The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study the critical behavior of such a system. The renormalized vertex parts are defined at zero external quasi-momenta, which makes the analysis particularly simple. The distance between the boundary plates $L$ characterizing the finite size system direction perpendicular to the hyperplanes plays a similar role here in comparison with our recent unified treatment for Neumann and Dirichlet boundary conditions. Critical exponents are computed using diagrammatic expansion at least up to two-loop order and are shown to be identical to those from the bulk theory (limit $L \rightarrow \infty$ ).The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study the critical behavior of such a system. The renormalized vertex parts are defined at zero external quasi-momenta, which makes the analysis particularly simple. The distance between the boundary plates $L$ characterizing the finite size system direction perpendicular to the hyperplanes plays a similar role here in comparison with our recent unified treatment for Neumann and Dirichlet boundary conditions. Critical exponents are computed using diagrammatic expansion at least up to two-loop order and are shown to be identical to those from the bulk theory (limit $L \rightarrow \infty$).

Jan 5, 20170 citations

The effects of surfaces on dynamic critical behavior

S. Dietrich, Horst Diehl

The European Physical Journal BJun 1, 19832 citations

The effects of surfaces on dynamic critical behavior

S. Dietrich, Hans Werner Diehl

The European Physical Journal BDec 1, 198359 citations

Surface critical behavior of coupled Haldane chains

Wenjing Zhu, Chengxiang Ding, Long Zhang +1 more

The nonordinary surface transitions at the ( $2+1$ )-dimensional quantum critical point precluded in the corresponding classical critical point have been found recently. The mechanism of such behavior that is only found in dimerized Heisenberg models to date is still under debate. To illuminate the role of symmetry-protected topological (SPT) phases in inducing such nonordinary behaviors, we study a system on a two-dimensional square lattice consisting of interacting spin-1 Haldane chains, which has a genuine SPT phase---the Haldane phase---at weak interchain interactions and a quantum critical point, belonging to the classical three-dimensional (3D) O(3) universality class, to the N\'eel phase. Different from previously studied models, there is no dimerization in the current model. Cutting the system along the chain direction or perpendicular to the chain direction exposes two different surfaces. Using unbiased quantum Monte Carlo simulations, we find that the two different types of surfaces show completely different surface critical behaviors at the bulk critical point, resulting from different surface states in the SPT phase. For the system with surfaces along the chain direction, the surface critical behavior is of ordinary type of the bulk 3D O(3) critical point, while for the surfaces perpendicular to the chain direction, the surface critical behavior is nonordinary, consistent with nonordinary transitions found in dimerized Heisenberg models. Our numerical results demonstrate that the gapless surface state in the gapped SPT phase together with the gapless mode of the critical point is a pure quantum scenario that leads to the nonordinary transition.The nonordinary surface transitions at the ($2+1$)-dimensional quantum critical point precluded in the corresponding classical critical point have been found recently. The mechanism of such behavior that is only found in dimerized Heisenberg models to date is still under debate. To illuminate the role of symmetry-protected topological (SPT) phases in inducing such nonordinary behaviors, we study a system on a two-dimensional square lattice consisting of interacting spin-1 Haldane chains, which has a genuine SPT phase---the Haldane phase---at weak interchain interactions and a quantum critical point, belonging to the classical three-dimensional (3D) O(3) universality class, to the N\'eel phase. Different from previously studied models, there is no dimerization in the current model. Cutting the system along the chain direction or perpendicular to the chain direction exposes two different surfaces. Using unbiased quantum Monte Carlo simulations, we find that the two different types of surfaces show completely different surface critical behaviors at the bulk critical point, resulting from different surface states in the SPT phase. For the system with surfaces along the chain direction, the surface critical behavior is of ordinary type of the bulk 3D O(3) critical point, while for the surfaces perpendicular to the chain direction, the surface critical behavior is nonordinary, consistent with nonordinary transitions found in dimerized Heisenberg models. Our numerical results demonstrate that the gapless surface state in the gapped SPT phase together with the gapless mode of the critical point is a pure quantum scenario that leads to the nonordinary transition.

arXiv:2010.10920Physical review. B./Physical review. BJan 11, 202142 citations

Role of finite-size effects in the critical behavior of itinerant fermions

Avraham Klein, Andrey V. Chubukov

We study the role of finite-size effects on critical behavior near a metallic $q=0$ critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent $z=3$ . We show that finite-size effects are particularly strong for $z=3$ criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within $z=3$ theory.We study the role of finite-size effects on critical behavior near a metallic $q=0$ critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent $z=3$. We show that finite-size effects are particularly strong for $z=3$ criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within $z=3$ theory.

arXiv:1701.07557Physical review. B./Physical review. BJul 27, 20173 citations

L

characterizing the finite size system direction perpendicular to the hyperplanes plays a similar role here in comparison with our recent unified treatment for Neumann and Dirichlet boundary conditions. Critical exponents are computed using diagrammatic expansion at least up to two-loop order and are shown to be identical to those from the bulk theory (limit

L \rightarrow \infty

The nonordinary surface transitions at the (

2+1

)-dimensional quantum critical point precluded in the corresponding classical critical point have been found recently. The mechanism of such behavior that is only found in dimerized Heisenberg models to date is still under debate. To illuminate the role of symmetry-protected topological (SPT) phases in inducing such nonordinary behaviors, we study a system on a two-dimensional square lattice consisting of interacting spin-1 Haldane chains, which has a genuine SPT phase---the Haldane phase---at weak interchain interactions and a quantum critical point, belonging to the classical three-dimensional (3D) O(3) universality class, to the N\'eel phase. Different from previously studied models, there is no dimerization in the current model. Cutting the system along the chain direction or perpendicular to the chain direction exposes two different surfaces. Using unbiased quantum Monte Carlo simulations, we find that the two different types of surfaces show completely different surface critical behaviors at the bulk critical point, resulting from different surface states in the SPT phase. For the system with surfaces along the chain direction, the surface critical behavior is of ordinary type of the bulk 3D O(3) critical point, while for the surfaces perpendicular to the chain direction, the surface critical behavior is nonordinary, consistent with nonordinary transitions found in dimerized Heisenberg models. Our numerical results demonstrate that the gapless surface state in the gapped SPT phase together with the gapless mode of the critical point is a pure quantum scenario that leads to the nonordinary transition.

We study the role of finite-size effects on critical behavior near a metallic

q=0

critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent

z=3

. We show that finite-size effects are particularly strong for

z=3

criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within

z=3

theory.