The Thermodynamics of Quantum Systems and Generalizations of Zamolodchikov's C-theorem

In this paper we examine the behavior in temperature of the free energy on quantum systems in an arbitrary number of dimensions. We define from the free energy a function $C$ of the coupling constants and the temperature, which in the regimes where quantum fluctuations dominate, is a monotonically increasing function of the temperature. We show that at very low temperatures the system is controlled by the zero-temperature infrared stable fixed point while at intermediate temperatures the behavior is that of the unstable fixed point. The $C$ function displays this crossover explicitly. This behavior is reminiscent of Zamolodchikov's $C$-theorem of field theories in 1+1 dimensions. Our results are obtained through a thermodynamic renormalization group approach. We find restrictions on the behavior of the entropy of the system for a $C$-theorem-type behavior to hold. We illustrate our ideas in the context of a free massive scalar field theory, the one-dimensional quantum Ising Model and the quantum Non-linear Sigma Model in two space dimensions. In regimes in which the classical fluctuations are important the monotonic behavior is absent.Comment: 25 pages, LateX, P-92-10-12

Entropic C-theorems in free and interacting two-dimensional field theories

The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative entropy analogous to Zamolodchikov's $c$ function. The one-dimensional quantum thermodynamic entropy gives rise to another monotonic dimensionless quantity. I illustrate these monotonicity theorems with examples ranging from free field theories to interacting models soluble with the thermodynamic Bethe ansatz. Both dimensionless entropies are explicitly shown to be monotonic in the examples that we analyze.Comment: 34 pages, 3 figures (8 EPS files), Latex2e file, continuation of hep-th/9710241; rigorous analysis of sufficient conditions for universality of the dimensionless relative entropy, more detailed discussion of the relation with Zamolodchikov's theorem, references added; to appear in Phys. Rev.

Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment

In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of quenched randomness, we introduce the idea of rare regions and discuss their importance. We then analyze in detail the different phenomena that can arise at magnetic quantum phase transitions in disordered metals, including quantum Griffiths singularities, smeared phase transitions, and cluster-glass formation. For each scenario, we discuss the resulting phase diagram and summarize the behavior of various observables. We then review several recent experiments that provide examples of these rare region phenomena. We conclude by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative Ising chain fixed, references added, v3: final version as publishe

Astrophysical structures from primordial quantum black holes

The characteristic sizes of astrophysical structures, up to the whole observed Universe, can be recovered, in principle, assuming that gravity is the overall interaction assembling systems starting from microscopic scales, whose order of magnitude is ruled by the Planck length and the related Compton wavelength. This result agrees with the absence of screening mechanisms for the gravitational interaction and could be connected to the presence of Yukawa corrections in the Newtonian potential which introduce typical interaction lengths. This result directly comes out from quantization of primordial black holes and then characteristic interaction lengths directly emerge from quantum field theory.Comment: 11 page

Interlayer hopping properties of electrons in layered metals

A formalism is proposed to study the electron tunneling between extended states, based on the spin-boson Hamiltonian previously used in two-level systems. It is applied to analyze the out--of--plane tunneling in layered metals considering different models. By studying the effects of in--plane interactions on the interlayer tunneling of electrons near the Fermi level, we establish the relation between departure from Fermi liquid behavior driven by electron correlations inside the layer and the out of plane coherence. Response functions, directly comparable with experimental data are obtained

Skymrion lattice melting in the quantum Hall system

The melting and magnetic disordering of the skyrmion lattice in the quantum Hall system at filling factor $\nu\approx 1$ are studied. A Berezinskii-Kosterlitz-Thouless renormalization group theory is employed to describe the coupled magnetic and translational degrees of freedom. The non-trivial magnetic properties of the skyrmion system stem from the in-plane components of the non-collinear magnetization in the vicinity of skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the `particles' are the topological defects of the XY model (vortices) and of the lattice (dislocations and disclinations). The latter frustrate the antiferromagnetic order and acquire fractional vorticity in order to minimize their energy. We find a number of melting/disordering scenarios for various lattice types. While these results do not depend on a particular model, we also consider a simple classical model for the skyrmion system. It results in a rich T=0 phase diagram. We propose that the triangular and square skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system.Comment: 15 pages with 5 figures. Minor revisions. Important reference to M. Rao, S. Sengupta, and R. Shankar, Phys. Rev. Lett. 79, 3998 (1997) adde

Observation of Events with an Energetic Forward Neutron in Deep Inelastic Scattering at HERA

In deep inelastic neutral current scattering of positrons and protons at the center of mass energy of 300 GeV, we observe, with the ZEUS detector, events with a high energy neutron produced at very small scattering angles with respect to the proton direction. The events constitute a fixed fraction of the deep inelastic, neutral current event sample independent of Bjorken x and Q2 in the range 3 · 10-4 \u3c xBJ \u3c 6 · 10-3 and 10 \u3c Q2 \u3c 100 GeV2