Two-point boundary correlation functions of dense loop models

Morin-Duchesne, Alexi; Jacobsen, Jesper Lykke

doi:10.21468/scipostphys.4.6.034

Cited by 3 publications

(10 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…. This is consistent with earlier known results for the weights of these fields [29,38]. The constant term forF 2 was also computed; it differs from the value of the same constant for F 2 by the simple factor −2 log((1 + x)/(2 √ x)).…”

supporting

confidence: 90%

“…The constant term has precisely the predicted form f (x) given in (1.6) for a two-point function of primary fields in CFT. The fields ϕ 1 and ϕ 4 have the dimension ∆ 1 = ∆ 4 = ∆ 1,d+1 , which is the known value for the boundary changing operator that accounts for the insertion of d defects on a boundary [29,38]. The two other fields are identity fields, with ∆ 2 = ∆ 3 = 0.…”

Section: )mentioning

confidence: 99%

See 1 more Smart Citation

Bipartite fidelity of critical dense polymers

Parez¹,

Morin-Duchesne²,

Ruelle³

2019

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

We investigate the bipartite fidelity F d for a lattice model described by a logarithmic CFT: the model of critical dense polymers. We define this observable in terms of a partition function on the pants geometry, where d defects enter at the top of the pants lattice and exit in one of the legs. Using the correspondence with the XX spin chain, we obtain an exact closed-form expression for F d and compute the leading terms in its 1/N asymptotic expansion as a function of x = N A /N , where N is the lattice width at the top of the pants and N A is the width of the leg where the defects exit. We find an agreement with the results of Stéphan and Dubail for rational CFTs, with the central charge and conformal weights specialised to c = −2 and ∆ = ∆ 1,d+1 = d(d−2) 8 . We compute a second instanceF 2 of the bipartite fidelity for d = 2 by imposing a different rule for the connection of the defects. In the conformal setting, this choice corresponds to inserting two boundary condition changing fields of weight ∆ = 0 that are logarithmic instead of primary. We compute the asymptotic expansion in this case as well and find a simple additive correction compared to F 2 , of the form −2 log((1 + x)/(2 √ x)). We confirm this lattice result with a CFT derivation and find that this correction term is identical for all logarithmic theories, independently of c and ∆.

show abstract

supporting

confidence: 90%

Section: )mentioning

confidence: 99%

Bipartite fidelity of critical dense polymers

Parez¹,

Morin-Duchesne²,

Ruelle³

2019

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…A common feature of such lattice models is the appearance of cellular algebras [32] of the Temperley-Lieb type. Logarithms in correlation functions were previously found in various lattice models, including the abelian sandpile model [33][34][35], critical dense polymers [36][37][38], critical percolation [39,40] and the Q-state Potts model [41,42]. In many cases, the results were obtained using conformal arguments and verified numerically on a computer.…”

Section: Introductionmentioning

confidence: 76%

“…In a previous paper [38], we have defined several types of two-point boundary correlation functions of critical dense polymers. We established their exact finite-size expressions on a semi-infinite strip of width n and compared the corresponding asymptotic expansions with the field-theoretical predictions.…”

Section: Introductionmentioning

confidence: 99%

“…subject to periodic boundary conditions) acting between two given boundary states with those of an open evolution operator (with given boundary conditions) acting in periodic imaginary time. Our setup similarly replaces the open evolution operator of [38] with a closed one, but we keep the defect points at the boundary. The correct interpretation of our results thus remains within the boundary version of LCFT.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Logarithmic correlation functions for critical dense polymers on the cylinder

Morin-Duchesne

Jacobsen

2019

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

We compute lattice correlation functions for the model of critical dense polymers on a semiinfinite cylinder of perimeter n. In the lattice loop model, contractible loops have a vanishing fugacity whereas non-contractible loops have a fugacity α ∈ (0, ∞). These correlators are defined as ratios Z(x)/Z 0 of partition functions, where Z 0 is a reference partition function wherein only simple half-arcs are attached to the boundary of the cylinder. For Z(x), the boundary of the cylinder is also decorated with simple half-arcs, but it also has two special positions 1 and x where the boundary condition is different. We investigate two such kinds of boundary conditions: (i) there is a single node at each of these points where a long arc is attached, and (ii) there are pairs of adjacent nodes at these points where two long arcs are attached.We find explicit expressions for these correlators for finite n using the representation of the enlarged periodic Temperley-Lieb algebra in the XX spin chain. The resulting asymptotics as n → ∞ are expressed as simple integrals that depend on the scaling parameter τ = x−1 n ∈ (0, 1). For small τ , the leading behaviours are proportional to τ 1/4 , τ 1/4 log τ , log τ and log 2 τ .We interpret the lattice results in terms of ratios of conformal correlation functions. We assume that the corresponding boundary changing fields are highest weight states in irreducible, Kac or staggered Virasoro modules, with central charge c = −2 and conformal dimensions ∆ = − 1 8 or ∆ = 0. With these assumptions, we obtain differential equations of order two and three satisfied by the conformal correlation functions, solve these equations in terms of hypergeometric functions, and find a perfect agreement with the lattice results. We use the lattice results to compute structure constants and ratios thereof which appear in the operator product expansions of the boundary condition changing fields. The fusion of these fields is found to be non-abelian.

show abstract

Bipartite fidelity for models with periodic boundary conditions

Morin-Duchesne¹,

Parez²,

Liénardy³

2021

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

For a given statistical model, the bipartite fidelity F is computed from the overlap between the groundstate of a system of size N and the tensor product of the groundstates of the same model defined on two subsystems A and B, of respective sizes N A and N B with N = N A + N B . In this paper, we study F for critical lattice models in the case where the full system has periodic boundary conditions. We consider two possible choices of boundary conditions for the subsystems A and B, namely periodic and open. For these two cases, we derive the conformal field theory prediction for the leading terms in the 1/N expansion of F , in a most general case that corresponds to the insertion of four and five fields, respectively. We provide lattice calculations of F , both exact and numerical, for two free-fermionic lattice models: the XX spin chain and the model of critical dense polymers. We study the asymptotic behaviour of the lattice results for these two models and find an agreement with the predictions of conformal field theory.

show abstract

Two-point boundary correlation functions of dense loop models

Cited by 3 publications

References 76 publications

Bipartite fidelity of critical dense polymers

Bipartite fidelity of critical dense polymers

Logarithmic correlation functions for critical dense polymers on the cylinder

Bipartite fidelity for models with periodic boundary conditions

Contact Info

Product

Resources

About