Area law violation for the mutual information in a nonequilibrium steady state

We study the nonequilibrium steady state of an infinite chain of free fermions, resulting from an initial state where the two sides of the system are prepared at different temperatures. The mutual information is calculated between two adjacent segments of the chain and is found to scale logarithmically in the subsystem size. This provides the first example of the violation of the area law in a quantum many-body system outside a zero temperature regime. The prefactor of the logarithm is obtained analytically and, furthermore, the same prefactor is shown to govern the logarithmic increase of mutual information in time, before the system relaxes locally to the steady state.Comment: 7 pages, 5 figures, final version, references adde

On the partial transpose of fermionic Gaussian states

We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two Gaussian operators that are uniquely defined in terms of the covariance matrix of the original state. In case of a reflection symmetric geometry, this result can be used to efficiently calculate a lower bound for a well-known entanglement measure, the logarithmic negativity. Furthermore, exact expressions can be derived for traces involving integer powers of the partial transpose. The method can also be applied to the quantum Ising chain and the results show perfect agreement with the predictions of conformal field theory.Comment: 22 pages, 4 figures, published version, typos corrected, references adde

Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left- and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.Comment: 19 pages, 7 figures, small changes, references added, published versio

Quantum Transport Enhancement by Time-Reversal Symmetry Breaking

Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.Comment: 6+5 page

Central charges of aperiodic holographic tensor-network models

Central to the AdS/CFT correspondence is a precise relationship between the curvature of an anti–de Sitter (AdS) space-time and the central charge of the dual conformal field theory (CFT) on its boundary. Our work shows that such a relationship can also be established for tensor network models of AdS/CFT based on regular bulk geometries, leading to an analytical form of the maximal central charges exhibited by the boundary states. We identify a class of tensors based on Majorana dimer states that saturate these bounds in the large curvature limit, while also realizing perfect and block-perfect holographic quantum error correcting codes. Furthermore, the renormalization group description of the resulting model is shown to be analogous to the strong disorder renormalization group, thus giving an example of an exact quantum error correcting code that gives rise to a well-understood critical system. These systems exhibit a large range of fractional central charges, tunable by the choice of bulk tiling. Our approach thus provides a precise physical interpretation of tensor network models on regular hyperbolic geometries and establishes quantitative connections to a wide range of existing models