Particles, conformal invariance and criticality in pure and disordered systems

Delfino, Gesualdo

doi:10.1140/epjb/s10051-021-00076-0

Cited by 8 publications

(19 citation statements)

References 107 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, our conjecture is consistent with the recent study of the RP 2 model based on the conformal scattering theory, and this O(5) universality class corresponds to the solution A + of the Ref. [60], while the remaining solution A − corresponds to the c = 5 2 SO(5) 1 WZW [65,66]. Interestingly, the central charge c = 2 of the ferromagnetic RP 2 model at zero temperature is none of them above, leaving the possibility to become a candidate for the solution B ±3 .…”

Section: Discussionsupporting

confidence: 91%

Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{RP^2}$ Models in Two Dimensions

Ueda,

Oshikawa

2022

Preprint

View full text Add to dashboard Cite

We study the classical two-dimensional RP 2 and Heisenberg models, using the Tensor-Network Renormalization (TNR) method. The determination of the phase diagram of these models has been challenging and controversial, owing to the very large correlation lengths at low temperatures. The finite-size spectrum of the transfer matrix obtained by TNR is useful in identifying the conformal field theory describing a possible critical point. Our results indicate that the ultraviolet fixed point for the Heisenberg model and the ferromagnetic RP 2 model in the zero temperature limit corresponds to a conformal field theory with central charge c = 2, in agreement with two independent would-be Nambu-Goldstone modes. On the other hand, the ultraviolet fixed point in the zero temperature limit for the antiferromagnetic Lebwohl-Lasher model, which is a variant of the RP 2 model, seems to have a larger central charge. This is consistent with c = 4 expected from the effective SO(5) symmetry. At T > 0, the convergence of the spectrum is not good in both the Heisenberg and ferromagnetic RP 2 models. Moreover, there seems no appropriate candidate of conformal field theory matching the spectrum, which shows the effective central charge c ∼ 1.9. These suggest that both models have a single disordered phase at finite temperatures, although the ferromagnetic RP 2 model exhibits a strong crossover at the temperature where the dissociation of Z2 vortices has been reported.

show abstract

Section: Discussionsupporting

confidence: 91%

Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{RP^2}$ Models in Two Dimensions

Ueda,

Oshikawa

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Notice that, since we derived the equations relying only on the symmetries of the Hamiltonian (12), the space of solutions contains both the fixed points of the ferromagnetic case (J > 0) and those of the antiferromagnetic case (J < 0). This point is explicitly illustrated in [33,39] for the case of the q-state Potts model.…”

Section: Fixed Point Equations Of the Cp N −1 Modelmentioning

confidence: 96%

“…Such a phase is related to the conformal dimension ∆ η of the chiral field that creates the particles as [31,39]…”

Section: Solutionsmentioning

confidence: 99%

“…While two-dimensional criticality has allowed for an impressive amount of exact solutions thanks to lattice integrability [25,26] and conformal field theory [27,28], models with local symmetries traditionally remained outside the range of application of these methods. Recently, however, we showed in [29,30] how the renormalization group fixed points of the RP N −1 model can be accessed in an exact way in the scale invariant scattering framework [31], which implements in the basis of particle excitations the infinite-dimensional conformal symmetry characteristic of critical points in two dimensions and has provided in the last years new results for pure and disordered systems [32,33,34,35,36,37,38] (see [39] for a review). We found that only O(N (N + 1)/2 − 1) fixed points exist for 1 N ≥ 3 and account for zero temperature criticality, while a line of fixed points yielding a BKT transition exists only for N = 2.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Critical points in the $CP^{N-1}$ model

Diouane,

Lamsen,

Delfino

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We use scale invariant scattering theory to obtain the exact equations determining the renormalization group fixed points of the two-dimensional CP N −1 model, for N real. Also due to special degeneracies at N = 2 and 3, the space of solutions for N ≥ 2 reduces to that of the O(N 2 − 1) model, and accounts for a zero temperature critical point. For N < 2 the space of solutions becomes larger than that of the O(N 2 − 1) model, with the appearance of new branches of fixed points relevant for criticality in gases of intersecting loops.

show abstract

“…We can mention for instance geometrical phase transitions such as percolation [4], recently analyzed in deep in [5,6], or disordered systems [7,8]. In particular, the latter are described by coupling copies of the original pure CFT to a relevant field, and then flow to a new fixed point whose properties are largely unknown, see [9][10][11].…”

Section: Jhep10(2021)175mentioning

confidence: 99%

Crossing-symmetric twist field correlators and entanglement negativity in minimal CFTs

Ares

Santachiara

Viti

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We study conformal twist field four-point functions on a ℤN orbifold. We examine in detail the case N = 3 and analyze theories obtained by replicated N-times a minimal model with central charge c < 1. A fastly convergent expansion of the twist field correlation function in terms of sphere conformal blocks with central charge Nc is obtained by exploiting covering map techniques. We discuss extensive applications of the formalism to the entanglement of two disjoint intervals in CFT, in particular we propose a conformal block expansion for the partially transposed reduced density matrix. Finally, we refine the bounds on the structure constants of unitary CFTs determined previously by the genus two modular bootstrap.

show abstract

Particles, conformal invariance and criticality in pure and disordered systems

Cited by 8 publications

References 107 publications

Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{RP^2}$ Models in Two Dimensions

Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{RP^2}$ Models in Two Dimensions

Critical points in the $CP^{N-1}$ model

Crossing-symmetric twist field correlators and entanglement negativity in minimal CFTs

Contact Info

Product

Resources

About