Related papers: Ground states for generalized gauge actions on UHF…
The paper contains a description of the KMS states and ground states of a generalized gauge action on the C*-algebra of a finite graph.
We study the KMS states and $KMS_{\infty}$ states of generalized gauge actions on the $C^*$-algebra of a pointed Cayley graph. Our results provide information for any finitely generated group, but they are only complete for nilpotent…
We describe KMS and ground states arising from a generalized gauge action on ultragraph C*-algebras. We focus on ultragraphs that satisfy Condition~(RFUM), so that we can use the partial crossed product description of ultragraph C*-algebras…
Given a positive function on the set of edges of an arbitrary directed graph $E=(E^0,E^1)$, we define a one-parameter group of automorphisms on the C*-algebra of the graph $C^*(E)$, and study the problem of finding KMS states for this…
It is shown that any bundle of KMS state spaces which can occur for a flow on a unital separable C*-algebra with a trace state can also be realized by a flow on any given unital infinite-dimensional simple AF algebra with a tracial state…
We determine the factor types of the extremal KMS weights for generalized gauge actions on a graph algebra, and the ground states for the restriction of the action to a corner defined from a vertex. The assumptions on the graph and the…
We consider operator-algebraic dynamical systems given by actions of the real line on unital $C^*$-algebras, and especially the equilibrium states (or KMS states) of such systems. We are particularly interested in systems built from the…
A set of new exact ground states of the generalized Hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. This is based on a simple method for constructing exact ground states for homogeneous quantum…
We prove that all strongly outer Z^N-actions on a UHF algebra of infinite type are strongly cocycle conjugate to each other. We also prove that all strongly outer, asymptotically representable Z^N-actions on a unital simple AH algebra with…
We give a complete classification up to cocycle conjugacy of uniformly outer actions of Z^2 on UHF algebras. In particular, it is shown that any two uniformly outer actions of Z^2 on a UHF algebra of infinite type are cocycle conjugate. We…
We derive the universal real time $U(1)$ topological gauge field action for mixed quantum states of weakly correlated fermions in all dimensions, and demonstrate its independence of the underlying equilibrium or non-equilibrium nature of…
KMS weights for generalized gauge actions on graph C*-algebras are studied and a complete description of the structure is obtained for the gauge action when the graph is strongly connected and has at most countably many exits. The structure…
Given a self-similar $K$ set defined from an iterated function system $\Gamma=(\gamma_1,\ldots,\gamma_n)$ and a set of function $H=\{h_i:K\to\mathbb{R}\}_{i=1}^d$ satisfying suitable conditions, we define a generalized gauge action on…
We show that every uniform state on the sphere is essentially a superposition of regular graphs. In addition, we develop a graph-based ansatz to construct trial FHQ ground states sharing the local properties of Jack polynomials. In…
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized…
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through…
We completely classify the KMS states for the gauge action on a $C^*$-algebra associated with a rational function $R$ introduced in our previous work. The gauge action has a phase transition at $\beta = \log \deg R$. We can recover the…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
Universal algebraic geometry is generalised from solutions of equations in a single algebra to the study of $\varphi$- or $K$-spectra, akin to the prime spectrum of a ring. We explore their basic properties and constructions, give a…
The main goal of this thesis is to study $\mathbb{K}$-uniruled sets that appear in affine geometry. At the beginning we discuss the property of $\mathbb{K}$-uniruledness and its equivalent conditions. Then we bound from above the degree of…