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.

Quenching through Dirac and semi-Dirac points in optical lattices: Kibble-Zurek scaling for anisotropic quantum critical systems

Abstract: We propose that Kibble-Zurek scaling can be studied in optical lattices by creating geometries that support Dirac, semi-Dirac and quadratic band crossings. On a honeycomb lattice with fermions, as a staggered on-site potential is varied through zero, the system crosses the gapless Dirac points, and we show that the density of defects created scales as 1/τ, where τ is the inverse rate of change of the potential, in agreement with the Kibble-Zurek relation. We generalize the result for a passage through a semi-Dirac point in d dimensions, in which spectrum is linear in m parallel directions and quadratic in the rest of the perpendicular (d-m) directions. We find that the defect density is given by 1/τmν||z||+(d-m)ν⊥z⊥ where ν||, z|| and ν⊥, z⊥ are the dynamical exponents and the correlation length exponents along the parallel and perpendicular directions, respectively. The scaling relations are also generalized to the case of non-linear quenching.

Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model

Abstract: We study the dynamics of a tilted one-dimensional Bose-Hubbard model for two distinct protocols using numerical diagonalization for a finite sized system ($N\ensuremath{\le}18$). The first protocol involves periodic variation of the effective electric field $E$ seen by the bosons which takes the system twice (per drive cycle) through the intermediate quantum critical point. We show that such a drive leads to nonmonotonic variation of the excitation density $D$ and the wave function overlap $F$ at the end of a drive cycle as a function of the drive frequency ${\ensuremath{\omega}}_{1}$, relate this effect to a generalized version of St\"uckelberg interference phenomenon, and identify special frequencies for which $D$ and $1\ensuremath{-}F$ approach zero leading to near-perfect dynamic freezing phenomenon. The second protocol involves a simultaneous linear ramp of both the electric field $E$ (with a rate ${\ensuremath{\omega}}_{1}$) and the boson hopping parameter $J$ (with a rate ${\ensuremath{\omega}}_{2}$) starting from the ground state for a low effective electric field up to the quantum critical point. We find that both $D$ and the residual energy $Q$ decrease with increasing ${\ensuremath{\omega}}_{2}$; our results thus demonstrate a method of achieving near-adiabatic protocol in an experimentally realizable quantum critical system. We suggest experiments to test our theory.

Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling

Abstract: We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes. Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths. We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism, i.e., it exhibits a universal power-law scaling with the driving speed through the critical points. We also optimize the finite-time thermodynamics as a function of the driving speed. The maximum power and the corresponding efficiency take a universal form, and are reached for an optimal speed that is governed by the critical exponents. We exemplify our results by considering a transverse-field Ising spin chain as the working medium. For this model, we also show how the efficiency and power vary as the engine becomes critical.

Reverse quenching in a one-dimensional Kitaev model

Abstract: We present an exact result for the nonadiabatic transition probability and hence the defect density in the final state of a one-dimensional Kitaev model following a slow quench of the parameter ${J}_{\ensuremath{-}}$, which estimates the anisotropy between the interactions, as ${J}_{\ensuremath{-}}(t)\ensuremath{\sim}\ensuremath{-}|t/\ensuremath{\tau}|$. Here, time $t$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$ and $\ensuremath{\tau}$ defines the rate of change in the Hamiltonian. In other words, the spin chain initially prepared in its ground state is driven by changing ${J}_{\ensuremath{-}}$ linearly in time up to the quantum critical point, which in the model considered here occurs at $t=0$, reversed and then gradually decreased to its initial value at the same rate. We have thoroughly compared the reverse quenching with its counterpart forward quenching, i.e., ${J}_{\ensuremath{-}}\ensuremath{\sim}t/\ensuremath{\tau}$. Our exact calculation shows that the probability of excitations is zero for the wave vector at which the instantaneous energy gap is zero at the critical point ${J}_{\ensuremath{-}}=0$ as opposed to the maximum value of unity in the forward quenching. It is also shown that the defect density in the final state following a reverse quenching, we propose here, is nearly half of the defects generated in the forward quenching. We argue that the defects produced when the system reaches the quantum critical point get redistributed in the wave-vector space at the final time in case of reverse quenching whereas it keeps on increasing until the final time in the forward quenching. We study the entropy density and also the time evolution of the diagonal entropy density in the case of the reverse quenching and compare it with the forward case.

The effect of the three-spin interaction and the next nearest neighbor interaction on the quenching dynamics of a transverse Ising model

Abstract: We study the zero-temperature quenching dynamics of various extensions of the transverse Ising model (TIM) for when the transverse field is linearly quenched from to (or zero) at a finite and uniform rate. The rate of quenching is dictated by a characteristic scale given by τ. The density of kinks produced in these extended models while crossing the quantum critical points during the quenching process is calculated using a many-body generalization of the Landau–Zener transition theory. The density of kinks in the final state is found to decay as τ−1/2. In the first model considered here, the transverse Ising Hamiltonian includes an additional ferromagnetic three-spin interaction term of strength J3. For J3 0.5. The point with J3 = 0.5 and the transverse field h = −0.5 is multicritical, where the density shows a slower decay given by τ−1/6. We also study the effect of ferromagnetic or antiferromagnetic next nearest neighbor (NNN) interactions on the dynamics of the TIM under the same quenching scheme. In a mean field approximation, the transverse Ising Hamiltonians with NNN interactions are identical to the three-spin Hamiltonian. The NNN interactions non-trivially modify the dynamical behavior; for example an antiferromagnetic NNN interaction results in a larger number of kinks in the final state in comparison to the case when the NNN interaction is ferromagnetic.

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.