Related papers: Equilibrium and ground states from Cayley graphs
We produce a complete descrption of the lattice of gauge-invariant ideals in $C^*(\Lambda)$ for a finitely aligned $k$-graph $\Lambda$. We provide a condition on $\Lambda$ under which every ideal is gauge-invariant. We give conditions on…
In this paper, we study a family of $C^*$-subalgebras defined by fixed points of generalized gauge actions of a Cuntz-Krieger algebra, by introducing a family of \'etale groupoids whose associated $C^*$-algebras are these $C^*$-subalgebras.…
We study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups, called extraspecial groups. By applying general results for graphs in association schemes we determine the precise conditions for perfect state…
We initiate the treatment of KMS states on uniform Roe algebras $\mathrm{C}^*_u(X)$ for a class of naturally occurring flows on these algebras. We show that KMS states on $\mathrm{C}^*_u(X)$ always factor through the diagonal operators…
For a set of quantum states generated by the action of a group, we consider the graph obtained by considering two group elements adjacent whenever the corresponding states are non-orthogonal. We analyze the structure of the connected…
We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and $ C^{\ast} $-algebras associated to these groupoids. We provide a new…
We define the notion of rough Cayley graph for compactly generated locally compact groups in terms of quasi-actions. We construct such a graph for any compactly generated locally compact group using quasi-lattices and show uniqueness up to…
We calculate the ordered K_0-group of a graph C*-algebra and mention applications of this result to AF-algebras, states on the K_0-group of a graph algebra, and tracial states of graph algebras.
A generalised Paley map is a Cayley map for the additive group of a finite field F, with a subgroup S=-S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the…
We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence…
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
We study the phase transition of KMS states for the C*-algebras of $ax+b$-semigroups of algebraic integers in which the multiplicative part is restricted to a congruence monoid, as in recent work of Bruce generalizing earlier work of Cuntz,…
We obtain a complete classification of graph products of finite abelian groups whose Cayley graphs with respect to the standard presentations are planar.
In this paper we study free actions of groups on separated graphs and their \cstar{}algebras, generalizing previous results involving ordinary (directed) graphs. We prove a version of the Gross-Tucker Theorem for separated graphs yielding a…
Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a)…
We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
Given an action of a compact quantum group on a unital C*-algebra, one can amplify the action with an adjoint representation of the quantum group on a finite dimensional matrix algebra, and consider the resulting inclusion of fixed point…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…