Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon Models

In this paper we compute the most general nondiagonal reflection matrices of the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter equations. We find new one-parameter family of reflection matrices for the RSOS model in addition to the previous result without any parameter. We also find three classes of reflection matrices for the SOS model, which has one or two parameters. For the hard hexagon model which can be mapped to RSOS(5) model by folding four RSOS heights into two, the solutions can be obtained similarly with a main difference in the boundary unitarity conditions. Due to this, the reflection matrices can have two free parameters. We show that these extra terms can be identified with the `decorated' solutions. We also generalize the hard hexagon model by `folding' the RSOS heights of the general RSOS(p) model and show that they satisfy the integrability conditions such as the Yang- Baxter and boundary Yang-Baxter equations. These models can be solved using the results for the RSOS models.Comment: 18pages,Late

The "topological" charge for the finite XX quantum chain

It is shown that an operator (in general non-local) commutes with the Hamiltonian describing the finite XX quantum chain with certain non-diagonal boundary terms. In the infinite volume limit this operator gives the "topological" charge.Comment: 5 page

Quantum boundary currents for nonsimply-laced Toda theories

We study the quantum integrability of nonsimply--laced affine Toda theories defined on the half--plane and explicitly construct the first nontrivial higher--spin charges in specific examples. We find that, in contradistinction to the classical case, addition of total derivative terms to the "bulk" current plays a relevant role for the quantum boundary conservation.Comment: 11 pages, latex, no figure

A Novel Data Augmentation Technique for Out-of-Distribution Sample Detection using Compounded Corruptions

Modern deep neural network models are known to erroneously classify out-of-distribution (OOD) test data into one of the in-distribution (ID) training classes with high confidence. This can have disastrous consequences for safety-critical applications. A popular mitigation strategy is to train a separate classifier that can detect such OOD samples at the test time. In most practical settings OOD examples are not known at the train time, and hence a key question is: how to augment the ID data with synthetic OOD samples for training such an OOD detector? In this paper, we propose a novel Compounded Corruption technique for the OOD data augmentation termed CnC. One of the major advantages of CnC is that it does not require any hold-out data apart from the training set. Further, unlike current state-of-the-art (SOTA) techniques, CnC does not require backpropagation or ensembling at the test time, making our method much faster at inference. Our extensive comparison with 20 methods from the major conferences in last 4 years show that a model trained using CnC based data augmentation, significantly outperforms SOTA, both in terms of OOD detection accuracy as well as inference time. We include a detailed post-hoc analysis to investigate the reasons for the success of our method and identify higher relative entropy and diversity of CnC samples as probable causes. We also provide theoretical insights via a piece-wise decomposition analysis on a two-dimensional dataset to reveal (visually and quantitatively) that our approach leads to a tighter boundary around ID classes, leading to better detection of OOD samples. Source code link: https://github.com/cnc-oodComment: 16 pages of the main text, and supplemental material. Accepted in Research Track ECML'22. Project webpage: https://cnc-ood.github.io

Quantum integrability in two-dimensional systems with boundary

In this paper we consider affine Toda systems defined on the half-plane and study the issue of integrability, i.e. the construction of higher-spin conserved currents in the presence of a boundary perturbation. First at the classical level we formulate the problem within a Lax pair approach which allows to determine the general structure of the boundary perturbation compatible with integrability. Then we analyze the situation at the quantum level and compute corrections to the classical conservation laws in specific examples. We find that, except for the sinh-Gordon model, the existence of quantum conserved currents requires a finite renormalization of the boundary potential.Comment: latex file, 18 pages, 1 figur

Boundary Yang-Baxter equation in the RSOS/SOS representation

We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS models with fixed and free boundary spins respectively. Applied to (1+1)-dimenional quantum field theory, these solutions give the boundary scattering amplitudes of the particles. For the diagonal solution, we propose an algebraic Bethe ansatz method to diagonalize the SOS-type transfer matrix with boundary and obtain the Bethe ansatz equations.Comment: 30 pages, 5 figures, uses Latex with eepic.sty and epic.sty. Paper substantially expanded; section on SOS model is revised and a new section on the Bethe ansatz equation is adde

Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System

We show that the 2-matrix string model corresponds to a coupled system of $2+1$-dimensional KP and modified KP (\KPm) integrable equations subject to a specific ``symmetry'' constraint. The latter together with the Miura-Konopelchenko map for \KPm are the continuum incarnation of the matrix string equation. The \KPm Miura and B\"{a}cklund transformations are natural consequences of the underlying lattice structure. The constrained \KPm system is equivalent to a $1+1$-dimensional generalized KP-KdV hierarchy related to graded ${\bf SL(3,1)}$. We provide an explicit representation of this hierarchy, including the associated ${\bf W(2,1)}$-algebra of the second Hamiltonian structure, in terms of free currents.Comment: 12+1 pgs., LaTeX, preprint: BGU-94 / 15 / June-PH, UICHEP-TH/94-

Boundary Flows in general Coset Theories

In this paper we study the boundary effects for off-critical integrable field theories which have close analogs with integrable lattice models. Our models are the $SU(2)_{k}\otimes SU(2)_{l}/SU(2)_{k+l}$ coset conformal field theories perturbed by integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the TBA method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion RSOS lattice models. For super CFTs ($k=2$) we show that these flows are possible only for the Neveu-Schwarz sector and are consistent with the lattice results. The models we considered cover a wide class of integrable models. In particular, we show how the the impurity spin is screened by electrons for the $k$-channel Kondo model by taking $l\to\infty$ limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.Comment: 22 pages, 3 postscript figure file