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Register a new userDissipative dynamics at first-order quantum transitions
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We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters and dissipative mechanisms modeled by a Lindblad master equation, with either local or global spin operators acting as dissipative operators. Analogously to what happens at continuous quantum transitions, we observe a regime where the system develops a nontrivial dynamic scaling behavior, which is realized when the dissipation parameter $u$ (globally controlling the decay rate of the dissipation within the Lindblad framework) scales as the energy difference $Delta$ of the lowest levels of the Hamiltonian, i.e., $usim Delta$. However, unlike continuous quantum transitions where $Delta$ is power-law suppressed, at first-order quantum transitions $Delta$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).
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We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter $lambda$ is varied across a quantum phase transition. For this purpose we consider a finite-size scaling (FSS) framework. Our working hypothesis is based on a scaling assumption of the fidelity in terms of the FSS variables associated to $lambda$ and to its variation $delta lambda$. This framework entails the FSS predictions for continuous transitions, and meanwhile enables to extend them to first-order transitions, where the FSS becomes qualitatively different. The latter is supported by analytical and numerical analyses of the quantum Ising chain along its first-order quantum transition line, driven by an external longitudinal field.
The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we first give a pedagogical introduction to the equilibrium behavior of systems in that context, whose scaling framework is essentially developed by exploiting the quantum-to-classical mapping and the renormalization-group theory of critical phenomena at continuous phase transitions. Then we specialize to protocols entailing the out-of-equilibrium quantum dynamics, such as instantaneous quenches and slow passages across quantum transitions. These are mostly discussed within dynamic scaling frameworks, obtained by appropriately extending the equilibrium scaling laws. We review phenomena at first-order quantum transitions as well, whose peculiar scaling behaviors are characterized by an extreme sensitivity to the boundary conditions, giving rise to exponentials or power laws for the same bulk system. In the last part, we cover aspects related to the effects of dissipative interactions with an environment, through suitable generalizations of the dynamic scaling at quantum transitions. The presentation is limited to issues related to, and controlled by, the quantum transition developed by closed many-body systems, treating the dissipation as a perturbation of the critical regimes, as for the temperature at the zero-temperature quantum transition. We focus on the physical conditions giving rise to a nontrivial interplay between critical modes and various dissipative mechanisms, generally realized when the involved mechanism excites only the low-energy modes of the quantum transitions.
We study the decoherence properties of a two-level (qubit) system homogeneously coupled to an environmental many-body system at a quantum transition, considering both continuous and first-order quantum transitions. In particular, we consider a d-dimensional quantum Ising model as environment system. We study the dynamic of the qubit decoherence along the global quantum evolution starting from pure states of the qubit and the ground state of the environment system. This issue is discussed within dynamic finite-size scaling frameworks. We analyze the dynamic finite-size scaling of appropriate qubit-decoherence functions. At continuous quantum transitions, they develop power laws of the size of the environment system, with a substantial enhancement of the growth rate of the qubit decoherence with respect to the case the environment system is in normal noncritical conditions. The enhancement of the qubit decoherence growth rate appears much larger at first-order quantum transitions, leading to exponential laws when increasing the size of the environment system.
We investigate the competition of coherent and dissipative dynamics in many-body systems at continuous quantum transitions. We consider dissipative mechanisms that can be effectively described by Lindblad equations for the density matrix of the system. The interplay between the critical coherent dynamics and dissipation is addressed within a dynamic finite-size scaling framework, which allows us to identify the regime where they develop a nontrivial competition. We analyze protocols that start from critical many-body ground states and put forward general dynamic scaling behaviors involving the Hamiltonian parameters and the coupling associated with the dissipation. This scaling scenario is supported by a numerical study of the dynamic behavior of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms such as local pumping, decaying, and dephasing.
We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven across the critical value of a zero-temperature quantum transition. In particular we address whether, and under which conditions, open quantum systems can develop a universal dynamic scaling regime similar to that emerging in closed systems. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation governing the time evolution of the systems density matrix. We argue that a dynamic scaling limit exists even in the presence of dissipation, whose main features are controlled by the universality class of the quantum transition. This requires a particular tuning of the dissipative interactions, whose decay rate $u$ should scale as $usim t_s^{-kappa}$ with increasing the time scale $t_s$ of the KZ protocol, where the exponent $kappa = z/(y_mu+z)$ depends on the dynamic exponent $z$ and the renormalization-group dimension $y_mu$ of the driving Hamiltonian parameter. Our dynamic scaling arguments are supported by numerical results for KZ protocols applied to a one-dimensional fermionic wire undergoing a quantum transition in the same universality class of the quantum Ising chain, in the presence of dissipative mechanisms which include local pumping, decay, and dephasing.
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