Temperature and correlation functions in an isolated spin system

U. Brandt, P. Solleder

Tanmoy Chakraborty, Harkirat Singh, Sourabh Singh +2 more

A quantitative estimation of quantum discord is performed for a Heisenberg spin 1/2 dimer compound (NH4CuPO4, H2O) by means of experimental magnetic and thermal measurements. Magnetic susceptibility and specific heat data were collected for NH4CuPO4, H2O and analyzed within the framework of the Heisenberg isolated dimer model. Internal energy as a function of temperature is obtained by integrating the specific heat versus temperature data. Subsequently, quantum discord, total correlations and spin-spin correlation function are quantified from susceptibility and internal energy and plotted as a function of temperature. Violation of Bell's inequality is also tested for NH4CuPO4, H2O via both experimental susceptibility and specific heat data signifying the presence of entanglement.

Philip C. Clapp

Tarek A. Elsayed, Boris V. Fine

We obtain a modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many-body quantum systems. We use the insights gained from this relation to show that high-temperature time correlation functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians, using instead the direct integration of the Schrödinger equation for randomly sampled pure states. This method is also applicable to quantum quenches and other situations describable by time-dependent many-body Hamiltonians. The method implies exponential reduction of the computer memory requirement in comparison with the complete diagonalization. We illustrate the method by numerically computing infinite-temperature correlation functions for translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we also test the spin diffusion hypothesis and find it in a satisfactory agreement with the numerical results. Both the derivation of the modified regression relation and the justification of the computational method are based on the notion of quantum typicality.

Smita Ota, Snehadri Bihari Ota

We have investigated the first-order transition in the classical two-dimensional (2D) extended XY-spin model using Monte Carlo simulations. The simulations have been carried out on a system with 100 spins in the microcanonical ensemble, which represents a finite-isolated system. The energy as a function of temperature is found to exhibit a 'S'-shape at the first-order transition. We conclude that the observed phenomena at the first-order transition should be interpreted as the equilibrium response of a finite-isolated system.

C.J.M. Schoutens, Jean-Sébastien Caux, Rob Hagemans