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

Chengxiang Ding; Long Zhang; Wenan Guo; Wenjing Zhu

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

WenJing Zhu, Chengxiang Ding, Long Zhang, Wenan Guo

Strongly Correlated Electrons · Submitted 24 Nov 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID2111.12336 (version 3)

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CitationChengxiang Ding, Long Zhang, Wenan Guo, Wenjing Zhu. "Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model." arXiv:2111.12336 (2021). https://pith.science/paper/AB33LM6R

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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 $S=1/2$ and $S=1$ 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 $S=1$ and $S=1/2$ spin systems. However, the dangling-chain surface shows much richer surface behaviors than in the Heisenberg limit. For the $S=1/2$ 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 $S=1$ 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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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 $S=1/2$ and $S=1$ spins using quantum Monte Carlo simulations.	contribution 0.97	0.93	0.05	asserted 0.77
s1	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.	result 0.94	0.83	0.44	asserted 1.00
s2	Similar to the Heisenberg limit, we find an ordinary transition on the dangling-ladder surface for both $S=1$ and $S=1/2$ spin systems.	result 1.00	0.94	0.11	asserted 1.00
s3	However, the dangling-chain surface shows much richer surface behaviors than in the Heisenberg limit.	result 0.99	0.87	0.16	asserted 1.00
s4	For the $S=1/2$ 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.	result 0.98	0.95	0.21	asserted 0.62
s5	The possibility that the state is an extraordinary-log state seems unlikely.	interpretation 0.54	0.77	0.06	hedged possibility 0.88
s6	For the $S=1$ 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.	result 0.73	0.94	0.20	hedged possibility 0.94

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Original abstract

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 $S=1/2$ and $S=1$ 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 $S=1$ and $S=1/2$ spin systems. However, the dangling-chain surface shows much richer surface behaviors than in the Heisenberg limit. For the $S=1/2$ 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 $S=1$ 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.

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References

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9 arXiv papers cite this in 13 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Compares with it 1 paper

The sharp difference from the BCB of XXZ antiferromagnet [ref] reflects the sensitivity of BCB to geometric settings and local operators.

Quantum extraordinary-log universality of boundary critical behavior · Introduction · 0.99

Cites it as background 7 papers

Motivated by the exotic surface effects of symmetry-protected topological phases, SC has been extensively studied in dimerized antiferromagnetic quantum Heisenberg and XXZ models [ref] , yet the existence of quantum ELU is still controversial.

Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge · Introduction · 0.85
Shortly afterwards, much attention was devoted to the BCB in classical [ref] and quantum [ref] systems.

Quantum extraordinary-log universality of boundary critical behavior · Introduction · 0.91
A series of related studies greatly promote the interest in this field [ref] , which includes the finding of the extraordinry-log phase [ref] , a great breakthrough in the research of critical phenomena.

Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model · Introduction · 0.81

What it cites · 10 sentences without a confident label

Uses data or values from 1 paper

Such behavior has been observed with $q=0.59(2)$ on the surface of the critical 3D classical O(2) model with sufficiently enhanced surface couplings [ref] ; see also Table [ref].

Extraordinary-log surface phase transition in the three-dimensional $XY$ model · $S=1/2$ models · 0.86

Cites as support 1 paper

Numerical works on classical 3D O(3) and 3D O(2) models support the existence of such a phase [ref] .

Extraordinary-log surface phase transition in the three-dimensional $XY$ model · $S=1/2$ models · 0.98

Cites as background 1 paper

To date, for the SCBs of the 3D O(2) universality class, only classical models have been studied [ref] .

Extraordinary-log surface phase transition in the three-dimensional $XY$ model · Introduction · 0.89

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