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Lattice Topological Defects in Non-Unitary Conformal Field Theories
Madhav Sinha, Thiago Silva Tavares, Hubert Saleur +1
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible…
Reflecting boundary conditions in critical loop models
Max Downing, Jesper Lykke Jacobsen, Rongvoram Nivesvivat +2
In critical loop models, we call a boundary sticky if loops can attach to it, and reflecting otherwise. Using analytic bootstrap methods, we show that reflecting boundaries are cha…
Integrability and lattice discretizations of all Topological Defect Lines in minimal CFTs
Madhav Sinha, Thiago Silva Tavares, Ananda Roy +1
We discuss in this paper the lattice discretizations of all topological defect lines (TDLs) for diagonal, minimal CFTs, using integrable restricted solid-on-solid (RSOS) models. Fo…
Integrable RG Flows on Topological Defect Lines in 2D Conformal Field Theories
Thiago Silva Tavares, Madhav Sinha, Linnea Grans-Samuelsson +2
Topological defect lines (TDLs) in two-dimensional conformal field theories (CFTs) are standard examples of generalized symmetries in quantum field theory. Integrable lattice incar…
Critical spin chains and loop models with symmetry
Paul Roux, Jesper Lykke Jacobsen, Sylvain Ribault +1
Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These inc…
Lattice Realizations of Topological Defects in the critical (1+1)-d Three-State Potts Model
Madhav Sinha, Fei Yan, Linnea Grans-Samuelsson +2
Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin c…
On currents in the loop model
Jesper Lykke Jacobsen, Rongvoram Nivesvivat, Hubert Saleur
Using methods from the conformal bootstrap, we study the properties of Noether currents in the critical loop model. We confirm that they do not give rise to a Kac-Moody alge…
From combinatorial maps to correlation functions in loop models
Linnea Grans-Samuelsson, Jesper Lykke Jacobsen, Rongvoram Nivesvivat +2
In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums asso…
Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via Symmetry
Dmitry Chernyak, Azat M. Gainutdinov, Jesper Lykke Jacobsen +1
We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint…
-invariant non-compact boundary conditions for the XXZ spin chain
Dmitry Chernyak, Azat M. Gainutdinov, Hubert Saleur
We introduce new -invariant boundary conditions for the open XXZ spin chain. For generic values of we couple the bulk Hamiltonian to an infinite-dimensional…
Entanglement entropy in the Ising model with topological defects
Ananda Roy, Hubert Saleur
Entanglement entropy~(EE) contains signatures of many universal properties of conformal field theories~(CFTs), especially in the presence of boundaries or defects. In particular, {…
Global symmetry and conformal bootstrap in the two-dimensional model
Linnea Grans-Samuelsson, Rongvoram Nivesvivat, Jesper Lykke Jacobsen +2
We define the two-dimensional conformal field theory as a theory that includes the critical dilute and dense models as special cases, and depends analytically on the…
A note on the identity module in CFTs
Yifei He, Hubert Saleur
It has long been understood that non-trivial Conformal Field Theories (CFTs) with vanishing central charge () are logarithmic. So far however, the structure of the identity mo…
Lattice regularisation of a non-compact boundary conformal field theory
Niall F. Robertson, Jesper Lykke Jacobsen, Hubert Saleur
Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance o…
The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
Linnea Grans-Samuelsson, Jesper Lykke Jacobsen, Hubert Saleur
We investigate the action of discretized Virasoro generators, built out of generators of the lattice Temperley-Lieb algebra ("Koo-Saleur generators"[arXiv:hep-th/9312156]), in the…
The action of the Virasoro algebra in the two-dimensional Potts and loop models at generic
Linnea Grans-Samuelsson, Lawrence Liu, Yifei He +2
The spectrum of conformal weights for the CFT describing the two-dimensional critical -state Potts model (or its close cousin, the dense loop model) has been known for more than…
Geometrical four-point functions in the two-dimensional critical -state Potts model: The interchiral conformal bootstrap
Yifei He, Jesper Lykke Jacobsen, Hubert Saleur
Based on the spectrum identified in our earlier work [arXiv:1809.02191], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connect…
Four-point geometrical correlation functions in the two-dimensional -state Potts model: connections with the RSOS models
Yifei He, Linnea Grans-Samuelsson, Jesper Lykke Jacobsen +1
The "bootstrap determination" of the geometrical correlation functions in the two-dimensional Potts model proposed in a paper [arXiv:1607.07224] was later shown in [arXiv:1809.0219…
Topological defects in lattice models and affine Temperley-Lieb algebra
J. Belletête, A. M. Gainutdinov, J. L. Jacobsen +2
This paper is the first in a series where we attempt to define defects in critical lattice models that give rise to conformal field theory topological defects in the continuum limi…
A fusion for the periodic Temperley-Lieb algebra and its continuum limit
Azat M. Gainutdinov, Jesper L. Jacobsen, Hubert Saleur
The equivalent of fusion in boundary conformal field theory (CFT) can be realized quite simply in the context of lattice models by essentially glueing two open spin chains. This ha…
On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories
Jonathan Belletête, Azat M. Gainutdinov, Jesper L. Jacobsen +2
The relationship between bulk and boundary properties is one of the founding features of (Rational) Conformal Field Theory. Our goal in this paper is to explore the possibility of…
The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0
A. M. Gainutdinov, N. Read, H. Saleur +1
The periodic sl(2|1) alternating spin chain encodes (some of) the properties of hulls of percolation clusters, and is described in the continuum limit by a logarithmic conformal fi…
Logarithmic Conformal Field Theory: a Lattice Approach
A. M. Gainutdinov, J. L. Jacobsen, N. Read +2
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of criti…
Lattice W-algebras and logarithmic CFTs
A. M. Gainutdinov, H. Saleur, I. Yu. Tipunin
This paper is part of an effort to gain further understanding of 2D Logarithmic Conformal Field Theories (LCFTs) by exploring their lattice regularizations. While all work so far h…