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arXiv:2110.04762 · SciPost Physics

Special transition and extraordinary phase on the surface of a two-dimensional quantum Heisenberg antiferromagnet

Chengxiang Ding, Wenjing Zhu, Wenan Guo, Long Zhang

Published Jul 18, 2023• 13 citations
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Abstract

Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into higher-dimensional boundary conformal field theories. In this work, we study the surface critical behavior of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength, and discover a direct special transition on the surface from the ordinary phase into an extraordinary phase. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmic decaying spin correlations in the 3D classical O(3) model. The special transition point has a new set of critical exponents, y_{s}=0.86(4) y s = 0.86 ( 4 ) and \eta_{\parallel}=-0.33(1) η ∥ = − 0.33 ( 1 ) , which are distinct from the special transition of the classical O(3) model and indicate a new surface universality class of the 3D O(3) Wilson-Fisher theory.

DOI
10.21468/scipostphys.15.1.012

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Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into higher-dimensional boundary conformal field theories. In this work, we study the surface critical behavior of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength, and discover a direct special transition on the surface from the ordinary phase into an extraordinary phase. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmic decaying spin correlations in the 3D classical O(3) model. The special transition point has a new set of critical exponents, y_{s}=0.86(4) y s = 0.86 ( 4 ) and \eta_{\parallel}=-0.33(1) η ∥ = − 0.33 ( 1 ) , which are distinct from the special transition of the classical O(3) model and indicate a new surface universality class of the 3D O(3) Wilson-Fisher theory.
Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized for the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into the higher-dimensional boundary conformal field theories. In this work, we discover a direct special transition from the ordinary phase into an extraordinary phase on the surface of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmically decaying spin correlations in the 3D classical O(2) and O(3) models. The anomalous dimension of the surface antiferromagnetic order in the extraordinary phase η∥=−0.29(1)\eta_{\parallel}=-0.29(1)η∥​=−0.29(1) is independent of the surface coupling strength. The special transition point also has a new set of critical exponents, ys=0.82(4)y_{s}=0.82(4)ys​=0.82(4) and η∥=−0.304(5)\eta_{\parallel}=-0.304(5)η∥​=−0.304(5), which are distinct from the special transition of the classical O(3) model and indicates a new surface universality class of the 3D O(3) Wilson-Fisher theory.
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We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision Monte Carlo simulations of an improved lattice model, where leading bulk scaling corrections are suppressed, we prove the existence of a special phase transition, with unusual exponents, and of an extraordinary phase with logarithmically decaying correlations. These findings contrast with naïve arguments on the bulk-surface phase diagram, and allow us to explain some recent puzzling results on the boundary critical behavior of quantum spin models.
We study the surface behavior of the two-dimensional columnar dimerized quantum antiferromagnetic XXZ model with easy-plane anisotropy, with particular emphasis on the surface critical behaviors of the (2+1)-dimensional quantum critical points of the model that belong to the classical three-dimensional O(2) universality class, for both S=1/2S=1/2S=1/2 and S=1S=1S=1 spins using quantum Monte Carlo simulations. We find completely different surface behaviors on two different surfaces of geometrical settings: the dangling-ladder surface, which is exposed by cutting a row of weak bonds, and 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. Similar to the Heisenberg limit, we find an ordinary transition on the dangling-ladder surface for both S=1S=1S=1 and S=1/2S=1/2S=1/2 spin systems. However, the dangling-chain surface shows much richer surface behaviors than in the Heisenberg limit. For the S=1/2S=1/2S=1/2 easy-plane model, at the bulk critical point, we provide evidence 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 extraordinary-log state seems unlikely. For the S=1S=1S=1 system, we find surface behaviors similar to that of the three-dimensional classical XY model with sufficiently enhanced surface coupling, suggesting an extraordinary-log state at the bulk critical point.
At the bulk upper critical dimension, marginally irrelevant interactions generate multiplicative logarithmic corrections to mean-field scaling. While these corrections are well understood for bulk observables, their consequences for boundary criticality, particularly for finite-size scaling, remain much less explored. Here we combine large-scale quantum Monte Carlo simulations with boundary renormalization-group analysis to study a (3 + 1)D O(3) quantum critical point. After verifying the known logarithmically modified bulk finite-size scaling, including the correlation-length scaling governed by the logarithmic finite-size exponent \hat{\coppa}, we tune the surface coupling to identify ordinary, special, and extraordinary boundary regimes. For the ordinary and special transitions, we derive logarithmic correction exponents and \hat{\coppa}-dependent finite-size scaling forms for boundary correlations, including results that have not been systematically established before. These predictions are quantitatively supported by Monte Carlo data. In the extraordinary regime, we find long-range surface magnetic order and a logarithmically enhanced surface-bulk correlation.