Shraddha Sharma

Quenches and dynamical phase transitions in a non-integrable quantum Ising model

We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagentic interactions in the presence of a longitudinal field which renders the model non-integrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field; the residual energy, as obtained numerically using a t-DMRG scheme, is found to satisfy analytically predicted scaling relations in both the cases. However, analyzing the temporal evolution of the Loschmidt overlap, we find different possibilities of the presence (or absence) of dynamical phase transitions (DPTs) manifested in the non-analyticities of the rate function. Even though the model is non-integrable, there are {periodic} occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic (FM) version of the model; this numerical finding is qualitatively explained by mapping the original model to an effective integrable spin model which is appropriate for describing such slow quenches. Furthermore, concerning the sudden quenches, our numerical results show that in some cases, DPTs can be present even when the spin chain is quenched within the same phase or even to the QCP while in some other situations they completely disappear even after quenching across the QCP. These observations lead us to the conclusion that it is the change in the nature of the ground state that determines the presence of DPTs following a sudden quench.

Quench dynamics of edge states in 2-D topological insulator ribbons

We study the dynamics of edge states of the two dimensional BHZ Hamiltonian in a ribbon geometry following a sudden quench to the quantum critical point separating the topological insulator phase from the trivial insulator phase. The effective edge state Hamiltonian is a collection of decoupled qubit-like two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Lochschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.

Tuning the presence of dynamical phase transitions in a generalized XY spin chain.

We study an integrable spin chain with three spin interactions and the staggered field (λ) while the latter is quenched either slowly [in a linear fashion in time (t) as t/τ, where t goes from a large negative value to a large positive value and τ is the inverse rate of quenching] or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist nonanalyticities [known as dynamical phase transitions (DPTs)] in the subsequent real-time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when τ exceeds a critical value τ_{1}), we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term (γ) and τ, thereby establishing the existence of boundaries in the (γ-τ) plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value λ_{i} to a final value λ_{f}, we show that the condition for the presence of DPTs is governed by relations involving λ_{i},λ_{f}, and γ, and the spin chain must be swept across λ=0 for DPTs to occur.

Loschmidt echo and dynamical fidelity in periodically driven quantum systems

We study the dynamical fidelity and the Loschmidt echo , following a periodic driving of the transverse magnetic field of a quantum Ising chain (back and forth across the quantum critical point) by calculating the overlap between the initial ground state and the state reached after n periods τ. We show that (the logarithm of the fidelity per site) reaches a steady value in the asymptotic limit , and we derive an exact analytical expression for this quantity. Remarkably, the steady-state value of shows memory of non-trivial phase information which is instead hidden in the case of thermodynamic quantities; this conclusion, moreover, is not restricted to 1-dimensional models.

Loschmidt echo with a nonequilibrium initial state: Early-time scaling and enhanced decoherence

We study the Loschmidt echo (LE) in a central spin model in which a central spin is globally coupled to an environment (E) which is subjected to a small and sudden quench at

Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment

t=0

One- and two-dimensional quantum models: Quenches and the scaling of irreversible entropy.

so that its state at

Role of marginality in quantum fidelity and Loschmidt echo: Dirac points in 2-D

t=0^+

Coexisting collective structure and Baryon resonances

, remains the same as the ground state of the initial environmental Hamiltonian before the quench; this leads to a non-equilibrium situation. This state now evolves with two Hamiltonians, the final Hamiltonian following the quench and its modified version which incorporates an additional term arising due to the coupling of the central spin to the environment. Using a generic short-time scaling of the decay rate, we establish that in the early time limit, the rate of decay of the LE (or the overlap between two states generated from the initial state evolving through two channels) close to the quantum critical point (QCP) of E is independent of the quenching. We do also study the temporal evolution of the LE and establish the presence of a crossover to a situation where the quenching becomes irrelevant. In the limit of large quench amplitude the non-equilibrium initial condition is found to result in a drastic increase in decoherence at large times, even far away from a QCP. These generic results are verified analytically as well as numerically, choosing E to be a transverse Ising chain where the transverse field is suddenly quenched.

Slow quenches in a quantum Ising chain: Dynamical phase transitions and topology

We study the temporal evolution of a central spin-1/2 (qubit) coupled to the environment which is chosen to be a spin-1/2 transverse XY spin chain. We explore the entire phase diagram of the spin-Hamiltonian and investigate the behavior of Loschmidt echo(LE) close to critical and multicritical point(MCP). To achieve this, the qubit is coupled to the spin chain through the anisotropy term as well as one of the interaction terms. Our study reveals that the echo has a faster decay with the system size (in the short time limit) close to a MCP and also the scaling obeyed by the quasiperiod of the collapse and revival of the LE is different in comparison to that close to a QCP. We also show that even when approached along the gapless critical line, the scaling of the LE is determined by the MCP where the energy gap shows a faster decay with the system size. This claim is verified by studying the short-time and also the collapse and revival behavior of the LE at a quasicritical point on the ferromagnetic side of the MCP. We also connect our observation to the decoherence of the central spin.