http://experimentationlab.berkeley.edu/sites/default/files/AFMImages/butt_AFM.pdf

Force measurements with the atomic force microscope: Technique, interpretation and applications

Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

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Entanglement in many-body systems

This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such ``area laws'' for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.

Colloquium: Area laws for the entanglement entropy

1: Magnetic Particles: Preparation, Properties and Applications: M. Ozaki. 2: Maghemite (gamma-Fe2O3): A Versatile Magnetic Colloidal Material C.J. Serna, M.P. Morales. 3: Dynamics of Adsorption and Oxidation of Organic Molecules on Illuminated Titanium Dioxide Particles Immersed in Water M.A. Blesa, R.J. Candal, S.A. Bilmes. 4: Colloidal Aggregation in Two-Dimensions A. Moncho-Jorda, F. Martinez-Lopez, M.A. Cabrerizo-Vilchez, R. Hidalgo Alvarez, M. Quesada-PMerez. 5: Kinetics of Particle and Protein Adsorption Z. Adamczyk.

Surface and Colloid Science

We compute exactly the spin-spin correlation functions 〈σ0,0σM,N〉 for the two-dimensional Ising model on a square lattice in zero magnetic field for T>Tc and T<Tc. We then analyze the correlation functions in the scaling limit T→Tc,M2+N2→∞ such that (T−Tc) is fixed. In this scaling limit 〈σ0,0σM,N〉=R−14F±(t)+R−54F1±(t)+o(R−54), where t is the scaling variable Rξ and F±(t) and F1±(t) are the scaling functions (ξ is the correlation length). We derive exact expressions for these scaling functions, in terms of a Painleve function of the third kind and analyze both the small- and large-t behavior. A table of values for F±(t) (good to ten significant digits) is also given. As an application we computer the coefficients C0± and C1± in the expansion kBTχ(T)=C0±|1−TcT|−74+C1±|1−TcT|−34+O(1) of the zero-field susceptibility χ(T) as T→Tc±.

Spin spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region

The spin-correlation functions of the one-dimensional $XY$ model are studied in the presence of a constant magnetic field. We find that the asymptotic behavior of these correlation functions depends strongly on the various parameters of the Hamiltonian.

Statistical Mechanics of the X Y Model. II. Spin-Correlation Functions

The Liouville equation for the $\mathrm{XY}$ model is solved exactly, and the magnetization is computed explicitly. Nonergodic behavior of the magnetization is found for a general class of time-dependent magnetic fields.

Statistical Mechanics of the XY Model. I

Zero-Field Susceptibility of the Two-Dimensional Ising Model near T c .

We compute the correlation functions $〈{S}_{0}^{x}(t){S}_{R}^{x}(0)〉$ and $〈{S}_{0}^{y}(t){S}_{R}^{y}(0)〉$ at $T=0$ for the one-dimensional $\mathrm{XY}$ model in the presence of a magnetic field.

Eytan Barouch

Papers

Spin spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region

Statistical Mechanics of the X Y Model. II. Spin-Correlation Functions

Statistical Mechanics of the XY Model. I

Zero-Field Susceptibility of the Two-Dimensional Ising Model near T c .

Statistical Mechanics of the XY Model. IV. Time-Dependent Spin-Correlation Functions