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

Biotransenergetica: a transpersonal psychotherapy. A description of BTE practices from a therapist and client perspective

In Biotransenergetica (BTE), a transpersonal psychotherapy model developed in the 1980s by Lattuada, the uniqueness of self-experience is pivotal. In the therapeutic process inner experiences and felt sense are essential. These are contained in the concept of Transe. During the psychotherapy session the psychotherapist favors the creation of the Transe, a field, using mindfulness techniques; the psychotherapist and the patient “indwell” together in this experience at a multilevel dimension (physical, emotional, energetic, mental and spiritual) to allow the psychotherapeutic process to happen. The present study was carried out to describe the psychotherapist and the patient lived experience of the Transe. The aim was to describe how this process actually works to the therapeutic effect and could relate to self-development. The study, involving 7 psychotherapists and 13 patients, for a total of 121 clinical sessions, comes within the field of qualitative research, using a heuristic methodology, to provide a conceptual and structural description of BTE practice based on its clinical application. The heuristic method described by Moustakas, has been adapted for this particular clinical setting. As it is described by the patients and the psychotherapists, the Transe, allows integration of the five levels, physical, emotional, mental, energetic and spiritual, to occur. At the same time a process of dis-identification from the mental and emotional contents might happen. Patients reported that the therapeutic process during the Transe would lead to a subjective state of well being, improving awareness about inner mechanisms, both on the mental and the emotional levels. The patients reported also an improved ability of self listening and also listening to others’ emotion, leading to more satisfying relationships. The Transe as a non ordinary state of consciousness will be discussed comparing it with other mindfulness practices applied in different therapeutic contexts, both for psychological support and for medical problems. Moreover, I will consider the Transe from the evidences coming from neuroscience studies about the effect of mindfulness practices on brain structure and functions. Results will also be discussed from BTE theoretical framework, contrasting BTE structural boundaries with other psychotherapy approaches, mainly Bioenergetic and Gestalt. A discussion about the heuristic method used, as a valid tool to study non ordinary state of consciousness in transpersonal psychotherapy research, will be also provided

Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations

Many alternative formulations of Einstein's evolution have lately been examined, in an effort to discover one which yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations, we instead develop analytic tools to discover which formulations are particularly ill-behaved. Specifically, we examine the growth of approximate (geometric-optics) solutions, studied only in the future domain of dependence of the initial data slice (e.g. we study transients). By evaluating the amplification of transients a given formulation will produce, we may therefore eliminate from consideration the most pathological formulations (e.g. those with numerically-unacceptable amplification). This technique has the potential to provide surprisingly tight constraints on the set of formulations one can safely apply. To illustrate the application of these techniques to practical examples, we apply our technique to the 2-parameter family of evolution equations proposed by Kidder, Scheel, and Teukolsky, focusing in particular on flat space (in Rindler coordinates) and Schwarzchild (in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.

Entanglement renormalization

In the context of real-space renormalization group methods, we propose a novel scheme for quantum systems defined on a D-dimensional lattice. It is based on a coarse-graining transformation that attempts to reduce the amount of entanglement of a block of lattice sites before truncating its Hilbert space. Numerical simulations involving the ground state of a 1D system at criticality show that the resulting coarse-grained site requires a Hilbert space dimension that does not grow with successive rescaling transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each rellevant length scale makes an equivalent contribution to the entanglement of a block with the rest of the system.Comment: 4 pages, 4 figures, updated versio

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

Entanglement Entropy in Extended Quantum Systems

After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of freedom in different regions of space. Close to a quantum phase transition it has universal features which serve as a diagnostic of such phenomena. In the second part I consider the unitary time evolution of such systems following a `quantum quench' in which a parameter in the hamiltonian is suddenly changed, and argue that finite regions should effectively thermalise at late times, after interesting transient effects.Comment: 6 pages. Plenary talk delivered at Statphys 23, Genoa, July 200

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

Exact boundary conditions in numerical relativity using multiple grids: scalar field tests

Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy code with an exterior characteristic code connected across a time-like interface, is a promising technique for the generation and extraction of gravitational waves. While it provides a tool for the exact specification of boundary conditions for the Cauchy evolution, it also allows to follow gravitational radiation all the way to infinity, where it is unambiguously defined. We present a new fourth order accurate finite difference CCM scheme for a first order reduction of the wave equation around a Schwarzschild black hole in axisymmetry. The matching at the interface between the Cauchy and the characteristic regions is done by transfering appropriate characteristic/null variables. Numerical experiments indicate that the algorithm is fourth order convergent. As an application we reproduce the expected late-time tail decay for the scalar field.Comment: 14 pages, 5 figures. Included changes suggested by referee

Entanglement entropy of random quantum critical points in one dimension

For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N>>1 spins with the remainder is logarithmic in N with a prefactor fixed by the central charge of the associated conformal field theory. We show that for a class of strongly random quantum spin chains, the same logarithmic scaling holds for mean entanglement at criticality and defines a critical entropy equivalent to central charge in the pure case. This effective central charge is obtained for Heisenberg, XX, and quantum Ising chains using an analytic real-space renormalization group approach believed to be asymptotically exact. For these random chains, the effective universal central charge is characteristic of a universality class and is consistent with a c-theorem.Comment: 4 pages, 3 figure