Engineering Surface Critical Behavior of (
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)-Dimensional O(3) Quantum Critical Points

Ding, Chengxiang; Zhang, Long; Guo, Wenan

doi:10.1103/physrevlett.120.235701

Cited by 50 publications

(93 citation statements)

References 39 publications

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“…For the S = 1/2 quantum spin models with SU(2) symmetry, the bulk transition is in the classical 3D O(3) universality class. [31] For the dangling-ladder edge, the surface critical exponents are found in agreement with the ordinary universality class [11,12]. This surface state is understandable since the edge can be viewed as a dangling ladder in the gapped dimer phase and the ladder is gapped since it has two legs, thus effectively forming an integer spin chain.…”

Section: Surface Critical Behaviors Of Dangling-ladder Edgesupporting

confidence: 55%

“…As a result, the surface critical behavior is nonordinary. [11,12] When the symmetry of the model is down to U (1), the gapped nature of the dangling ladder does not change. Therefore, we expect ordinary SCBs of 3D O(2) class on the edge.…”

Section: Surface Critical Behaviors Of Dangling-ladder Edgementioning

confidence: 99%

“…For dimerized antiferromagnetic Heisenberg systems, where the couplings are not distributed homogeneously on the lattice and are anisotropic in directions, making it possible to expose different surfaces by geometrical settings, one finds different SCBs in different surfaces without adapting surface couplings. [10][11][12] In particular, on the surface formed by dangling spins, nonordinary SCBs are found. The mechanism of such behavior is not yet clear.…”

Section: Introductionmentioning

confidence: 99%

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Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model

Zhu¹,

Ding²,

Zhang³

et al. 2021

Preprint

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We study the surface behavior of the two-dimensional columnar dimerized quantum antiferromagnetic XXZ model with easy-plane anisotropy, putting special attention on the surface critical behaviors of the (2+1)-dimensional quantum critical points of the model, belonging to the classical three-dimensional O(2) universality class, for both S = 1/2 and S = 1 spins using quantum Monte Carlo simulations. We found utterly different surface behaviors at two different surfaces of geometrical settings: one surface is the dangling-ladder surface, which is exposed by cutting a row of weak bonds, and the other is the dangling-chain surface, which is formed by cutting a row of strong bonds along the direction perpendicular to the strong bonds of a periodic system. We find an ordinary transition on the dangling-ladder surface for both S = 1 and S = 1/2 spin systems, similar to what found in the Heisenberg limit. However, the dangling-chain surface shows much richer surface behaviors than in the Heisenberg limit. For the S = 1/2 easy-plane model, we find the surface undergoes an unexpected phase transition from a Tomonaga-Luttinger liquid to an unknown critical state in the gapped bulk state as the dimerization strength is weaken. We denote this state as a bulk induced surface critical state (BISC). At the bulk critical point, we show evidences supporting an extraordinary surface transition with a long-range order established by effective long-range interactions due to bulk critical fluctuations. The possibility that the state is an extra-ordinary-log state seems unlikely. For the S = 1 system, we find surface behaviors similar to that of the three-dimensional classical XY model with surface coupling enhanced strong enough, suggesting an extra-ordinary-log state at the bulk critical point.

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Section: Surface Critical Behaviors Of Dangling-ladder Edgesupporting

confidence: 55%

Section: Surface Critical Behaviors Of Dangling-ladder Edgementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model

Zhu¹,

Ding²,

Zhang³

et al. 2021

Preprint

Self Cite

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show abstract

“…In the two-dimensional (2D) Affleck-Kennedy-Lieb-Tasaki (AKLT) model, the gapless edge state changes the universality class of the surface critical behavior of the (2+1)D O(3) Wilson-Fisher QCP 13 . This new surface universality class is also realized in similar models with dangling spin chains on the edge [14][15][16][17] and has triggered further theoretical studies [18][19][20][21][22][23][24][25][26] .…”

Section: Introductionmentioning

confidence: 73%

Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model

Xu¹,

Xiong²,

Zhang³

2021

Preprint

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The fate of the gapless or degenerate edge modes of topological states at the bulk quantum critical points (QCPs) has triggered intensive research recently. In this work, we numerically study the critical behavior of the corner states at the QCP of a plaquette Heisenberg model with open boundary condition, which in the disorder phase hosts both a dangling corner state with a symmetry-protected spin-1/2 mode as a hallmark of the higher-order topological phase, and nondangling corners. We show that the dangling spin mode induces a new universality class of the corner critical behavior, which is distinct from the ordinary case of the nondangling corner. In particular, we show that the degenerate spin mode persists at the QCP despite its coupling to the critical spin fluctuations in the bulk. This shows the unexpected robustness of the corner mode of the higher-order topological phase.

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“…The surface critical behavior of classical statistical systems has been extensively studied [24,25]. The interest in the surface criticality has been revived recently partly motivated by the fate of topological edge states at quantum critical points (QCPs), leading to the discovery of new surface universality classes [26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

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confidence: 99%

Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains

Yu¹,

Huang²,

Song³

et al. 2021

Preprint

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Some quantum critical states cannot be smoothly deformed into each other without explicitly breaking certain symmetries even if they belong to the same universality class. This brings up the notion of "symmetry-enriched" quantum criticality. In this work, we propose that the conformal boundary condition (b.c.) is a more generic characteristic of such quantum critical states than the robust edge degeneracy studied recently. We show that in two families of quantum spin chains, which generalize the Ising and the three-state Potts models, the quantum critical point between a symmetry-protected topological phase and a symmetry-breaking order realizes a conformal b.c. distinct from the simple Ising and Potts chains. Furthermore, we argue that the conformal b.c. can be derived from the bulk effective field theory, which constitutes a novel bulk-boundary correspondence in symmetry-enriched quantum critical states.

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Engineering Surface Critical Behavior of ( 2+1 )-Dimensional O(3) Quantum Critical Points

Cited by 50 publications

References 39 publications

Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model

Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model

Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model

Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains

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