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:2010.11129 · Physical review. B./Physical review. B

Deconfined quantum phase transition of a higher-order symmetry-protected topological state

Chen Peng, Long Zhang, Zhong-Yi Lu

Published Aug 10, 2021• 6 citations
arXivHTMLPDF

Abstract

A higher-order (HO) symmetry-protected topological (SPT) state can be realized in a plaquette-modulated square lattice antiferromagnet, which hosts a spin-$1/2$ degenerate mode on each corner of the lattice with open boundaries. In this work, we show with the field-theoretic analysis and quantum Monte Carlo simulations that the plaquette modulation can drive a direct topological quantum phase transition from the HOSPT to a trivial disordered phase across the deconfined quantum critical point (DQCP) between the antiferromagnetic (AF) order and the valence bond solid (VBS) order, thus the DQCP is a multicritical point bridging both the AF-VBS transition and the topological transition of the HOSPT phase. Our work thus reveals the ubiquitous duality between topological transitions of SPT phases and DQCPs.

DOI
10.1103/physrevb.104.075112

Related papers

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

Persistent corner spin mode at the quantum critical point of a plaquette Heisenberg model

Yining Xu, Chen Peng, Zijian Xiong +1 more

Gapless edge states are the hallmark of a large class of topological states of matter. Recently, intensive research has been devoted to understanding the physical properties of the edge states at the quantum phase transitions of the bulk topological states. A higher-order symmetry-protected topological state is realized in a plaquette Heisenberg model on the square lattice. In its disordered phase, the lattice with an open boundary hosts either dangling corner states with spin-$1/2$ degeneracy characterizing the topological phase or nondangling corner states without degeneracy, which depends on the bond configuration near the corners. In this work, we study the critical behavior of these corner states at the quantum critical point (QCP) and find that the spin-$1/2$ corner state induces a new universality class of the corner critical behavior, which is distinct from the ordinary transition of the nondangling corners. In particular, we find that the dangling spin-$1/2$ corner state persists at the QCP despite its coupling to the critical spin fluctuations in the bulk. This shows the robustness of the corner state of the higher-order topological state.

arXiv:2112.04616•Physical review. B./Physical review. B•Dec 8, 2022•3 citations

Multicritical Deconfined Quantum Criticality and Lifshitz Point of a Helical Valence-Bond Phase

Bowen Zhao, Jun Takahashi, Anders W. Sandvik

The S=1/2 square-lattice J-Q model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model-a term projecting staggered singlets, as well as a modulation of the J terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point-the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method.

arXiv:2005.10184•Physical Review Letters•Dec 17, 2020•56 citations

Plaquette valence bond solid to antiferromagnet transition and deconfined quantum critical point of the Shastry-Sutherland model

Ning Xi, Hongyu Chen, Z. Y. Xie +1 more

We study the ground-state phase diagram of the Shastry-Sutherland model by using a variational optimization of the infinite tensor network states, and identify a weakly first-order transition between the plaquette valence bond solid and the antiferromagnetic states. The full plaquette state is found to strongly compete with the empty plaquette ground state, and can be stabilized as the ground state when a staggered ring-exchange interaction preserving the Shastry-Sutherland lattice symmetry is introduced. We propose the triple point where the full plaquette, empty plaquette, and antiferromagnetic phases meet as a deconfined quantum critical point (DQCP). The analysis of susceptibilities provides evidence of an emergent $\text{SO}(5)$ symmetry at this point. These results shed light on the study of DQCP in quantum magnets and provide a way to understand the proximate DQCP signatures in recent experiments on ${\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}$.

arXiv:2111.07368•Physical review. B./Physical review. B•Jun 29, 2023•32 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

Deconfined Boundary Phase Transition of a Quantum Critical Heisenberg Model

Chengxiang Ding, Long Zhang

We investigate the boundary phases of a (2+1)-dimensional quantum critical Heisenberg model with a dangling spin chain. By introducing a multispin $Q$-term along the boundary, we drive a continuous boundary transition from an antiferromagnetic (AF) order to a valence-bond solid (VBS) order. Using large-scale quantum Monte Carlo simulations, we locate the critical point at $Q_{c}=0.310(11)$, and obtain the critical exponents at $Q_{c}$, including $y_{s}=0.81(4)$ and the scaling dimensions of AF and VBS order parameters $Δ_{s}=0.660(15)$ and $Δ_{v}=0.204(14)$. The weak long-range AF order for $Q

arXiv:2605.19011•May 18, 2026•0 citations
A higher-order (HO) symmetry-protected topological (SPT) state can be realized in a plaquette-modulated square lattice antiferromagnet, which hosts a spin-1/21/21/2 degenerate mode on each corner of the lattice with open boundaries. In this work, we show with the field-theoretic analysis and quantum Monte Carlo simulations that the plaquette modulation can drive a direct topological quantum phase transition from the HOSPT to a trivial disordered phase across the deconfined quantum critical point (DQCP) between the antiferromagnetic (AF) order and the valence bond solid (VBS) order, thus the DQCP is a multicritical point bridging both the AF-VBS transition and the topological transition of the HOSPT phase. Our work thus reveals the ubiquitous duality between topological transitions of SPT phases and DQCPs.
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.
Gapless edge states are the hallmark of a large class of topological states of matter. Recently, intensive research has been devoted to understanding the physical properties of the edge states at the quantum phase transitions of the bulk topological states. A higher-order symmetry-protected topological state is realized in a plaquette Heisenberg model on the square lattice. In its disordered phase, the lattice with an open boundary hosts either dangling corner states with spin-1/21/21/2 degeneracy characterizing the topological phase or nondangling corner states without degeneracy, which depends on the bond configuration near the corners. In this work, we study the critical behavior of these corner states at the quantum critical point (QCP) and find that the spin-1/21/21/2 corner state induces a new universality class of the corner critical behavior, which is distinct from the ordinary transition of the nondangling corners. In particular, we find that the dangling spin-1/21/21/2 corner state persists at the QCP despite its coupling to the critical spin fluctuations in the bulk. This shows the robustness of the corner state of the higher-order topological state.
The S=1/2 square-lattice J-Q model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model-a term projecting staggered singlets, as well as a modulation of the J terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point-the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method.
We study the ground-state phase diagram of the Shastry-Sutherland model by using a variational optimization of the infinite tensor network states, and identify a weakly first-order transition between the plaquette valence bond solid and the antiferromagnetic states. The full plaquette state is found to strongly compete with the empty plaquette ground state, and can be stabilized as the ground state when a staggered ring-exchange interaction preserving the Shastry-Sutherland lattice symmetry is introduced. We propose the triple point where the full plaquette, empty plaquette, and antiferromagnetic phases meet as a deconfined quantum critical point (DQCP). The analysis of susceptibilities provides evidence of an emergent SO(5)\text{SO}(5)SO(5) symmetry at this point. These results shed light on the study of DQCP in quantum magnets and provide a way to understand the proximate DQCP signatures in recent experiments on SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​.
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.
We investigate the boundary phases of a (2+1)-dimensional quantum critical Heisenberg model with a dangling spin chain. By introducing a multispin QQQ-term along the boundary, we drive a continuous boundary transition from an antiferromagnetic (AF) order to a valence-bond solid (VBS) order. Using large-scale quantum Monte Carlo simulations, we locate the critical point at Qc=0.310(11)Q_{c}=0.310(11)Qc​=0.310(11), and obtain the critical exponents at QcQ_{c}Qc​, including ys=0.81(4)y_{s}=0.81(4)ys​=0.81(4) and the scaling dimensions of AF and VBS order parameters Δs=0.660(15)Δ_{s}=0.660(15)Δs​=0.660(15) and Δv=0.204(14)Δ_{v}=0.204(14)Δv​=0.204(14). The weak long-range AF order for $Q