We consider two quantum Ising chains initially prepared at thermal equilibrium but with different temperatures and coupled at a given time through one of their end points. In the long-time limit the system reaches a nonequilibrium steady state. We discuss properties of this nonequilibrium steady state and characterize the convergence to the steady regime. We compute the mean energy flux through the chain and show that the heat transport is ballistic. We derive also the large-deviation function for the quantum and thermal fluctuations of this energy transfer.
We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a
T=0 quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum
S=1∕2 Ising chain is exactly solvable and extensively studied, results for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ of such model are lacking, and we supply them here. They are obtained numerically, via the transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to the thermal ones.
We consider bosonic transport through one-dimensional spin systems. Transport is induced by coupling the spin systems to bosonic reservoirs kept at different temperatures. In the limit of weak-coupling between spins and bosons we apply the quantum-optical master equation to calculate the energy transmitted from source to drain reservoirs. At large thermal bias, we find that the current for longitudinal transport becomes independent of the chain length and is also not drastically affected by the presence of disorder. In contrast, at small temperatures, the current scales inversely with the chain length and is further suppressed in the presence of disorder. We also find that the critical behaviour of the ground state is mapped to critical behaviour of the current--even in configurations with infinite thermal bias.
Energy transport in quantum many-body systems with well defined quasiparticles has recently attracted interest across different fields, including out of equilibrium conformal field theories, one-dimensional quantum lattice models, and holographic matter. Here we study energy transport between two interacting quantum baths without quasiparticles made by two Sachdev-Ye-Kitaev (SYK) models at temperatures ${T}_{L}\ensuremath{\ne}{T}_{R}$ and connected by a Fermi-liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling
V. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature ${T}^{*}(V)\ensuremath{\sim}{V}^{4}$ is parametrically enhanced with respect to the linear-
T behavior expected in systems with quasiparticles. Interestingly, below
T∗(V) the linear thermal conductance behavior is restored, yet transport is not due to quasiparticles. Rather the system gets strongly renormalized by the bath and becomes non-Fermi liquid and maximally chaotic. Finally, we discuss the full nonequilibrium energy current and show that its form is compatible with the structure $\mathcal{J}=\mathrm{\ensuremath{\Phi}}({T}_{L})\ensuremath{-}\mathrm{\ensuremath{\Phi}}({T}_{R})$, with $\mathrm{\ensuremath{\Phi}}(T)\ensuremath{\sim}{T}^{\ensuremath{\gamma}}$ and power law crossing over from $\ensuremath{\gamma}=3/2$ to $\ensuremath{\gamma}=2$ below
T∗.
Energy transport in quantum many-body systems with well defined quasiparticles has recently attracted interest across different fields, including out of equilibrium conformal field theories, one dimensional quantum lattice models and holographic matter. Here we study energy transport between \emph{strange quantum baths} without quasiparticles, made by two Sachdev-Ye-Kitaev (SYK) models at temperatures
TL=TR and connected by a Fermi-Liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling
V. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature
T∗(V)∼V4 is parametrically enhanced with respect to the linear-
T behavior expected in systems with quasiparticles. Interestingly, below
T∗(V) the linear thermal conductance behavior is restored, yet transport is not due to quasiparticles. Rather the system gets strongly renormalized by the strange bath and becomes Non-Fermi-Liquid and maximally chaotic. Finally, we discuss the full nonequilibrium energy current and show that its form is compatible with the structure
J=Φ(TL)−Φ(TR), with
Φ(T)∼Tγ and power law crossing over from
γ=3/2 to
γ=2 below
T∗.
Lindbladian formalism, as tuned to dissipative and open systems, has been all-pervasive to interpret non-equilibrium steady states of quantum many-body systems. We study the fate of free fermionic and superconducting phases in a dissipative one-dimensional Kitaev model-where the bath acts both as a source and a sink of fermionic particles with different coupling rates. As a function of these two couplings, we investigate the steady state, its entanglement content, and its approach from varying initial states. Interestingly, we find that the steady state phase diagram retains decipherable signatures of ground state critical physics. We also show that early-time fidelity is a useful marker to find a subclass of phase transitions in such situations. Moreover, we show that the survival of critical signatures at late-times, strongly depend on the thermal nature of the steady state. This connection hints at a correspondence between quantum observables and classical magnetism in the steady state of such systems. Our work uncovers interesting connections between dissipative quantum many-body systems, thermalization of a classical spin and many-body quantum critical phenomena.