Universality class of the Mott transition in two dimensions

Moukouri, S.; Eidelstein, Eitan

doi:10.1103/physrevb.86.155112

Cited by 17 publications

(19 citation statements)

References 41 publications

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“…[30,31] Increasing interchain coupling J x , the model will be brought into a Néel phase. The quantum critical point between the SPT Haldane and the Néel phase [30,[32][33][34][35][36][37] locates at J x = 0.043648 (8) and the transition belongs to the 3D O(3) universality class. [36] To study the SCBs of the model, we use periodic boundary condition along one direction and make open boundary boundaries along the other direction by cutting a row/column of bonds perpendicular to this direction.…”

Section: Introductionmentioning

confidence: 99%

Surface critical behaviors of coupled Haldane chains

Zhu,

Ding,

Zhang

et al. 2020

Preprint

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The special surface transition at (2+1)-dimensional quantum critical point is precluded in corresponding classical critical point. The mechanism of such behavior which is only found in dimerized Heisenberg models so far is still under debate. To illuminate the role of symmetry protected topological (SPT) phase in inducing such nonordinary behaviors, we study a system on a two-dimensional square lattice consisted by 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 3D O(3) universality class to the Néel phase. Different from models studied previously, 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 surface show completely different surface critical behaviors at the bulk critical point, resulted 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 special 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 critical point is a pure quantum scenario that leads to the nonordinary transition.

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Section: Introductionmentioning

confidence: 99%

Surface critical behaviors of coupled Haldane chains

Zhu,

Ding,

Zhang

et al. 2020

Preprint

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“…A general universality class, the O(N ) universality class treated here, encompasses the particular models: Ising (N = 1), XY (N = 2), Heisenberg (N = 3), self-avoiding random walk (N = 0) and spherical (N → ∞) for short-range interactions [17]. Recently there were many studies on the dependence of the critical exponents on the more obvious parameters as d [18,19] and N [20][21][22] as well as on the less intuitive symmetry of the order parameter [23,24]. Studying the effect of a symmetry breaking mechanism on the values for the critical exponents is the aim of this work.…”

Section: Introductionmentioning

confidence: 99%

Renormalization group approach for Lorentz-violating scalar field theory at all loop orders

Vieira

Carvalho

2016

Int. J. Geom. Methods Mod. Phys.

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We compute, both explicitly up to next-to-leading order and in a proof by induction for all loop levels, the critical exponents for thermal Lorentz-violating O(N ) self-interacting scalar field theory. They are evaluated in a massless theory renormalized at arbitrary external momenta, where a reduced number of Feynman diagrams is needed. The results are presented and shown to be identical to that found previously in distinct theories renormalized at different renormalization schemes. At the end we give both mathematical explanation and physical interpretation for them based on coordinates redefinition techniques and symmetry ideas, respectively.

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“…[21]. Of course, the d [22,23] and N [24][25][26] parameters are easier to probe than symmetry effects [27,28]. Probing the effect of the latter in a curved spacetime is the aim of the present work.…”

Section: Introductionmentioning

confidence: 98%

Diffeomorphism symmetry effect on the O( N ) universality class

Costa

Carvalho

2019

Class. Quantum Grav.

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We probe the effect of diffeomorphism symmetry on the critical exponents values for massive O(N ) λφ 4 scalar field theories in curved spacetime. We apply field-theoretic renormalization group tools, where we use only momentum coordinates as opposed to the earlier standard procedure with both space and momentum coordinates, for computing analytically the critical exponents up to three-loop order for one of them and up to two-loop level for the remaining ones. We found that the curved spacetime critical exponents are the same as their flat spacetime counterparts, at least up to the level considered. At the conclusions we present the physical interpretation for the results.

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Universality class of the Mott transition in two dimensions

Cited by 17 publications

References 41 publications

Surface critical behaviors of coupled Haldane chains

Surface critical behaviors of coupled Haldane chains

Renormalization group approach for Lorentz-violating scalar field theory at all loop orders

Diffeomorphism symmetry effect on the O( N ) universality class

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