scholarly journals Dissipative chaotic quantum maps: Expectation values, correlation functions and the invariant state

2000 ◽  
Vol 11 (1) ◽  
pp. 3
Author(s):  
D. Braun
Keyword(s):  
Correlation Functions ◽  
Invariant State ◽  
Expectation Values

scholarly journals Forward-walking Green's Function Monte Carlo Method for Correlation Functions

1999 ◽  
Vol 52 (4) ◽  
pp. 637 ◽  
Author(s):  
M. Samaras ◽  
C. J. Hamer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Exact Results ◽  
Expectation Values ◽  
Trial Wavefunction ◽  
Local Observables ◽  
Green's Function Monte Carlo

The forward-walking Green's Function Monte Carlo method is used to compute expectation values for the transverse Ising model in (1 + 1)D, and the results are compared with exact values. The magnetisation Mz and the correlation function p z (n) are computed. The algorithm reproduces the exact results, and convergence for the correlation functions seems almost as rapid as for local observables such as the magnetisation. The results are found to be sensitive to the trial wavefunction, however, especially at the critical point.

scholarly journals Fermion-current basis and correlation functions for the integrable spin-1 chain

2019 ◽  
Vol 34 (15) ◽  
pp. 1950075 ◽  
Author(s):  
C. Babenko ◽  
F. Smirnov
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Main Tool ◽  
Local Operator ◽  
Expectation Values ◽  
Local Operators ◽  
Integrable Spin ◽  
Fermion Current

We use the fermion-current basis in the space of local operators for the computation of the expectation values for the integrable spin chain of spins 1. Our main tool consists in expressing a given local operator in the fermion-current basis. For this, we use the same method as in the spin-1/2 case which is based on the arbitrariness of the Matsubara data.

scholarly journals Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Claudius Hubig ◽  
Annabelle Bohrdt ◽  
Michael Knap ◽  
Fabian Grusdt ◽  
Ignacio Cirac
Keyword(s):  
Real Time ◽  
Time Evolution ◽  
Correlation Functions ◽  
Spin Correlation ◽  
Quantum States ◽  
Time Dependent ◽  
Two Dimensional ◽  
Quantum Gas ◽  
Expectation Values ◽  
Equal Time

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-Jt−J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

Perturbative quantum field theory (QFT): Algebraic methods

2021 ◽  
pp. 125-159
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Correlation Functions ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Expectation Values ◽  
Generating Functional ◽  
Euclidean Time ◽  
Functional Measure ◽  
Scalar Quantum

This chapter discusses systematically the algebraic properties of perturbation theory in the example of a local, relativistic scalar quantum field theory (QFT). Although only scalar fields are considered, many results can be easily generalized to relativistic fermions. The Euclidean formulation of QFT, based on the density matrix at thermal equilibrium, is studied, mainly in the simpler zero-temperature limit, where all d coordinates, Euclidean time and space, can be treated symmetrically. The discussion is based on field integrals, which define a functional measure. The corresponding expectation values of product of fields called correlation functions are analytic continuations to imaginary (Euclidean) time of the vacuum expectation values of time-ordered products of field operators. They have also an interpretation as correlation functions in some models of classical statistical physics, in continuum formulations or, at equal time, of finite temperature QFT. The field integral, corresponding to an action to which a term linear in the field coupled to an external source J has been added, defines a generating functional Z(J) of field correlation functions. The functional W(J) = ln Z(J) is the generating functional of connected correlation functions, to which contribute only connected Feynman diagrams. In a local field theory connected correlation functions, as a consequence of locality, have cluster properties. The Legendre transform Γ(φ) [N1]of W(J) is the generating functional of vertex functions. To vertex functions contribute only one-line irreducible Feynman diagrams, also called one-particle irreducible (1PI).

THE TENSOR PRODUCT OF TENSOR OPERATORS OVER QUANTUM ALGEBRAS: SOME APPLICATIONS TO QUANTUM SPIN CHAINS

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3655-3669
Author(s):  
M. SCHEUNERT
Keyword(s):  
Tensor Product ◽  
Correlation Functions ◽  
Recent Article ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Algebras ◽  
Quantum Spin Chains ◽  
Expectation Values ◽  
Point Correlation ◽  
Tensor Operators

The present work is a direct sequel to a recent article by the author, in which he has analysed the tensor product of tensor operators over quantum algebras. Here the results obtained there are summarized and then specialized and extended to prepare possible applications to quantum spin chains. In particular, certain invariant two-point operators are introduced (whose expectation values yield the invariant two-point correlation functions) and their multiplicative properties are derived.

HOLOGRAPHY OF ROTATING DUAL GIANT WILSON LOOPS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2267-2268
Author(s):  
AKITSUGU MIWA ◽  
YOSKE SUMITOMO ◽  
KENTAROH YOSHIDA
Keyword(s):  
Correlation Functions ◽  
Wilson Loops ◽  
Wick Rotation ◽  
Expectation Values ◽  
Giant Graviton

We briefly review a tunneling picture of rotating D3-brane solutions. By applying the "double Wick rotation" to the Lorentzian solutions, we construct Euclidean solutions. The solutions are composed of dual giant gravitons and spike D3-brane solutions, and their classical actions reproduce expectation values of the k-th symmetric Wilson loops as well as correlation functions of dual giant graviton operators as expected.

scholarly journals Universal optimal quantum correlator

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560002 ◽  
Author(s):  
Francesco Buscemi ◽  
Michele Dall'Arno ◽  
Masanao Ozawa ◽  
Vlatko Vedral
Keyword(s):  
Correlation Functions ◽  
Quantum Correlation ◽  
Uncertainty Relations ◽  
Optical Technology ◽  
Expectation Values ◽  
Operational Strategy ◽  
Statistical Sense ◽  
Quantum Optical ◽  
Test Uncertainty

Recently, a novel operational strategy to access quantum correlation functions of the form Tr[AρB] was provided in [F. Buscemi, M. Dall'Arno, M. Ozawa and V. Vedral, arXiv:1312.4240]. Here we propose a realization scheme, that we call partial expectation values, implementing such strategy in terms of a unitary interaction with an ancillary system followed by the measurement of an observable on the ancilla. Our scheme is universal, being independent of ρ, A, and B, and it is optimal in a statistical sense. Our scheme is suitable for implementation with present quantum optical technology, and provides a new way to test uncertainty relations.

The isotope effect in electronic expectation values: an all-quantum study of C6H6 and C6D6

1998 ◽  
Vol 93 (5) ◽  
pp. 801-807
Author(s):  
JOACHIM SCHULTE ◽  
MICHAEL BOHM ◽  
RAFAEL RAMIREZ
Keyword(s):  
Isotope Effect ◽  
Expectation Values
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