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:0707.2961 · Physical Review Letters

Scaling in the Fan of an Unconventional Quantum Critical Point

Roger G. Melko, Ribhu K. Kaul

Published Jan 8, 2008• 223 citations
arXivHTMLPDF

Abstract

We present results of extensive finite-temperature quantum Monte Carlo simulations on a SU(2) symmetric S=1/2 quantum antiferromagnet with four-spin interaction [A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007)10.1103/PhysRevLett.98.227202]. Our simulations, which are free of the sign problem and carried out on lattices containing in excess of 1.6 x 10(4) spins, indicate that the four-spin interaction destroys the Néel order at an unconventional z = 1 quantum critical point, producing a valence-bond solid paramagnet. Our results are consistent with the "deconfined quantum criticality" scenario.

DOI
10.1103/physrevlett.100.017203

Related papers

Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions

Anders W. Sandvik

Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.

arXiv:cond-mat/0611343•Physical Review Letters•Jun 1, 2007•517 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

Impurity spin texture at a deconfined quantum critical point

Argha Banerjee, Kedar Damle, Fabien Alet

The spin texture surrounding a nonmagnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a N\'eel ordered phase and a valence-bond solid phase in square lattice $S=1/2$ antiferromagnets. Using a newly developed $T=0$ quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.

arXiv:1002.1375•Physical Review B•Oct 26, 2010•68 citations

Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet

Vikas Vijigiri, Sumiran Pujari, Nisheeta Desai

Abstract Berry phase interference arguments that underlie the theory of deconfined quantum criticality (DQC) for S = 1 / 2 antiferromagnets have also been invoked to allow for continuous transitions in S = 1 magnets including a Néel to (columnar) valence bond solid (cVBS) transition. We provide a microscopic model realization of this transition on the square lattice consisting of Heisenberg exchange ( J H ) and biquadratic exchange ( J B ) that favor a Néel phase, and a designed Q -term ( Q B ) interaction which favors a cVBS through large-scale quantum Monte Carlo (QMC) simulations. For J H = 0 , this model is equivalent to the SU(3) JQ model with a Néel-cVBS transition that has been argued to be DQC through QMC. Upon turning on J H which brings down the symmetry to SU(2), we find multiple signatures—a single critical point, high quality collapse of correlation ratios and order parameters, ‘U(1)-symmetric’ cVBS histograms and lack of double-peak in order parameter histograms for largest sizes studied near the critical point—that are highly suggestive of a continuous transition scenario. However, Binder analysis finds negative dips that grow sub-extensively that we interpret as these transitions rather being pseudocritical. This, along with recent results on spin- 1 2 models, suggests that deconfined pseudocriticality is the more generic scenario.

arXiv:2307.14254•Journal of Physics Condensed Matter•Jan 5, 2026•0 citations

Tunable deconfined quantum criticality and interplay of different valence-bond solid phases*

Bowen Zhao, Jun Takahashi, Anders W. Sandvik

We use quantum Monte Carlo simulations to study an S = 1/2 spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS–AFM and AFM–cVBS boundaries merge into a direct sVBS–cVBS transition. Unlike previous models with putative deconfined AFM–cVBS transitions, e.g., the standard J–Q model, in our extended J–Q model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically Z 4 symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order, the clock-like Z 4 fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries.

arXiv:2003.07844•Chinese Physics B•Apr 12, 2020•9 citations

Néel-State to Valence-Bond-Solid Transition on the Honeycomb Lattice: Evidence for Deconfined Criticality

Sumiran Pujari, Kedar Damle, Fabien Alet

We study a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange J that favors Néel order and competing six-spin interactions Q that favor a valence-bond-solid (VBS) state in which the bond energies order at the "columnar" wave vector K=(2π/3,-2π/3). We present quantum Monte Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a description in terms of deconfined criticality, the measured threefold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behavior at the critical point.

arXiv:1302.1408•Physical Review Letters•Aug 21, 2013•114 citations
We present results of extensive finite-temperature quantum Monte Carlo simulations on a SU(2) symmetric S=1/2 quantum antiferromagnet with four-spin interaction [A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007)10.1103/PhysRevLett.98.227202]. Our simulations, which are free of the sign problem and carried out on lattices containing in excess of 1.6 x 10(4) spins, indicate that the four-spin interaction destroys the Néel order at an unconventional z = 1 quantum critical point, producing a valence-bond solid paramagnet. Our results are consistent with the "deconfined quantum criticality" scenario.
Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.
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.
The spin texture surrounding a nonmagnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a N\'eel ordered phase and a valence-bond solid phase in square lattice S=1/2S=1/2S=1/2 antiferromagnets. Using a newly developed T=0T=0T=0 quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.
Abstract Berry phase interference arguments that underlie the theory of deconfined quantum criticality (DQC) for S = 1 / 2 antiferromagnets have also been invoked to allow for continuous transitions in S = 1 magnets including a Néel to (columnar) valence bond solid (cVBS) transition. We provide a microscopic model realization of this transition on the square lattice consisting of Heisenberg exchange ( J H ) and biquadratic exchange ( J B ) that favor a Néel phase, and a designed Q -term ( Q B ) interaction which favors a cVBS through large-scale quantum Monte Carlo (QMC) simulations. For J H = 0 , this model is equivalent to the SU(3) JQ model with a Néel-cVBS transition that has been argued to be DQC through QMC. Upon turning on J H which brings down the symmetry to SU(2), we find multiple signatures—a single critical point, high quality collapse of correlation ratios and order parameters, ‘U(1)-symmetric’ cVBS histograms and lack of double-peak in order parameter histograms for largest sizes studied near the critical point—that are highly suggestive of a continuous transition scenario. However, Binder analysis finds negative dips that grow sub-extensively that we interpret as these transitions rather being pseudocritical. This, along with recent results on spin- 1 2 models, suggests that deconfined pseudocriticality is the more generic scenario.
We use quantum Monte Carlo simulations to study an S = 1/2 spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS–AFM and AFM–cVBS boundaries merge into a direct sVBS–cVBS transition. Unlike previous models with putative deconfined AFM–cVBS transitions, e.g., the standard J–Q model, in our extended J–Q model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically Z 4 symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order, the clock-like Z 4 fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries.
We study a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange J that favors Néel order and competing six-spin interactions Q that favor a valence-bond-solid (VBS) state in which the bond energies order at the "columnar" wave vector K=(2π/3,-2π/3). We present quantum Monte Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a description in terms of deconfined criticality, the measured threefold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behavior at the critical point.