Related papers: Supergroup approach to the Hubbard model
In this work, we move beyond the traditional complex-valued representations, introducing more expressive hypercomplex representations to model entities and relations for knowledge graph embeddings. More specifically, quaternion embeddings,…
Induced supersymmetry representations on composite operators are studied. In superspace the ensuing transformation rules (trivially) lead to an effective superfield. On the other hand, an induced representation must exist for non-linear…
We present an alternative scheme to the widely used method of representing the basis of one-band Hubbard model through the relation $I=I_{\uparrow}+2^{M}I_{\downarrow}$ given by H. Q. Lin and J. E. Gubernatis [Comput. Phys. 7, 400 (1993)],…
Spinor representation of group GL(4,R) on special spinor space is developed. Representation space has a structure of the fiber space with the space of diagonal metricses as the base and standard spinor space as typical fiber. Non-isometric…
We introduce a new framework for manipulating and interacting with deep generative models that we call network bending. We present a comprehensive set of deterministic transformations that can be inserted as distinct layers into the…
All possible permutations in the discrete $S_4$ group are classified by three rotation angles associated with the orthogonal group $O(3)$. We construct a spinor representation ${\bf 2}_D$ of $O(3)$, which is transformed by three 4$\times$4…
Cluster variables have recently revolutionized numerical work in certain models involving fermionic variables. This novel representation of fermionic partition functions is continuing to find new applications. After describing results from…
The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the…
An extension of the Lorentz group to include generators $\Gamma^\mu$ carrying a space-time index is demonstrated to explicitly construct the Minkowski metric within the internal group space as a consequence of the non-vanishing commutation…
In previous work by two of the present authors, twistors were re-interpreted as 4-d spinors with a position dependence within the formalism of geometric (Clifford) algebra. Here we extend that approach and justify the nature of the position…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…
An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the infinite-dimensional Hubbard model is developed on the basis of a…
We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
In this review we show that a Clifford algebra possesses a unique irreducible representation; the spinor representation. We discuss what types of spinors can exist in Minkowski space-times and we explain how to construct all the…
The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory…
We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest…
New method for construction of gauge-invariant deformed theory from an initial gauge theory proposed in our previous papers [1], [2] for closed/open gauge algebras is extended to the case of reducible gauge algebras. The deformation…
We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an…
A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized…