Correlations in quantum many-body systems and quantum information theoretic measures

Javier Faba, Vicente Martín, Luis Miguel Robledo

Typically in many-body systems the correlation energy, which is defined as the difference between the exact ground-state energy and the mean-field solution, has been a measure of the system's total correlations. However, under the quantum information context, it is possible to define some quantities in terms of the system's constituents that measure the classical and quantum correlations, such as the entanglement entropy, mutual information, quantum discord, one-body entropy, etc. In this work we apply concepts of quantum information in fermionic systems in order to study traditional correlation measures (the relative correlation energy). Concretely, we analyze the two- and three-level Lipkin models, which are exactly solvable (but nontrivial) models commonly used in the context of the many-body problem. We conclude that the correlation energy is not a good estimator of the total correlation of the system, and information theoretic measures should be considered.

Xhek Turkeshi

P. Kiran, Harsha Miriam Reji, Hemant Shreepad Hegde +1 more

The shareability of quantum correlations among the constituent parties of a multiparty quantum system is restricted by the quantum information theoretic concept called monogamy. Depending on the multiparty quantum systems, different measures of quantum correlations show disparate signatures for monogamy. We characterize the shareability of quantum correlations, from both entanglement-separability and information-theoretic kinds, in a multiparty quantum spin system containing two- and three-body interactions with respect to its system parameters and external applied magnetic field. Monogamy score in this system exhibits both monogamous and nonmonogamous traits depending on the quantum correlation measure, strengths of system parameters, and external magnetic field. The percentage of nonmonogamous states when the information-theoretic quantum correlations are considered is higher than that of the entanglement-separability kind in allowed ranges of these variables. The integral powers of the quantum correlation measures for which the nonmonogamous states become monogamous are identified.

Daniel Manzano

Paola Ruggiero

Richard M. Martin, Lucia Reining, David M. Ceperley

Preparation, I have often said, is rightly two-thirds of any venture. Amelia Earhart Summary Correlation functions provide a direct way to characterize and analyze many-body systems, both theoretically and experimentally. In this chapter we review the properties of one- and two-body correlation functions in quantum systems, with emphasis on several key quantities: static density correlations that determine the energy and thermodynamic potentials, dynamic correlation functions such as response functions that describe excitations of the system, and Green's functions that are basic tools in the theory of interacting many-body systems. Correlation functions are central quantities in the description of interacting many-body systems, both in the theoretical formulation and in the analysis of experiments. In contrast to single numbers like the total energy, correlation functions reveal far more information about the electrons, how they arrange themselves, and the spectra of their excitations. In contrast to the many-body wavefunctions that contain all the information on the system, correlation functions extract the information most directly relevant to experimentally measurable properties. Dynamic current–current correlation functions are sufficient to determine the electrical and optical properties: one-body Green's functions describe the spectra of excitations when one electron is added to or removed from the system, static and dynamic correlations are measured using scattering techniques, and so forth. In this chapter we present the basic definitions and properties of correlation functions and Green's functions that are the basis for much of the developments in the following chapters. In general, a correlation function quantifies the correlation between two or more quantities at different points in space r , time t , or spin σ . Very often the correlation function can be specified as a function of the Fourier-transformed variables, momentum (wavevector) k , and frequency ω . It is useful to distinguish between a dynamic correlation function which describes the correlation between events at different times and a static or equal-time correlation function, by which we mean that of a property measured or computed with “snapshots” of the system. Also, the different correlation functions can be classified by the number of particles and/or fields involved.