Dynamics of the entanglement spectrum in spin chains

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.Comment: 16 pages, 8 figures, comments are welcome! Version published in JSTAT special issue on "Quantum Entanglement In Condensed Matter Physics

Andreev tunneling into a one-dimensional Josephson junction array

In this letter we consider Andreev tunneling between a normal metal and a one dimensional Josephson junction array with finite-range Coulomb energy. The $I-V$ characteristics strongly deviate from the classical linear Andreev current. We show that the non linear conductance possesses interesting scaling behavior when the chain undergoes a T=0 superconductor-insulator transition of Kosterlitz-Thouless-Berezinskii type. When the chain has quasi-long range order, the low lying excitation are gapless and the $I-V$ curves are power-law (the linear relation is recovered when charging energy can be disregarded). When the chain is in the insulating phase the Andreev current is blocked at a threshold which is proportional to the inverse correlation length in the chain (much lower than the Coulomb gap) and which vanishes at the transition point.Comment: 8 pages LATEX, 3 figures available upon reques

Coherent response of a low T_c Josephson junction to an ultrafast laser pulse

By irradiating with a single ultrafast laser pulse a superconducting electrode of a Josephson junction it is possible to drive the quasiparticles (qp's) distribution strongly out of equilibrium. The behavior of the Josephson device can, thus, be modified on a fast time scale, shorter than the qp's relaxation time. This could be very useful, in that it allows fast control of Josephson charge qubits and, in general, of all Josephson devices. If the energy released to the top layer contact $S1$ of the junction is of the order of $\sim \mu J$, the coherence is not degradated, because the perturbation is very fast. Within the framework of the quasiclassical Keldysh Green's function theory, we find that the order parameter of $S1$ decreases. We study the perturbed dynamics of the junction, when the current bias is close to the critical current, by integrating numerically its classical equation of motion. The optical ultrafast pulse can produce switchings of the junction from the Josephson state to the voltage state. The switches can be controlled by tuning the laser light intensity and the pulse duration of the Josephson junction.Comment: 17 pages, 5 figure

Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions

We introduce a theoretical scheme for the analog quantum simulation of long-range XYZ models using current trapped-ion technology. In order to achieve fully-tunable Heisenberg-type interactions, our proposal requires a state-dependent dipole force along a single vibrational axis, together with a combination of standard resonant and detuned carrier drivings. We discuss how this quantum simulator could explore the effect of long-range interactions on the phase diagram by combining an adiabatic protocol with the quasi-periodic drivings and test the validity of our scheme numerically. At the isotropic Heisenberg point, we show that the long-range Hamiltonian can be mapped onto a non-linear sigma model with a topological term that is responsible for its low-energy properties, and we benchmark our predictions with Matrix-Product-State numerical simulations.Comment: closer to published versio

Thermal transport driven by charge imbalance in graphene in magnetic field, close to the charge neutrality point at low temperature: Non local resistance

Graphene grown epitaxially on SiC, close to the charge neutrality point (CNP), in an orthogonal magnetic field shows an ambipolar behavior of the transverse resistance accompanied by a puzzling longitudinal magnetoresistance. When injecting a transverse current at one end of the Hall bar, a sizeable non local transverse magnetoresistance is measured at low temperature. While Zeeman spin effect seems not to be able to justify these phenomena, some dissipation involving edge states at the boundaries could explain the order of magnitude of the non local transverse magnetoresistance, but not the asymmetry when the orientation of the orthogonal magnetic field is reversed. As a possible contribution to the explanation of the measured non local magnetoresistance which is odd in the magnetic field, we derive a hydrodynamic approach to transport in this system, which involves particle and hole Dirac carriers, in the form of charge and energy currents. We find that thermal diffusion can take place on a large distance scale, thanks to long recombination times, provided a non insulating bulk of the Hall bar is assumed, as recent models seem to suggest in order to explain the appearance of the longitudinal resistance. In presence of the local source, some leakage of carriers from the edges generates an imbalance of carriers of opposite sign, which are separated in space by the magnetic field and diffuse along the Hall bar generating a non local transverse voltage.Comment: 25 pages, 12 figure

Boundary quantum critical phenomena with entanglement renormalization

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilson's RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.Comment: 8 pages, 12 figures, for a related work see arXiv:0912.289

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law

This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasi-exact results in systems with sizes well beyond the reach of exact diagonalisation techniques. We describe an algorithm to approximate the ground state of a local Hamiltonian on a L times L lattice with the topology of a torus. Accurate results are obtained for L={4,6,8}, whereas approximate results are obtained for larger lattices. As an application of the approach, we analyse the scaling of the ground state entanglement entropy at the quantum critical point of the model. We confirm the presence of a positive additive constant to the area law for half a torus. We also find a logarithmic additive correction to the entropic area law for a square block. The single copy entanglement for half a torus reveals similar corrections to the area law with a further term proportional to 1/L.Comment: Major rewrite, new version published in Phys. Rev. B with highly improved numerical results for the scaling of the entropies and several new sections. The manuscript has now 19 pages and 30 Figure

Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling

We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the spin chain and D is the dimension of the MPS matrices. In the first regime MPS can be used to perform finite size scaling (FSS). In the complementary regime the MPS simulations show instead the clear signature of finite entanglement scaling (FES). In the thermodynamic limit (or large N limit), only MPS in the FSS regime maintain a finite overlap with the exact ground state. This observation has implications on how to correctly perform FSS with MPS, as well as on the performance of recent MPS algorithms for systems with PBC. It also gives clear evidence that critical models can actually be simulated very well with MPS by using the right scaling relations; in the appendix, we give an alternative derivation of the result of Pollmann et al. [Phys. Rev. Lett. 102, 255701 (2009)] relating the bond dimension of the MPS to an effective correlation length.Comment: 18 pages, 13 figure