We propose the use of entanglement renormalization techniques to study boundary critical phenomena on a lattice system. The multiscale entanglement renormalization ansatz ͑MERA͒, 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 MERA, an accurate approximation to the ground state of a semi-infinite critical chain with an open boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. As in Wilson's renormalization-group formulation of the Kondo problem, our construction produces, as a side result, an effective chain displaying explicit separation of energy scales. We present benchmark results for the quantum Ising and quantum XX models with free and fixed boundary conditions.
We show that gauge transformations can be simulated on systems of ultracold atoms. We discuss observables that are invariant under these gauge transformations and compute them using a tensor network ansatz that escapes the phase problem. We determine that the Mott-insulator-to-superfluid critical point is monotonically shifted as the induced magnetic flux increases. This result is stable against the inclusion of a small amount of entanglement in the variational ansatz.
We construct a quantum algorithm that creates the Laughlin state for an arbitrary number of particles $n$ in the case of filling fraction one. This quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates and its depth scales as $2n-3$. We further prove the optimality of the circuit using permutation theory arguments and we compute exactly how entanglement develops along the action of each gate. Finally, we discuss its experimental feasibility decomposing the qudits and the gates in terms of qubits and two qubit-gates as well as the generalization to arbitrary filling fraction.Comment: 4 pages, 5 figure
We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce the problem of approximating for the ground state of a spin chain to an analytical minimization. This allows to show that results of standard simulations, e.g. density matrix renormalization group and infinite time evolving block decimation, do correspond to the result obtained by this minimization strategy and, thus, both methods deliver optimal MPS with the same energy but, otherwise, different properties. We also find that translational and rotational symmetries cannot be maintained simultaneously by the MPS ansatz of minimum energy and present explicit constructions for each case. Furthermore, we analyze symmetry restoration and quantify it to uncover new scaling relations. The method we propose can be extended to any translational invariant Hamiltonian.
La teoria quàntica representa una de les fites més importants de la història de la ciència del segle XX, tant pel que fa a les seues implicacions teòriques i tecnològiques com pel que fa als problemes conceptuals que planteja la seua interpretació. Aquest article constitueix una revisió de les propostes interpretatives del formalisme quàntic d'ençà que la teoria es va axiomatitzar a les acaballes de la dècada dels anys 20 del segle passat. Aquestes propostes incideixen en problemes filosòfics com la no-localitat, l'indeterminisme, la probabilitat o el realisme científic, per a cadascun dels quals s'ofereix una resposta temptativa a partir de la interpretació del formalisme corresponent.
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