Uma Divakaran

Bio: Uma Divakaran is an academic researcher from Indian Institutes of Technology. The author has contributed to research in topics: Quantum phase transition & Quantum critical point. The author has an hindex of 15, co-authored 54 publications receiving 883 citations. Previous affiliations of Uma Divakaran include Saarland University & Indian Institute of Technology Kanpur.

Fidelity susceptibility and Loschmidt echo for generic paths in a three spin interacting transverse Ising model

Abstract: We study the effect of presence of different types of critical points such as ordinary critical point, multicritical point and quasicritical point along different paths on the Fidelity susceptibility and Loschmidt echo of a three spin interacting transverse Ising chain using a method which does not involve the language of tensors. We find that the scaling of fidelity susceptibility and Loschmidt echo with the system size at these special critical points of the model studied, is in agreement with the known results, thus supporting our method.

Sudden quenches in a quasiperiodic Ising model

Abstract: We present here the nonequilibrium dynamics of the recently studied quasiperiodic Ising model. The zero temperature phase diagram of this model mainly consists of three phases, where each of these three phases can have extended, localized, or critically delocalized low-energy excited states. We explore the nature of excitations in these different phases by studying the evolution of entanglement entropy after performing sudden quenches of different strengths to different phases. Our results on nonequilibrium dynamics of entanglement entropy are concurrent with the nature of excitations predicted in Chandran and Laumann [Phys. Rev. X 7, 031061 (2017)].

Long-range connections, quantum magnets and dilute contact processes

Abstract: In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold p c of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at p c . The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Abstract: 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

Quantum Phase Transitions

Abstract: We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

A quantum Newton's cradle

Abstract: It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.