suitable large NNN limit. We find a stable critical fixed point and estimate its critical exponents, thereby providing an example of deconfined criticality beyond the universality class of the CPNC{P}^{N}CPN model. In addition we present a complementary route towards the critical field theory by studying topological defects of the trimerized SU(3) singlet phase.
In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard ``$\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$'' noncollinear antiferromagnetic order (or the so-called ${120}^{\ensuremath{\circ}}$ state) and the ``$\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$'' valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the ``intertwinement'' between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ antiferromagnetic order and the $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the Nf=4{N}_{f}=4Nf​=4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z4{Z}_{4}Z4​ symmetry only at the critical point. The aforementioned topological term is also naturally derived from the Nf=4{N}_{f}=4Nf​=4 QED. We also point out that physics around this DQCP is analogous to the boundary of a 3d3d3d bosonic symmetry- protected topological state with only on-site symmetries.
We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a Z3{\mathbb{Z}}_{3}Z3​ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with ${\mathbb{Z}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{3}$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)SU(3)SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a Z3{\mathbb{Z}}_{3}Z3​ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order and is part of a family of deconfined quantum critical points described by walking of renormalization group flows.
Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-12\frac{1}{2}21​ quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and N\'eel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.
We study the impurity physics at a continuous quantum phase transition from an SU(3) symmetric N\'eel-ordered state to a valence-bond-solid state that breaks lattice symmetries, using quantum Monte Carlo techniques. This continuous transition is expected to be an example of ``deconfined criticality'' in an SU(3) symmetric system. We find that the spin-texture induced by a missing-spin defect at the transition takes on a finite-size scaling form consistent with expectations from standard scaling arguments at a scale-invariant quantum critical point, albeit with significant subleading power-law finite size corrections that we analyze in detail. Together with recently found logarithmic violations of scaling at similar continuous transitions in the SU(2) case, our results provide indirect evidence of the existence of operators that become marginal as NNN is reduced to 222 in the field theoretical description of these deconfined critical points.
We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transition between two such VBS phases is studied. In some cases, an interesting second-order transition controlled by a fixed line with varying critical exponents is found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gapped spin-1∕21∕21∕2 spinon excitations emerge right at the transition. The low-energy physics of this critical point (up to marginally irrelevant interactions) contains just a free quadratically dispersing ``photon.'' The phase structure on one side of this continuous transition is very intricate, consisting of a series of infinitely closely spaced further transitions in a ``devil's staircase'' form. Analogies with previous examples of deconfined quantum criticality are emphasized. Closely related transitions in single layer systems are explored. These are second order only at some multicritical points. The solvable Rokshar-Kivelson point of quantum dimer models of single layer systems is found to correspond to a nongeneric multicritical point.
Abstract Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu2(BO3)2, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a Néel antiferromagnetic phase. Remarkably, SrCu2(BO3)2 has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the Néel state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.