Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench

At thermal equilibrium, the concept of effective central charge for massive deformations of two-dimensional conformal field theories (CFT) is well understood, and can be defined by comparing the partition function of the massive model to that of a CFT. This temperature-dependent effective charge interpolates monotonically between the central charge values corresponding to the IR and UV fixed points at low and high temperatures, respectively. We propose a non-equilibrium, time-dependent generalization of the effective central charge for integrable models after a quantum quench, $c_{\rm eff}(t)$, obtained by comparing the return amplitude to that of a CFT quench. We study this proposal for a large mass quench of a free boson, where the charge is seen to interpolate between $c_{\rm eff}=0$ at $t=0$, and $c_{\rm eff}\sim 1$ at $t\to\infty$, as is expected. We use our effective charge to define an "Ising to Tricritical Ising" quench protocol, where the charge evolves from $c_{\rm eff}=1/2$ at $t=0$, to $c_{\rm eff}=7/10$ at $t\to\infty$, the corresponding values of the first two unitary minimal CFT models. We then argue that the inverse "Tricritical Ising to Ising" quench is impossible with our methods. These conclusions can be generalized for quenches between any two adjacent unitary minimal CFT models. We finally study a large mass quench into the "staircase model" (sinh-Gordon with a particular complex coupling). At short times after the quench, the effective central charge increases in a discrete "staircase" structure, where the values of the charge at the steps can be computed in terms of the central charges of unitary minimal CFT models. When the initial state is a pure state, one always finds that $c_{\rm eff}(t\to\infty)\geq c_{\rm eff}(t=0)$, though $c_{\rm eff}(t)$, generally oscillates at finite times. We explore how this constraint may be related to RG flow irreversibility.Comment: Some discussion modified. Title slightly modified. References added. Scipost submissio

Confinement-Higgs Phase Crossover as a Lattice Artifact in 1+1 Dimensions

We examine the phase structure of massive Yang-Mills theory in 1+1 dimensions. This theory is equivalent to a gauged principal chiral sigma model. It has been previously shown that the gauged theory has only a confined phase, and no Higgs phase in the continuum, and at infinite volume. There are no massive gluons, but only hadron-like bound states of sigma-model particles. The reason is that the gluon mass diverges, being proportional to the two-point correlation function of the renormalized field of the sigma model at $x=0$. We use exact large-$N$ results to show that after introducing a lattice regularization and typical values of the coupling constants used in Monte Carlo simulations, the gluon mass becomes finite, and even sometimes small. A smooth crossover into a Higgs phase can then appear. For small volumes and large $N$, we find an analytic expression for the gluon mass, which depends on the coupling constants and the volume. We argue that this Higgs phase is qualitatively similar to the one observed in lattice computations at $N=2$.Comment: Version accepted for publication in JHEP. Improved discussion of results, references adde

The Integrable Bootstrap Program at Large N and its Applications in Gauge Theory

We present results for the large-$N$ limit of the (1+1)-dimensional principal chiral sigma model. This is an asymptotically-free $N\times N$ matrix-valued field with massive excitations. All the form factors and the exact correlation functions of the Noether-current operator and the energy-momentum tensor are found, from Smirnov's form-factor axioms. We consider (2+1)-dimensional $SU(\infty)$ Yang-Mills theory as an array of principal chiral models with a current-current interaction. We discuss how to use our new form factors to calculate physical quantities in this gauge theory.Comment: Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany. Some references added in the updated versio

Using APL to build science tutors for the high school level

This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in APL Quote Quad, http://dx.doi.org/10.1145/327600.327644This paper describes the procedure used to build several courses on the sciences for the high school level. An APL2 program has been written that accepts problem models, including explanation models, and uses them to generate many different problems. Each course is provided with about one hundred problem models, from which the student is invited to solve many thousands of different actual problems. The unique features of APL2 have made it very simple to develop the program that supports the courses, which exists in both DOS and Windows versions

Hidden symmetries, instabilities, and current suppression in Brownian ratchets

The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied, symmetry-related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by finely tuning the driving parameters. Here we demonstrate, by studying a prototypical Brownian ratchet system, the existence of {\it hidden} symmetries, which escape the identification by the standard symmetry analysis, and require different theoretical tools for their revelation. Furthermore, we show that system instabilities may lead to spontaneous symmetry breaking with unexpected generation of directed transport.Comment: To appear in Phys. Rev. Let

Asymptotic theory of quasiperiodically driven quantum systems

The theoretical treatment of quasi-periodically driven quantum systems is complicated by the inapplicability of the Floquet theorem, which requires strict periodicity. In this work we consider a quantum system driven by a bi-harmonic driving and examine its asymptotic long-time limit, the limit in which features distinguishing systems with periodic and quasi-periodic driving occur. Also, in the classical case this limit is known to exhibit universal scaling, independent of the system details, with the system's reponse under quasi-periodic driving being described in terms of nearby periodically driven system results. We introduce a theoretical framework appropriate for the treatment of the quasi-periodically driven quantum system in the long-time limit, and derive an expression, based on Floquet states for a periodically driven system approximating the different steps of the time evolution, for the asymptotic scaling of relevant quantities for the system at hand. These expressions are tested numerically, finding excellent agreement for the finite-time average velocity in a prototypical quantum ratchet consisting of a space-symmetric potential and a time-asymmetric oscillating force