Annual review of condensed matter physics

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

Dynamical quantum phase transitions: a review.

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.

https://iopscience.iop.org/article/10.1088/1361-6633/aaaf9a/pdf

Dynamical quantum phase transitions: a review

Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.

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Genuine quantum correlations in quantum many-body systems: a review of recent progress.

Signaled by nonanalyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic topological order parameters (DTOPs). In this Letter, we report the experimental study of DQPTs using discrete-time quantum walks of single photons. We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics and experimentally characterize DQPTs and the underlying DTOPs through interference-based measurements. The versatile photonic quantum-walk platform further allows us to experimentally investigate DQPTs for mixed states and in parity-time-symmetric nonunitary dynamics for the first time. Our experiment directly confirms the relation between DQPTs and DTOPs in quench dynamics of topological systems and opens up the avenue of simulating emergent topological phenomena using discrete-time quantum-walk dynamics.

Simulating Dynamic Quantum Phase Transitions in Photonic Quantum Walks.

We study the behavior of Fisher zeros (FZs) and dynamical quantum phase transitions (DQPTs) for a linearly ramped Haldane model occurring in the subsequent temporal evolution of the same, and we probe the intimate connection with the equilibrium topology of the model. Here, we investigate the temporal evolution of the final state of the Haldane Hamiltonian (evolving with the time-independent final Hamiltonian) reached following a linear ramping of the staggered (Semenoff) mass term from an initial to a final value, first selecting a specific protocol, so chosen that the system is ramped from one nontopological phase to the other through a topological phase. We establish the existence of three possible behaviors of areas of FZs corresponding to a given sector: (i) no-DQPT, (ii) one-DQPT (intermediate), and (iii) two-DQPTs (reentrant), depending on the inverse quenching rate $\ensuremath{\tau}$. Our study also reveals that the appearance of the areas of FZs is an artefact of the nonzero (quasi-momentum-dependent) Haldane mass (${M}_{H}$), whose absence leads to an emergent one-dimensional behavior indicated by the shrinking of the area's FZs to lines and the nonanalyticity in the dynamical ``free energy'' itself. Moreover, the characteristic rates of crossover between the three behaviors of FZs are determined by the time-reversal-invariant quasimomentum points of the Brillouin zone where ${M}_{H}$ vanishes. Thus, we observe that through the presence or absence of ${M}_{H}$, there exists an intimate relation to the topological properties of the equilibrium model even when the ramp drives the system far away from equilibrium.

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

We study the quantum critical behavior of the Dicke Hamiltonian with finite number of atoms and explore the signature of quantum chaos using measures like the ground-state fidelity and the Loschmidt echo and the time-averaged Loschmidt echo. We show that these quantities clearly point to the classically chaotic nature of the system in the superradiant (SR) phase. While the ground-state fidelity shows aperiodic oscillations as a function of the coupling strength, the echo shows aperiodic oscillations in time and decays rapidly when the system is in the SR phase. We clearly demonstrate how the time-averaged value of the echo already incorporates the information about the ground-state fidelity and stays much less than unity, indicating the classically chaotic nature of the model in the SR phase.

Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo

We study the effect of a half wave rectified sinusoidal electromagnetic (EM) wave on the Kitaev honeycomb model with an additional magneto-electric coupling term arising due to induced polarization of the bonds. Within the framework of Floquet analysis, we show that merging of a pair of Dirac points in the gapless region of the Kitaev model leading to a semi-Dirac spectrum is indeed possible by externally varying the amplitude and the phase of the EM field.

Amit Dutta

Papers

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo

Dynamical merging of Dirac points in the periodically driven Kitaev honeycomb model

Quantum Phase Transitions in Transverse Field Spin Models: References

Quantum Phase Transitions in Transverse Field Spin Models: Preface