A class of quantum many-body states that can be efficiently simulated

We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive causal structure, the MERA allows for an exact evaluation of local expectation values. It is also the structure underlying entanglement renormalization, a coarse-graining scheme for quantum systems on a lattice that is focused on preserving entanglement.Comment: 4 pages, 5 figure

The role of initial conditions in the ageing of the long-range spherical model

The kinetics of the long-range spherical model evolving from various initial states is studied. In particular, the large-time auto-correlation and -response functions are obtained, for classes of long-range correlated initial states, and for magnetized initial states. The ageing exponents can depend on certain qualitative features of initial states. We explicitly find the conditions for the system to cross over from ageing classes that depend on initial conditions to those that do not.Comment: 15 pages; corrected some typo

Critical behavior of vector models with cubic symmetry

We report on some results concerning the effects of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. The analysis of the six-loop three-dimensional series provides an accurate description of the renormalization-group flow.Comment: 6 pages. Talk given at the V International Conference Renormalization Group 2002, Strba, Slovakia, March 10-16 200

Dynamic crossover in the global persistence at criticality

We investigate the global persistence properties of critical systems relaxing from an initial state with non-vanishing value of the order parameter (e.g., the magnetization in the Ising model). The persistence probability of the global order parameter displays two consecutive regimes in which it decays algebraically in time with two distinct universal exponents. The associated crossover is controlled by the initial value m_0 of the order parameter and the typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo simulations of the two-dimensional Ising model with Glauber dynamics display clearly this crossover. The measured exponent of the ultimate algebraic decay is in rather good agreement with our theoretical predictions for the Ising universality class.Comment: 5 pages, 2 figure

Entanglement entropy and D1-D5 geometries

http://dx.doi.org/10.1103/PhysRevD.90.066004Giusto, Stefano, and Rodolfo Russo. "Entanglement Entropy and D1-D5 geometries." Physical Review D 90.6 (2014): 066004

Entanglement properties of quantum spin chains

We investigate the entanglement properties of a finite size 1+1 dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure

Entropy in quantum chromodynamics

We review the role of zero-temperature entropy in several closely-related contexts in QCD. The first is entropy associated with disordered condensates, including $$. The second is vacuum entropy arising from QCD solitons such as center vortices, yielding confinement and chiral symmetry breaking. The third is entanglement entropy, which is entropy associated with a pure state, such as the QCD vacuum, when the state is partially unobserved and unknown. Typically, entanglement entropy of an unobserved three-volume scales not with the volume but with the area of its bounding surface. The fourth manifestation of entropy in QCD is the configurational entropy of light-particle world-lines and flux tubes; we argue that this entropy is critical for understanding how confinement produces chiral symmetry breakdown, as manifested by a dynamically-massive quark, a massless pion, and a $< \bar{q}q>$ condensate.Comment: 22 pages, 2 figures. Preprint version of invited review for Modern Physics Letters

Entanglement of quantum spin systems: a valence-bond approach

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; submitted for a special issue of Modern Physics Letters

Entanglement of excited states in critical spin chians

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the Conformal Field Theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done in reference (Alcaraz et. al., Phys. Rev. Lett. 106, 201601 (2011)), of which this work is a completion. An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c=1,1/2 universality classes. Oscillations of the Renyi entropy in excited states and descendant fields are also discussed.Comment: 23 pages, 13 figure

Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.Comment: 19 pages, 12 figure