Critical dynamics of a double chain of spins with four spin interactions

O. F. de Alcantara Bonfim, A. Saguia, B. Boechat +1 more

M. Santos, W. Figueiredo

We study the dynamical critical behaviour of a double chain of spins where we take into account short-range four-spin interactions. This system is exactly soluble only in the thermodynamical equilibrium. We use the initial response rate of the order parameter to establish a lower bound to the dynamical critical exponent z. We show that, for the one- and two-spin-flip Glauber transition rates, the exponent z depends on the microscopic details of the Hamiltonian, that is, the dynamical critical exponent appears non-universal. This type of non-universal behaviour has already been seen in the one-dimensional Ising model with non-uniform exchange interactions.

Uwe Krey

Pierre Nataf, Alexandre Baksic, Cristiano Ciuti

The quantum ground-state and excitation properties of two independent chains of pseudospins (two-level systems) interacting with the same bosonic field are theoretically investigated. Each chain is coupled to a different quadrature of the field, leading to two independent symmetry breakings for increasing values of the two collective spin-boson interaction constants ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. A phase diagram is provided in the plane (${\ensuremath{\Omega}}_{C}$,${\ensuremath{\Omega}}_{I}$), with four phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via geometric Berry effects. In particular, when ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$ are both larger than two critical values, the fundamental subspace has a fourfold degeneracy. Finite-size properties are shown for both critical and ultrastrong values of ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. Possible implementations in superconducting quantum circuits are detailed.

Uwe Krey

Uwe Krey