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arXiv:1701.04214 · Physical review. B./Physical review. B

Dynamical quantum phase transitions in the quantum Potts chain

Christoph Karrasch, Dirk Schuricht

Published Feb 23, 2017• 58 citations
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Abstract

The time evolution of a quantum system after a sudden change of one of its parameters may show characteristic nonanalyticities, provided that this quench crosses a quantum phase transition. The authors investigate the relation between such dynamical quantum phase transitions and the universal properties of the corresponding quantum critical point.

DOI
10.1103/physrevb.95.075143

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The time evolution of a quantum system after a sudden change of one of its parameters may show characteristic nonanalyticities, provided that this quench crosses a quantum phase transition. The authors investigate the relation between such dynamical quantum phase transitions and the universal properties of the corresponding quantum critical point.
The dynamics in the vicinity of quantum phase transitions entails a variety of important and universal phenomena, such as critical slowing down or the Kibble-Zurek mechanism, which are associated with the low-energy and long-time properties at criticality. Here, the author reveals that the opposite regime of transient nonequilibrium time evolution at criticality can similarly host universal temporal behavior. By strongly perturbing a quantum critical state through quenching the associated order parameter, the system experiences a dynamical quantum phase transition with physical quantities becoming nonanalytic at critical times. These dynamical quantum phase transitions are caused by superextensive energy fluctuations induced by the particular protocol, which turn out to have profound consequences for quantum speed limits and potential restricted thermalization despite the nonintegrability of the system.
Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.
A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to nonanalytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this Letter we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely nonanalytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse-field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.
We investigate the dynamics following sudden quenches across quantum critical points belonging to different universality classes. Specifically, we use matrix product state methods to study the quantum Ising chain in the presence of two additional terms which break integrability. We find that in all models the rate function for the return probability to the initial state becomes a nonanalytic function of time in the thermodynamic limit. This so-called ``dynamical phase transition'' was first observed in a recent work by Heyl, Polkovnikov, and Kehrein [Phys. Rev. Lett. 110, 135704 (2013)] for the exactly-solvable quantum Ising chain, which can be mapped to free fermions. Our results for ``interacting theories'' indicate that nonanalytic dynamics is a generic feature of sudden quenches across quantum critical points. We discuss potential connections to the dynamics of the order parameter.
Short-time dynamics of many-body systems may exhibit nonanalytical behavior of the systems' properties at particular times, thus dubbed dynamical quantum phase transition. Simulations showed that in the presence of disorder, new critical times appear in the quench evolution of the Ising model. We study the physics behind these new critical times. We discuss the spectral features of the Ising model responsible for the disorder-induced phase transitions. We found the critical value of the disorder sufficient to induce the dynamical phase transition as a function of the number of spins. Most importantly, we argue that this dynamical phase transition while nontopological lacks a local order parameter.
Considerable theoretical and experimental efforts have been devoted to the quench dynamics, in particular, the dynamical quantum phase transition (DQPT) and the steady-state transition. These developments have motivated us to study the quench dynamics of the topological systems, from which we find the connection between these two transitions, that is, the DQPT, accompanied by a nonanalytic behavior as a function of time, always merges into a steady-state transition signaled by the nonanalyticity of observables in the steady limit. As the characteristic time of the DQPT diverges, it exhibits universal scaling behavior, which is related to the scaling behavior at the corresponding steady-state transition.