Paul Fendley

Abstract:

Arrays of Rydberg atoms in the blockade regime realize a wealth of strongly correlated quantum physics, but theoretical analysis beyond the chain is rather difficult. Here we study a tractable model of Rydberg-blockade atoms on the square ladder with a Z2×Z2 symmetry and at most one excited atom per square. We find D4, Z2, and Z3 density-wave phases separated by critical and first-order quantum phase transitions. A noninvertible remnant of U(1) symmetry applies to our full three-parameter space of couplings, and its presence results in a larger critical region as well as two distinct Z3-broken phases. Along an integrable line of couplings, the model exhibits a self-duality that is spontaneously broken along a first-order transition. Aided by numerical results, perturbation theory, and conformal field theory, we also find critical Ising2 and three-state Potts transitions, and provide good evidence that the latter can be chiral.

Abstract:

Strong zero modes (SZMs) are conserved operators localised at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyse analogous operators in one-dimensional classical stochastic systems. For concreteness, we focus on chains with single occupancy and nearest-neighbour transitions, in particular particle hopping and pair creation and annihilation. For integrable choices of parameters we find the exact form of the SZM operators. Being in general non-diagonal in the classical basis, the dynamical consequences of stochastic SZMs are very different from those of their quantum counterparts. We show that the presence of a stochastic SZM is manifested through a large class of exact transient relations between time-correlation functions, absent in the same system with periodic boundaries.