Search results for "statistical"
showing 10 items of 4960 documents
Universal scaling of a classical impurity in the quantum Ising chain
2017
We study finite size scaling for the magnetic observables of an impurity residing at the endpoint of an open quantum Ising chain in a transverse magnetic field, realized by locally rescaling the magnetic field by a factor $\mu \neq 1$. In the homogeneous chain limit at $\mu = 1$, we find the expected finite size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit, $\mu = 0$, we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. For this case, we provide both analytic approximate expressions for the magnetization and the susceptib…
Fine Grained Tensor Network Methods.
2020
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse-graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2d tensor networks - such as Corner Transfer Matrix Renormalization schemes - which are more involved on complex lattice structu…
Theory of ground state factorization in quantum cooperative systems.
2008
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground states in a large variety of, generally non-exactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
Quantifying nonclassicality: global impact of local unitary evolutions
2012
We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord (defined via the Hilbert- Schmidt norm), thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish that two-qubit Werner states are maximally quantum correlated, and are thus the ones that maximize t…
Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
2011
In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid (SOS) model with one reflecting end and domain wall boundary conditions. We show that these two problems are related through a gauge transformation (so-called vertex-face transformation) and can be solved using the same dynamical reflection algebras.
Entanglement in continuous-variable systems: recent advances and current perspectives
2007
We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures, and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillabil…
SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
2013
The analysis of the transfer matrices associated to the most general representations of the 8-vertex reflection algebra on spin-1/2 chains is here implemented by introducing a quantum separation of variables (SOV) method which generalizes to these integrable quantum models the method first introduced by Sklyanin. More in detail, for the representations reproducing in their homogeneous limits the open XYZ spin-1/2 quantum chains with the most general integrable boundary conditions, we explicitly construct representations of the 8-vertex reflection algebras for which the transfer matrix spectral problem is separated. Then, in these SOV representations we get the complete characterization of t…
Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
2014
We derive the low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain by summing up the asymptotically dominant terms of their expansion into form factors of the quantum transfer matrix. Our asymptotic formulae are numerically efficient and match well with known results for vanishing magnetic field and for short distances and magnetic fields below the saturation field.
Ostrogradsky's Hamilton formalism and quantum corrections
2010
By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are equivalent at the classical level, differences appear due to the quantum corrections.
Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime
2015
We consider the spectrum of correlation lengths of the spin-$\frac{1}{2}$ XXZ chain in the antiferromagnetic massive regime. These are given as ratios of eigenvalues of the quantum transfer matrix of the model. The eigenvalues are determined by integrals over certain auxiliary functions and by their zeros. The auxiliary functions satisfy nonlinear integral equations. We analyse these nonlinear integral equations in the low-temperature limit. In this limit we can determine the auxiliary functions and the expressions for the eigenvalues as functions of a finite number of parameters which satisfy finite sets of algebraic equations, the so-called higher-level Bethe Ansatz equations. The behavio…