Order by disorder in a four flavor Mott-insulator on the fcc lattice

The classical ground states of the SU(4) Heisenberg model on the face centered cubic lattice constitute a highly degenerate manifold. We explicitly construct all the classical ground states of the model. To describe quantum fluctuations above these classical states, we apply linear flavor-wave theory. At zero temperature, the bosonic flavor waves select the simplest of these SU(4) symmetry breaking states, the four-sublattice ordered state defined by the cubic unit cell of the fcc lattice. Due to geometrical constraints, flavor waves interact along specific planes only, thus rendering the system effectively two dimensional and forbidding ordering at finite temperatures. We argue that longer range interactions generated by quantum fluctuations can shift the transition to finite temperatures

Generalized Kac's Lemma for Recurrence Time in Iterated Open Quantum Systems

We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special case of unital channels, including unitary channels. We prove that for a more general class of quantum channels the expected return time can be given as the inverse of the weight of the initial state in the steady state. This statement is a generalization of the Kac lemma for classical Markov chains

Quantized recurrence time in iterated open quantum dynamics

The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a general quantum channel, in each timestep followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the relevant Hilbert space (the part of the Hilbert space explored by the system), then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work connects the previously known quantization of the expected return time for bistochastic Markov chains and for unitary quantum walks, and shows that these are special cases of a more general statement. The expected return time is thus a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state

Spin liquid phases of alkaline earth atoms at finite temperature

We study spin liquid phases of spin-5/2 alkaline earth atoms on a honeycomb lattice at finite temperatures. Our analysis is based on a Gutzwiller projection variational approach recast to a path-integral formalism. In the framework of a saddle-point approximation we determine spin liquid phases with lowest free energy and study their temperature dependence. We identify a critical temperature, where all the spin liquid phases melt and the system goes to the paramagnetic phase. We also study the stability of the saddle-point solutions and show that a time-reversal symmetry breaking state, a so called chiral spin liquid phase is realized even at finite temperatures. We also determine the spin structure factor, which, in principle, is an experimentally measurable quantity and is the basic tool to map the spectrum of elementary excitations of the system