Critical exponents of steady-state phase transitions in fermionic lattice models

Abstract

We discuss reservoir-induced phase transitions of lattice fermions in the nonequilibrium steady state of an open system with local reservoirs. These systems may become critical in the sense of a diverging correlation length on changing the reservoir coupling. We here show that the transition to a critical state is associated with a vanishing gap in the damping spectrum. It is shown that, although in linear systems there can be a transition to a critical state, there is no reservoir-induced quantum phase transition between distinct phases with a nonvanishing damping gap. We derive the static and dynamical critical exponents corresponding to the transition to a critical state and show that their possible values, defining universality classes of reservoir-induced phase transitions, are determined by the coupling range of the independent local reservoirs. If a reservoir couples to N neighboring lattice sites, the critical exponent can assume all fractions from 1 to 1/(N − 1).

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

“…(22)(23)(24)(25)(26), it is easy to show that C aa † (ω) = A aa † (ω) and the frequency integral over the Keldysh Green's function is unity yielding â †â = 0. As expected, the steady state corresponds to the cavity vacuum.…”

“…We expect the Keldysh approach to be directly applicable to other dissipative models such as the recently discussed central spin model [22] or fermionic lattice models [23][24][25][26]. We believe the Keldysh calculations are not more involved, and sometimes simpler, than those of the usual quantum optics frameworks [27,28].…”

Relaxation times of dissipative many-body quantum systems

“…An example we are going to present has a nonzero Hamiltonian and nonzero dissipation. It is a XX chain with an incoherent "hopping" given by Lindblad operator The gap g in the 1−particle sector of the XX chain with an incoherent one-way hopping (16). The kink at L = 10 is because the eigenvalue responsible for g goes from being complex to real.…”

“…Rapid mixing also implies the stability of steady state to local perturbations [10][11][12]. If the gap on the other hand closes in the thermodynamic limit this can lead to a nonequilibrium phase transition [13][14][15][16][17][18] and can result in a non-exponential relaxation [19,20] towards a steady state. Understanding how the gap scales with the system size is therefore of fundamental importance.…”

Spatial correlations of one-dimensional driven-dissipative systems of Rydberg atoms

“…The question is then what happens in quantum driven-dissipative systems. Although one might expect dissipation to lead to trivial states, it has been shown that ordered phases can exist for systems with quasi-local dissipative mechanisms [3][4][5][6], in the presence of 1/f noise [7], and for a quadratic Hamiltonian with local dissipation [8]. These works show that it is possible for nontrivial states to exist even when dissipation is present, although they either assume a dissipation mechanism that creates coherence between neighbors or a noise process of a particular form.…”