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We present a generic and systematic approach for constructing D-dimensional lattice models with exactly solvable d-dimensional boundary states localized to corners, edges, hinges and surfaces. These solvable models represent a class of…
We construct a lattice model for two-dimensional N=(2,2) supersymmetric QCD (SQCD), with the matter multiplets belonging to the fundamental or anti-fundamental representation of the gauge group U(N) or SU(N). The construction is based on…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…
In this paper we deal with the problem of extending Zadeh's operators on fuzzy sets (FSs) to interval-valued (IVFSs), set-valued (SVFSs) and type-2 (T2FSs) fuzzy sets. Namely, it is known that seeing FSs as SVFSs, or T2FSs, whose membership…
Symmetry plays an important role in the topological band theory. In contrary, study on the topological properties of the asymmetric systems is rather limited, especially in higher-dimensional systems. In this work, we explore a new theory…
Quasi-one-dimensional (Q1D) systems, i.e., three- and two-dimensional (3D/2D) arrays composed of weakly coupled one-dimensional lattices of interacting quantum particles, exhibit rich and fascinating physics. They are studied across various…
A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle…
In this paper, we construct and investigate two supersymmetric versions of the Fokas-Gel'fand formula for the immersion of 2D surfaces associated with a supersymmetric integrable system. The first version involves an infinitesimal…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent…
We devise a generic recipe for constructing $D$-dimensional lattice models whose $d$-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying…
Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity…
We use the intrinsic one-form and two-form global symmetries of (3+1)$d$ bosonic field theories to classify quantum phases enriched by ordinary ($0$-form) global symmetry. Different symmetry-enriched phases correspond to different ways of…
Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete…
This paper is the first part in a 2 part study of an elementary functorial construction from the category of finite non-abelian groups to a category of singular compact, oriented 2-manifolds. After a desingularization process this…
The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go…
The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of…
We introduce weak Hopf symmetry as a tool to explore (1+1)-dimensional topological phases with non-invertible symmetries. Drawing inspiration from Symmetry Topological Field Theory (SymTFT), we construct a lattice model featuring two…
Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a…
We extend our exploration of nonstandard continuum quantum field theories in 2+1 dimensions to 3+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising…