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Author

Shraddha Sharma

Other affiliations: Saarland University
Bio: Shraddha Sharma is an academic researcher from Indian Institute of Technology Kanpur. The author has contributed to research in topics: Quantum critical point & Spin model. The author has an hindex of 12, co-authored 21 publications receiving 389 citations. Previous affiliations of Shraddha Sharma include Saarland University.

Papers
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Journal ArticleDOI
TL;DR: In this article, the authors studied the slow quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyzed the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function with the final time independent Hamiltonian.
Abstract: We study the slow quenching dynamics (characterized by an inverse rate ${\ensuremath{\tau}}^{\ensuremath{-}1}$) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the Loschmidt overlap measured using the subsequent temporal evolution of the final wave function (reached at the end of the quenching) with the final time-independent Hamiltonian. Studying the Fisher zeros of the corresponding generalized ``partition function,'' we probe nonanalyticities manifested in the rate function of the return probability known as dynamical phase transitions (DPTs). In contrast to the sudden quenching case, we show that DPTs survive in the subsequent temporal evolution following the quenching across two critical points of the model for a sufficiently slow rate; furthermore, an interesting ``lobe'' structure of Fisher zeros emerge. We have also made a connection to topological aspects studying the dynamical topological order parameter $[{\ensuremath{ u}}_{D}(t)]$ as a function of time $(t)$ measured from the instant when the quenching is complete. Remarkably, the time evolution of ${\ensuremath{ u}}_{D}(t)$ exhibits drastically different behavior following quenches across a single QCP and two QCPs. In the former case, ${\ensuremath{ u}}_{D}(t)$ increases stepwise by unity at every DPT (i.e., $\mathrm{\ensuremath{\Delta}}{\ensuremath{ u}}_{D}=1$). In the latter case, on the other hand, ${\ensuremath{ u}}_{D}(t)$ essentially oscillates between 0 and 1 (i.e., successive DPTs occur with $\mathrm{\ensuremath{\Delta}}{\ensuremath{ u}}_{D}=1$ and $\mathrm{\ensuremath{\Delta}}{\ensuremath{ u}}_{D}=\ensuremath{-}1$, respectively), except for instants where it shows a sudden jump by a factor of unity when two successive DPTs carry a topological charge of the same sign.

100 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagnetic interactions in the presence of a longitudinal field which renders the model nonintegrable.
Abstract: We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagnetic interactions in the presence of a longitudinal field which renders the model nonintegrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field. 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 nonanalyticities of the rate function of the return probability. Even though the model is nonintegrable, there are periodic occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic 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.

88 citations

Journal ArticleDOI
TL;DR: It is shown 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.
Abstract: 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.

41 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the Loschmidt echo in a central spin model and showed that the decay rate of the LE close to the quantum critical point (QCP) is independent of the quenching.
Abstract: 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 $t=0$, so that its state at $t={0}^{+}$ remains the same as the ground state of the initial environmental Hamiltonian before the quench; this leads to a nonequilibrium 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 close to the quantum critical point (QCP) of $E$ is independent of the quenching. We 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 nonequilibrium 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.

35 citations

Journal ArticleDOI
TL;DR: In this article, 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 ones were studied.
Abstract: 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.

32 citations


Cited by
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Journal Article
TL;DR: In this paper, the authors show that a homogeneous 1D Bose gas with point-like collisional interactions is integrable, and that it is possible to construct a system with many degrees of freedom that does not reach thermal equilibrium even after thousands of collisions.
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.

941 citations

Journal ArticleDOI
TL;DR: The application of quark models to the spectra and strong and electromagnetic couplings of baryons is reviewed in this paper, where the authors focus on calculations which attempt a global description of the masses and decay properties of Baryons, although recent developments in appling large Nc QCD and lattice QCD to the baryon spectrum are described.

372 citations

Journal ArticleDOI
Markus Heyl1
TL;DR: The theory of dynamical quantum phase transitions as mentioned in this paper attempts to identify general principles by lifting the concept of phase transitions to coherent quantum real-time evolution, by defining phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times.
Abstract: Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium paradigm While these states promise to show properties not constrained by equilibrium principles such as the equal a priori probability of the microcanonical ensemble, identifying general properties of nonequilibrium quantum dynamics remains a major challenge especially in view of the lack of conventional concepts such as free energies The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution This review provides a pedagogical introduction to this field Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook onto major open questions as well as future directions of research

362 citations

Journal ArticleDOI
Markus Heyl1
TL;DR: This review provides a pedagogical introduction to the theory of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times.
Abstract: Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.

301 citations

Posted Content
TL;DR: This review discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum- classical Liouville dynamics, as well as methods for simulating the dynamics.
Abstract: Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

221 citations